Fast bitonal to gray scale image scaling

• US 4,829,587 A
• Filed: 03/02/1987
• Issued: 05/09/1989
• Est. Priority Date: 03/02/1987
• Status: Expired due to Term

• Current Assignee: Hewlett-Packard Development Company, L.P. (HP Inc.)
• Original Assignee: Digital Equipment Corporation (HP Inc.)
• Inventors: Glazer, Frank C., Trimper, John K.
• Primary Examiner(s): Boudreau, Leo H.
• Assistant Examiner(s): Mancuso, Joseph
• Application Number:
  US07/020,267
• Time in Patent Office: 799 Days
• Field of Search: 382/44, 382/47, 382/50, 382/27, 358/140, 358/288, 358/287, 358/180, 340/731, 340/741, 340/728, 364/577, 364/723
• US Class Current: 382/299
• CPC Class Codes: G06T 3/4023 based on decimating pixels or lines of pixels; based on inserting pixels or lines of pixels

Abstract

A device for re-scaling an image to change the resolution with which discrete pixel values represent it includes a scan-line interface (40) and an alignment circuit (45) that assemble sets of the original pixel values into submatrices and apply them to a convolution engine (46), which computes new pixel values from them. X and Y scaling engines (58 and 60) control the re-scaling without having to generate original-pixel address at the rate at which new pixels are generated. The X scaling engine (58) simply indicates whether an output the currently supplied input data should be used to generate an output intensity value and, if so, whether it should be retained for generation of the subsequent intensity value, too. Similarly, the Y scaling engine (60) indicates whether the next scan line to be received should be used for generation of a scan line of output intensity values and, if so, whether it should be retained for generation of a subsequent scan line of output intensity values. In generating the new pixel values, the convolution engine (46) converts from the binary, black-and-white levels of the original pixels to gray-scale values for the new pixels to reduce the jaggedness that scale changes can cause.

Claims

1. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, and each output intensity value being generated from the input data associated with the input location in whose location neighborhood that output location is positioned, an apparatus comprising:

A. output-intensity means, operating in location cycles and adapted to receive during each location cycle input-data signals representing the input data associated with an input location, for processing the input data represented by the input-data signals applied thereto to generate output intensity signals representing the intensity of the image at an output location therein;

B. advancement means, adapted to receive a stall-in-column signal that assumes alternatively an advance value and a stall value, the advancement means operating in each location cycle to apply to the output-intensity means (a) when the stall-in-column signal assumes the stall value, input-data signals representing the input data associated with the input location whose data it applied during the previous location cycle and (b) when the stall-in-column signal assumes the advance value, input-data signals representing the input data associated with the next input location; and

C. an X scaling engine comprising;

(i) X relative-position means, adapted to receive an X update signal representing an X update value, for storing the X update value as a relative-position quantity representing the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location and for producing an X relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output location is inside or outside the location neighborhood associated with the given input location;

(ii) X increments means, responsive to the X relative-position signal, for producing an X increment output representing, (a) when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if the given input and output locations are both advanced by one location and, (b) when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location;

(iii) an X adder responsive to the X increment and relative-position signals for generating and applying to the X relative-position means as the X update signal a signal representing the sum of the quantities represented by the X increment and relative-position signals; and

(iv) X stall-in-column-signal means responsive to the X relative-position signal for generating and applying to the advancement means a stall-in-column signal that assumes the advance value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and that assumes the stall value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location.

2. An apparatus as defined in claim 1 wherein:

A. the data associated with each input location consists of a submatrix of intensity values representing the intensities in the image at each input location in an input-array subarray associated with that input location; and

B. the output-intensity means generates each output intensity value by mutliplying a convolution kernel element-by element by the submatrix associated with an input location.

3. An apparatus as defined in claim 2 wherein:

A. each location neighborhood consists of a plurality of sub-neighborhoods defined by sub-neighborhood boundaries;

B. the apparatus comprises sub-neighborhood means for receiving the relative-position signal and generating therefrom a sub-neighborhood signal indicating the sub-neighborhood in which the given output location is positioned; and

C. the output-intensity means associates different kernels with different sub-neighborhoods in the same neighborhood and is responsive to the sub-neighborhood signal to multiply the submatrix by the kernel associated with the sub-neighborhood that the sub-neighborhoood signal indicates.

4. An apparatus as defined in claim 3 wherein:

A. the arrays of input and output locations are organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the location neighborhoods associated with the input locations in that input row;

B. the output-intensity means operates in row cycles, is adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, and processes the input data represented by the input-data signals applied thereto during a row cycle to generate the output intensity signals representing the intensity values for the output locations in an output row;

C. the advancement means is adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes the stall value, input-data signals representing the input data associated with the input location in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row;

D. the apparatus further comprises a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row;

(iii) a Y adder reponsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment the relative-position signals; and

(iv) stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

E. the sub-neighborhood means receives both the X and the Y the relative-position signals and generates the sub-neighborhood signal therefrom.

5. An apparatus as defined in claim 4 wherein:

A. the X scaling engine is operable alternatively in an expansion mode and in a reduction mode;

B. the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location is (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode;

C. the X stall-in-column-signal means;

(i) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(ii) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position sigal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stall value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location;

D. the X scaling engine further includes validity-signal means responsive to the X relative-position signal for generating a validity signal that;

(i) assumes a valid value whenever the X scaling engine is in the expansion mode; and

(ii) whenever the X scaling engine is in the reduction mode, assumes the valid value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes an invalid value when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location; and

E. the output-intensity means is responsive to the validity signal to generate the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value.

6. An apparatus as defined in claim 1 wherein:

A. the arrays of input and output locations are organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input location in that input row and being defined by row boundaries consisting of location boundaries that define the location neighborhoods associated with the input locations in that input row;

B. the output-intensity means operates in row cycles, is adapted to receive during each row cycle input-data signals representing the input data assocated with the input locations in an input row, and processes the input data represented by the input-data signals applied thereto during a row cycle to generate the output intensity signals representing the intensity values for the output locations in an output row;

C. the advancement means is adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes the stall value, input-data signals representing the input data associated with the input location in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row; and

D. the apparatus further comprises a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

(iv) Y stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row.

7. An apparatus as defined in claim 6 wherein:

A. the X scaling engine is operable alternatively in an expansion mode and in a reduction mode;

B. the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location is (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode;

C. the X stall-in-column-signal means;

(i) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(ii) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stal value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location;

D. the X scaling engine further includes validity-signal means responsive to the X relative-position signal for generating a validity signal that;

(i) assumes a valid value whenever the X scaling engine is in the expansion mode; and

(ii) whenever the X scaling engine is in the reduction mode, assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes an invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location; and

E. the output-intensity means is responsive to the validity signal to generate the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value.

8. An apparatus as defined in claim 1 wherein:

A. the X scaling engine is operable alternatively in an expansion mode and in a reduction mode;

B. the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location is (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode;

C. the X stall-in-column-signal means;

(i) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(ii) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stall value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location;

D. the X scaling engine further includes validity-signal means responsive to the relative-position signal for generating a validity signal that;

(i) assumes a valid value whenever the X scaling engine is in the expansion mode; and

(ii) whenever the X scaling engine is in the reduction mode, assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes an invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location; and

E. the output-intensity means is responsive to the validity signal to generate the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value.

9. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the neighborhoods associated with the input locations in that input row, and each output intensity value being generated from the input data associated with the input location in whose neighborhood that output location is positioned, an apparatus comprising:

A. output-intensity means, operating in row cycles and adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, for processing the input data represented by the input-data signals applied thereto during a row cycle to generate output intensity signals representing the intensities of the image at the output locations in a row of output locations therein;

B. advancement means, adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes that stall value, input-data signals representing the input data associated with the input locations in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row; and

C. a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities representing by the Y increment and relative-position signals; and

(iv) Y stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row.

10. An apparatus as defined in claim 9 wherein:

A. the data associated with each input location consists of a submatrix of intensity values representing the intensities in the image at each input location in an input-array subarray associated with that input location; and

B. the output-intensity means generates each output intensity value by multiplying a convolution kernel element-by-element by the submatrix associated with an input location.

11. An apparatus as defined in claim 10 wherein:

A. each location neighborhood consists of a plurality of sub-neighborhoods defined by sub-neighborhood boundaries;

B. the apparatus comprises sub-neighborhood means for receiving the relative-position signal and generating therefrom a sub-neighborhood signal indicating the sub-neighborhood in which the given output location is positioned; and

C. the output-intensity means associates different kernels with different sub-neighborhoods in the same neighborhood and is responsive to the sub-neighborhood signal to multiply the submatrix by the kernel associated with the sub-neighborhood that the sub-neighborhood signal indicates.

12. An apparatus as defined in claim 11 wherein:

A. the Y scaling engine operates alternatively in an expansion mode and in a reduction mode;

B. the Y increment output that the Y increment means produces when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row is (a) the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row when the Y scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row when the Y scaling engine is in its reduction mode;

C. the Y stall-in-row-signal means;

(i) assumes the advance value whenever the Y scaling engine is in its reduction mode; and

(ii) whenever the Y scaling engine is in its expansion mode, assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

D. the Y scaling engine further incoudes bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that;

(i) assumes a no-bypass value whenever the Y scaling engine is in the expansion mode; and

(ii) whenever the Y scaling engine is in the reduction mode, assumes the no-bypass value when the relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes a bypass value when the relative-position signal indicates that the given output row is outside the neighborhood associated with the given input row; and

E. the output-intensity means is responsive to the bypass-row signal to generate the next row of output intensity signals (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal has the bypass value.

13. An apparatus as defined in claim 9 wherein:

A. the Y scaling engine operates alternatively in an expansion mode and in a reduction mode;

B. the Y increment output that the Y increment means produces when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row is (a) the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row when the Y scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row when the Y scaling engine is in its reduction mode;

C. the Y stall-in-row-signal means;

(i) assumes the advance value whenever the Y scaling engine is in its reduction mode; and

(ii) whenever the Y scaling engine is in its expansion mode, assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

D. the Y scaling engine further includes bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that;

(i) assumes a no-bypass value whenever the Y scaling engine is in the expansion mode; and

(ii) whenever the Y scaling engine is in the reduction mode, assumes the no-bypass value when the relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes a bypass value when the relative-position signal indicates that the given output row is outside the neighborhood associated with the given input row; and

E. the output-intensity means is responsive to the bypass-row signal to generate the next row of output intensity signals (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value.

14. For generating output intensity signals representing the intensities in an image at output locaions in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, and each output intensity value being generated from the input data associated with the input location in whose location neighborhood that output location is positioned, an apparatus comprising:

A. output-intensity means, adapted to receive a validity signal associated with each input location and assuming one of a valid and an invalid value to indicate whether an output intensity value should be generated from the input data associated with the input location with which that validity signal is associated, the output-intensity means operating in location cycles and being adapted to receive during each location cycle input-data signals representing the input data associated with an input location, for processing the input data represented by the input-data signals applied thereto to generate output intensity signals representing the intensity of the image at an output location therein, the output-intensity means generating the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value;

B. advancement means operating in each location cycle to apply to the output-intensity means input-data signals representing the input data associated with the next input location; and

C. an X scaling engine comprising;

(i) X relative-position means, adapted to receive an X update signal representing an X update value, for storing the X update value as a relative-position quantity representing the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location and for producing an X relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output location is inside or outside the location neighborhood of the given input location;

(ii) X increment means, responsive to the X relative-position signal, for producing an X increment output representing, (a) when the X relative-position signal indicates that the given output location is within the location neighborhood of the given input location, the amount by which the relative positions of the given input and output locations will change if the given input and the output locations are both advanced by one location and, (b) when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location;

(iii) an X adder responsive to the X increment and relative-position signals for generating and applying to the X relative-position means as the X update signal a signal representing the sum of the quantities represented by the X increment and relative-position signals; and

(iv) X validity-signal means responsive to the relative-position signal for generating and applying to the output-intensity means a validity signal that assumes that valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and that assumes that invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location.

15. An apparatus as defined in claim 14 wherein:

A. the data associated with each input location consists of a submatrix of intensity values representing the intensities in the image at each input location in an input-array subarray associated with that input location; and

B. the output-intensity means generates each output intensity value by multiplying a convolution kernel element-by element by the submatrix associated with an input location.

16. An apparatus as defined in claim 15 wherein:

A. each location neighborhood consists of a plurality of sub-neighborhoods defined by sub-neighborhood boundaries;

B. the apparatus comprises sub-neighborhood means for receiving the X relative-position signal and generating therefrom a sub-neighborhood signal indicating the sub-neighborhood in which the given output location is positioned; and

C. the output-intensity means associates different kernels with different sub-neighborhoods in the same neighborhood and is responsive to the sub-neighborhood signal to multiply the submatrix by the kernel associated with the sub-neighborhood that the sub-neighborhood signal indicates.

17. An apparatus as defined in claim 16 wherein:

A. the arrays of input and output locations are organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with each input location in that input row and being defined by row boundaries consisting of location boundaries that define the location neighborhoods associated with the input locations in that input row;

B. the output-intensity means operates in row cycles, is adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, and processes the input data represented by the input-data signals applied thereto during a row cycle to generate the output intensity values for the output locations in an output row;

C. the advancement means operates in each row cycle to apply to the output-intensity means input-data signals representing the input data associated with the input locations in the next input row; and

D. the apparatus further comprises a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given output row, the amount by which the relative positions of the given input and output rows will change if the given input and the output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

(iv) Y bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal, associated with the given input row, that assumes the no-bypass value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the bypass value when the relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row;

E. the output-intensity means is responsive to the bypass-row signal to generate output intensity signals representing the inftensities in the next output row (i) from the input data associated with the next input row if the bypass row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value; and

F. the sub-neighborhood means receives both the X and the Y relative-position signals and generates the sub-neighborhood signal therefrom.

18. An apparatus as defined in claim 14 wherein:

A. the arrays of input and output locations are organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with each input location in that input row and being defined by row boundaries consisting of locatoion boundaries that define the location neighborhoods associated with the input locations in that input row;

B. the output-intensity means operates in row cycles, is adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, and processes the input data represented by the input-data signals applied thereto during a row cycle to generate the output intensity values for the output locations in an output row;

C. the advancement means operates in each row cycle to apply to the output-intensity means input-data signals representing the input data associated with the input locations in the next input row; and

D. the apparatus further comprises a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given output row, the amount by which the relative positions of the given input and output rows will change if the given input and the output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

(iv) Y bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal, associated with the given input row, that assumes the no-bypass value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the bypass value when the relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

E. the output-intensity means is responsive to the bypass-row signal to generate the output intensity signals representing the intensities in the next output row (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value.

19. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with each input location in that input row and being defined by row boundaries consisting of location boundaries that define the location neighborhoods associated with the input locations in that input row, and each output intensity value being generated from the input data associated with the input location in whose neighborhood that output location is positioned, an apparatus comprising:

A. output-intensity means, adapted to receive a bypass-row signal associated with each input row and assuming one of a bypass and a no-bypass value to indicate whether a row of output intensity values should be generated from the row of input data with which that bypass-row signal is associated, the output-intensity means operating in row cycles and being adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, for processing the input data represented by the input-data signals applied thereto during a row cycle to generate output intensity signals representing the intensity of the image at the output locations in an output row therein, the output-intensity means generating the output intensity signals representing the intensities in the next output row (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value;

B. advancement means for operating in each row cycle to apply to the output-intensity means input-data signals representing the input data associated with the input locations in the next input row; and

C. a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and the output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

(iv) Y bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that assumes a no-bypass value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the bypass value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row.

20. An apparatus as defined in claim 19 wherein:

A. the data associated with each input location consists of a submatrix of intensity values representing the intensities in the image at each input location in an input-array subarray associated with that input location; and

B. the output-intensity means generates each output intensity value by multiplying a convolution kernel element-by element by the submatrix associated with an input location.

21. An apparatus as defined in claim 20 wherein:

A. each location neighborhood consists of a plurality of sub-neighborhoods defined by sub-neighborhood boundaries;

B. the apparatus comprises sub-neighborhood means for receiving the X relative-position signal and generating therefrom a sub-neighborhood signal indicating the sub-neighborhood in which the given output location is positioned; and

C. the output-intensity means associates different kernels with different sub-neighborhoods in the same neighborhood and is responsive to the sub-neighborhood signal to multiply the submatrix by the kernel associated with the sub-neighborhood that the sub-neighborhood signal indicates.

22. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the neighborhoods associated with the input locations in that input row, and each output intensity value being generated from the input data associated with the input location in whose neighborhood that output location is positioned, an apparatus comprising:

A. output-intensity means, adapted to receive a validity signal associated with each input location and assuming one of a valid and an invalid value to indicate whether an output intensity value should be generated from the input data associated with the input location with which that validity signal is associated, the output-intensity means being further adapted to receive a bypass-rows signal associated with each input row and assuming one of a bypass and a no-bypass value to indicate whether a row of output intensity values should be generated from the row of input data with which that bypass-row signal is associated, the output-intensity means operating in location cycles and in row cycles that include a plurality of location cycles and being adapted to receive during each location cycle input-data signals representing the input data associated with an input location, the input-data signals received during a row cycle representing the input data associated with the input locations in an input row, for processing the input data represented by the input-data signals applied thereto during a location cycle to generate output intensity signals representing the intensity of the image at an output location therein, the output intensity signals generated by the output-intensity means during a row cycle representing the intensity of the image at the output locationss in an output row, therein, the output-intensity means generating the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value, the output-intensity means generating the output intensity signals representing the intensities in the next output row (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value;

B. advancement means, adapted to receive a stall-in-column signal that assumes alternatively an advance value and a stall value, the advancement means operating in each location cycle to apply to the output-intensity means (a) when the stall-in-column signal assumes the stall value, input-data signals representing the input data associated with the input location whose data it applied during the previous location cycle and (b) when the stall-in-column signal assumes the advance value, input-data signals representing the input data associated with the next input location the advancement means further being adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes the stall value, input-data signals representing the input data associated with the input location in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row;

C. an X scaling engine operable alternatively in an expansion mode and in a reduction mode, and comprising;

(i) X relative-position means, adapted to receive an X update signal representing an X update value, for storing the X update value as a relative-position quantity representing the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location and for producing an X relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output location is inside or outside the location neighborhood associated with the given input location;

(ii) X increment means, responsive to the X relative-position signal, for producing an X increment output, the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location representing (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode, the X increment output representing, when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if the given input and output locations are both advanced by one location;

(iii) an X adder responsive to the X increment and relative-position signals for generating and applying to the X relative-position means as the X update signal a signal representing the sum of the quantities represented by the X increment and relative-position signals;

(iv) X stall-in-column-signal means responsive to the X relative-position signal for generating and applying to the advancement means a stall-in-column signal that;

(a) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(b) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stall value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location; and

(v) validity-signal means responsive to the X relative-position signal for generating a validity signal that;

(a) assumes the valid value whenever the X scaling engine is in the expansion mode; and

(b) whenever the X scaling engine is in the reduction mode, assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location; and

D. a Y scaling engine operable alternatively in an expansion mode and in a reduction mode and comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representinfg the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output, the Y increment output that the Y increment means produces when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row representing (a) the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row when the Y scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row when the Y scaling engine is in its reduction mode, the Y increment output representing, when the Y relative-position signal indicates that the given output row is within the row neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals;

(iv) Y stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that;

(a) assumes the advance value whenever the Y scaling engine is in its reduction mode; and

(b) whenever the Y scaling engine is in its expansion mode, assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

(v) bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that;

(a) assumes the no-bypass value whenever the Y scaling engine is in the expansion mode; and

(b) whenever the Y scaling engine is in the reduction mode, assumes the no-bypass value when the relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the bypass value when the relative-position signal indicates that the given output row is outside the neighborhood associated with the given input row.

23. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, each location neighborhood consisting of a plurality of sub-neighborhoods defined by sub-neighborhood boundaries, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the neighborhoods associated with the input locations in that input row, and each output intensity value being generated from the input data associated with the input location in whose neighborhood that output location is positioned, an apparatus comprising:

A. output-intensity means, adapted to receive a validity signal associated with each input location and assuming one of a valid and an invalid value to indicate whether an output intensity value should be generated from the input data associated with the input location with which that validity signal is associated, the output-intensity means being further adapted to receive a sub-neighborhood signal that indicates a sub-neighborhood and also being adapted to receive a bypass-row signal associated with each input row and assuming one of a bypass and a no-bypass value to indicate whether a row of output intensity values should be generated from the row of input data with which that bypass-row signal is associated, the output-intensity means operating in location cycles and in row cycles that include a plurality of location cycles and being adapted to receive during each location cycle input-data signals representing the input data associated with an input location, the input-data signals received during a row cycle representing the input data associated with the input locations in an input row, the data associated with each input location consisting of a submatrix of intensity values representing the intensities in the image at each input location in an input-array subarray associated with that input location, for processing the input data represented by the input-data signals applied thereto during a location cycle to generate output intensity signals representing the intensity of the image at an output location therein, by multiplying the submatrix associated with each input location element-by-element by the kernel associated with the sub-neighborhood that the sub-neighborhood signal indicates, the output intensity signals generated by the output-intensity means during a row cycle representing the intensity of the image at the output locations in an output row, therein, the output-intensity means generating the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value, the output-intensity means generating the output intensity signals representing the intensities in the next output row (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value;

B. advancement means, adapted to receive a stall-in-column signal that assumes alternatively an advance value and a stall value, the advancement means operating in each location cycle to apply to the output-intensity means (a) when the stall-in-column signal assumes the stall value, input-data signals representing the input data associated with the input location whose data it applied during the previous location cycle and (b) when the stall-in-column signal assumes the advance value, input-data signals representing the input data associated with the next input location the advancement means further being adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes the stall value, input-data signals representing the input data associated with the input location in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row;

C. an X scaling engine operable alternatively in an expansion mode and in a reduction mode, and comprising;

(i) X relative-position means, adapted to receive an X update signal representing an X update value, for storing the X update value as a relative-position quantity representing the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location and for producing an X relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output location is inside or outside the location neighborhood associated with the given input location;

(ii) X increment means, responsive to the X relative-position signal, for producing an X increment output, the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location representing (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode, the X increment output representing, when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if the given input and output locations are both advanced by one location;

(iii) an X adder responsive to the X increment and relative-position signals for generating and applying to the X relative-position means as the X update signal and signal representing the sum of the quantities represented by the X increment and relative-position signals;

(iv) X stall-in-column-signal means responsive to the X relative-position signal for generating and applying to the advancement means a stall-in-column signal that;

(a) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(b) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stall value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location; and

(v) validity-signal means responsive to the X relative-position signal for generating a validity signal that;

(a) assumes the valid value whenever the X scaling engine is in the expansion mode; and

(b) whenever the X scaling engine is in the reduction mode, assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location;

D. a Y scaling engine operable alternatively in an expansion mode and in a reduction mode and comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output, the Y increment output that the Y increment means produces when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row representing (a) the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row when the Y scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row when the Y scaling engine is in its reduction mode, the Y increment output representing, when the Y relative-position signal indicates that the given output row is within the row neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal and signal representing the sum of the quantities represented by the Y increment and relative-position signals;

(iv) Y stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that;

(a) assumes the advance value whenever the Y scaling engine is in its reduction mode; and

(b) whenever the Y scaling engine is in its expansion mode, assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

(v) bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that;

(a) assumes the no-bypass value whenever the Y scaling engine is in the expansion mode; and

(b) whenever the Y scaling engine is in the reduction mode, assumes the no-bypass value when the relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the bypass value when the relative-position signal indicates that the given output row is outside the neighborhood associated with the given input row; and

E. sub-neighborhood means for receiving the X and Y relative-position signals, generating therefrom a sub-neighborhood signal indicating the sub-neighborhood in which the given output location is positioned, and applying the sub-neighborhood signal to the output-intensity means.

24. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, and each output intensity being generated from the input data associated with the input location in whose location neighborhood that output location is positioned, a method comprising the steps of:

A. receiving input-data signals representing the input data associated with input locations;

B. maintaining an X relative-position quantity that represents the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location, the X relative-position quantity thereby indicating whether the given output location is inside or outside the location neighborhood associated with the given input location;

C. computing the output intensity at the output location that precedes the given output location from the data associated with the input location that precedes the given input location;

D. generating an output intensity signal representing the output intensity computed in step C;

E. selectively advancing the input and output locations by;

(i) if the X relative-position quantity indicates that the given output location is outside the location neighborhood associated with the given input location, incrementing the X relative-position quantity by the amount by which the relative positions of the input and output locations change when only the given output location is advanced by one location; and

(ii) if the X relative-position quantity indicates that the given output location is inside the location neighborhood associated with the given input location, incrementing the X relative-position quantity by the amount by which the relative positions of the given input and output locations change when the input and output locations are both advanced by one location; and

F. repeating steps C, D, and E a plurality of times.

25. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, and each output intensity being generated from the input data associated with the input location in whose location neighborhood that output location is positioned, a method comprising the steps of:

A. receiving input-data signals representing the input data associated with input locations;

B. maintaining an X relative-position quantity that represents the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location, the X relative-position quantity thereby indicating whether the given output location is inside or outside the location neighborhood associated with the given input location;

C. if the X relative-position quantity indicates that the given output location is inside the location neighborhood associated with the given input location, computing the output intensity at the given output location from the data associated with the given input location;

D. if the X relative-position quantity indicates that the given output location is inside the location neighborhood associated with the given input location, generating an output intensity signal representing the output intensity computed in step C;

E. selectively advancing the given input and output locations by;

(i) if the X relative-position quantity indicates that the given output location is outside the location neighborhood associated with the given input location, incrementing the X relative-position quantity by the amount by which the relative positions of the given input and output locations change when only the given input location is advanced by one location; and

(ii) if the X relative-position quantity indicates that the given output location is inside the location neighborhood associated with the given input location, incrementing the X relative-position quantity by the amount by which the relative positions of the given input and output locations change when the given input and the given output locations are both advanced by one location; and

F. repeating steps C, D, and E a plurality of times.

26. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the neighborhoods associated with the input locations in that input row, and each output intensity being generated from the input data associated with the input location in whose neighborhood that output location is positioned, a method comprising the steps of:

A. receiving input-data signals representing the input data associated with the input locations in input rows;

B. maintaining a Y relative-position quantity that represents the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row, the Y relative-position position quantity thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

C. computing the output intensities in the output row preceding the given output row from the data associated with the input row that precedes the given input row;

D. generating output intensity signals representing the output intensities computed in step C;

E. selectively advancing the given input and output rows by;

(i) if the Y relative-position quantity indicates that the given output row is outside the row neighborhood associated with the given output row, incrementing the Y relative-position quantity by the amount by which the relative positions of the given input and output rows change when only the given output row is advanced by one location; and

(ii) if the Y relative-position quantity indicates that the given output row is inside the row neighborhood associated with the given input row, incrementing the Y relative-position quantity by the amount by which the relative positions of the given input and output rows change when the given input and the given output rows are both advanced by one row; and

F. repeating steps C, D, and E a plurality of times.

27. For generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the neighborhoods associated with the input locations in that input row, and each output intensity being generated from the input data associated with the input location in whose neighborhood that output location is positioned, a method comprising the steps of:

A. receiving input-data signals representing the input data associated with the input locations in input rows;

B. maintaining a Y relative-position quantity that represents the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row, the Y relative-position quantity thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

C. if the Y relative-position quantity indicates that the given output row is inside the row neighborhood associated with the given input row, computing the output intensities in the given output row from the data associated with the given input row;

D. generating output intensity signals representing the output intensities computed in step C;

E. selectively advancing the input and output rows by;

(i) if the Y relative-position quantity indicates that the given output row is outside the row neighborhood associated with the given input row, incrementing the Y relative-position quantity by the amount by which the relative positions of the given input and output rows change when only the given input row is advanced by one row; and

(ii) if the Y relative-position quantity indicates that the given output row is within the row neighborhood associated with the given input row, incrementing the Y relative-position quantity by the amount by which the relative positions of the given input and output rows change when the given input and the given output rows are both advanced by one row; and

F. repeating steps C, D, and E a plurality of times.

28. A scaling circuit for use in an apparatus for generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, and each output intensity value being generated from the input data associated with the input location in whose location neighborhood that output location is positioned, which apparatus includes output-intensity means, operating in location cycles and adapted to receive during each location cycle input-data signals representing the input data associated with an input location, for processing the input data represented by the input-data signals applied thereto to generate output intensity signals representing the intensity of the image at an output location therein and advancement means, adapted to receive a stall-in-column signal that assumes alternatively an advance value and a stall value, the advancement means operating in each location cycle to apply to the output-intensity means (a) when the stall-in-column signal assumes the stall value, input-data signals representing the input data associated with the input location whose data it applied during the previous location cycle and (b) when the stall-in-column signal assumes the advance value, input-data signals representing the input data associated with the next input location, the scaling circuit comprising an X scaling engine that includes:

A. X relative-position means, adapted to receive an X update signal representing an X update value, for storing the X update value as a relative-position quantity representing the difference in position between a given output location and a location boundary of the location neighborhood associated with given input location and for producing an X relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output location is inside or outside the location neighborhood associated with the given input location;

B. X increment means, responsive to the X relative-position signal, for producing an X increment output representing, (a) when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if the given input and output locations are both advanced by one location and, (b) when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location;

C. an X adder responsive to the X increment and relative-position signals for generating and applying to the X relative-position means as the X update signal a signal representing the sum of the quantities represented by the X increment and relative-position signals; and

D. X stall-in-column-signal means responsive to the X relative-position signal for generating and applying to the advancement means a stall-in-column-signal that assumes the advance value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and that assumes the stall value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location.

29. A scaling circuit as defined in claim 28 wherein:

A. the arrays of input and output locations are organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input location in that input row and being defined by row boundaries consisting of location boundaries that define the location neighborhoods associated with the input locations in that input row;

B. the output-intensity means operates in row cycles, is adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, and processes the input data represented by the input-data signals applied thereto during a row cycle to generate the output intensity signals representing the intensity values for the output locations in an output row;

C. the advancement means is adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes the stall value, input-data signals representing the input data associated with the input location in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row; and

D. the scaling circuit further comprises a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

(iv) Y stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row.

30. A scaling circuit as defined in claim 29 wherein:

A. the X scaling engine is operable alternatively in an expansion mode and in a reduction mode;

B. the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location is (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode;

C. The X stall-in-column-signal means;

(i) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(ii) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stall value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location;

D. the X scaling engine further includes validity-signal means responsive to the X relative-position signal for generating a validity signal that;

(i) assumes a valid value whenever the X scaling engine is in the expansion mode; and

(ii) whenever the X scaling engine is in the reduction mode, assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes an invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location; and

E. the output-intensity means is responsive to the validity signal to generate the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value.

31. A scaling circuit as defined in claim 28 wherein:

A. the X scaling engine is operable alternatively in an expansion mode and in a reduction mode;

B. the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location is (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode;

C. the X stall-in-column-signal means;

(i) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(ii) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stall value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location;

D. the X scaling engine further includes validity-signal means responsive to the relative-position signal for generating a validity signal that;

(i) assumes a valid value whenever the X scaling engine is in the expansion mode; and

(ii) whenever the X scaling engine is in the reduction mode, assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes an invaid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location; and

E. the output-intensity means is responsive to the validity signal to generate the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value.

32. A scaling circuit for use in an apparatus for generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the neighborhoods associated with the input locations in that input row, and each output intensity value being generated from the input data associated with the input location in whose neighborhood that output location is positioned, which apparatus includes output-intensity means, operating in row cycles and adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, for processing the input data represented by the input-data signals applied thereto during a row cycle to generate output intensity signals representing the intensities of the image at the output locations in a row of output locations therein and advancement means, adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes the stall value, input-data signals representing the input data associated with the input locations in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row, the scaling circuit comprising a Y scaling engine that includes:

A. Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

B. Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row;

C. a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

D. Y stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row.

33. A scaling circuit as defined in claim 32 wherein:

A. the Y scaling engine operates alternatively in an expansion mode and in a reduction mode;

B. the Y increment output that the Y increment means produces when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row is (a) the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row when the Y scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row when the Y scaling engine is in its reduction mode;

C. the Y stall-in-row-signal means;

(i) assumes the advance value whenever the Y scaling engine is in its reduction mode; and

(ii) whenever the Y scaling engine is in its expansion mode, assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

D. the Y scaling engine further includes bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that;

(i) assumes a no-bypass value whenever the Y scaling engine is in the expansion mode; and

(ii) whenever the Y scaling engine is in the reduction mode, assumes the no-bypass value when the relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes a bypass value when the relative-position signal indicates that the given output row is outside the neighborhood associated with the given input row; and

E. the output-intensity means is responsive to the bypass-row signal to generate the next row of output intensity signals (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value.

34. A scaling circuit for use in an apparatus for generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, and each output intensity value being generated from the input data associated with the input location in whose location neighborhood that output location is positioned, which apparatus includes output-intensity means, adapted to receive a validity signal associated with each input location and assuming one of a valid and an invalid value to indicate whether an output intensity value should be generated from the input data associated with the input location with which that validity signal is associated, the output-intensity means operating in location cycles and being adapted to receive during each location cycle input-data signals representing the input data associated with an input location, for processing the input data represented by the input-data signals applied thereto to generate output intensity signals representing the intensity of the image at an output location therein, the output-intensity means generating the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value and advancement means operating in each location cycle to apply to the output-intensity means input-data signals representing the input data associated with the next input location, the scaling circuit comprising an X scaling engine that includes:

A. X relative-position means, adapted to receive an X update signal representing an X update value, for storing the X update value as a relative-position quantity representing the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location and for producing an X relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output location is inside or outside the location neighborhood of the given input location;

B. X increment means, responsive to the X relative-position signal, for producing an X increment output representing, (a) when the X relative-position signal indicates that the given output location is within the location neighborhood of the given input location, the amount by which the relative positions of the given input and output locations will change if the given input and the output locations are both advanced by one location and, (b) when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location;

C. an X adder responsive to the X increment and relative-position signals for generating and applying to the X relative-position means as the X update signal a signal representing the sum of the quantities represented by the X increment and relative-position signals; and

D. X validity-signal means responsive to the relative-position signal for generating and applying to the output-intensity means a validity signal that assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and that assumes the invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location.

35. A scaling circuit as defined in claim 34 wherein:

A. the arrays of input and output locations are organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with each input location in that input row and being defined by row boundaries consisting of location boundaries that define the location neighborhoods associated with the input locations in that input row;

B. The output-intensity means operates in row cycles, is adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in an input row, and processes the input data represented by the input-data signals applied thereto during a row cycle to generate the output intensity values for the output locations in an output row;

C. the advancement means operates in each row cycle to apply to the output-intensity means input-data signals representing the input data associated with the input locations in the next input row; and

D. the scaling circuit further comprises a Y scaling engine comprising;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given output row, the amount by which the relative positions of the given input and output rows will change if the given input and the output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

(iv) Y bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal, associated with the given input row, that assumes the no-bypass value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the bypass value when the relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

E. the output-intensity means is responsive to the bypass-row signal to generate the output intensity signals representing the intensities in the next output row (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value.

36. A scaling circuit for use in an apparatus for generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with each input location in that input row and being defined by row boundaries consisting of location boundaries that define the location neighborhoods associated with the input locations in that input row, and each output intensity value being generated from the input data associated with the input location in whose neighborhood that output location is positioned, which apparatus includes output-intensity means, adapted to receive a bypass-row signal associated with each input row and assuming one of a bypass and a no-bypass value to indicate whether a row of output intensity values should be generated from the row of input data with which that bypass-row signal is associated, the output-intensity means operating in row cycles and being adapted to receive during each row cycle input-data signals representing the input data associated with the input locations in a input row, for processing the input data represented by the input-data signals applied thereto during a row cycle to generate output intensity signals representing the intensity of the image at the output locations in an output row therein, the output-intensity means generating the output intensity signals representing the intensities in the next output row (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value, the apparatus further including advancement means for operating in each row cycle to apply to the output-intensity means input-data signals representing the input data associated with the input locations in the next input row, the scaling circuit comprising a Y scaling engine that includes:

A. Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

B. Y increment means, responsive to the Y relative-position signal, for producing a Y increment output representing, (a) when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and the output rows are both advanced by one row and, (b) when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row, the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row;

C. a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals; and

D. Y bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that assumes a no-bypass value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and that assumes the bypass value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row.

37. A scaling circuit for use in an apparatus for generating output intensity signals representing the intensities in an image at output locations in an array of output locations from input-data signals representing input data associated with input locations in an array of input locations in the same image, each input location having associated therewith a location neighborhood defined by location boundaries in the image, the arrays of input and output locations being organized into input rows and columns and output rows and columns, respectively, each input row having associated therewith a row neighborhood consisting of the location neighborhoods associated with the input locations in that input row and being defined by row boundaries consisting of location boundaries that define the neighborhoods associated with the input locations in that input row, and each output intensity value being generated from the input data associated with the input location in whose neighborhood that output location is positioned, which apparatus includes output-intensity means, adapted to receive a validity signal associated with each input location and assuming one of a valid and an invalid value to indicate whether an output intensity value should be generated from the input data associated with the input location with which that validity signal is associated, the output-intensity means being further adapted to receive a bypass-row signal associated with each input row and assuming one of a bypass and a no-bypass value to indicate whether a row of output intensity values should be generated from the row of input data with which that bypass-row signal is associated, the output-intensity means operating in location cycles and in row cycles that include a plurality of location cycles and being adapted to receive during each location cycle input-data signals representing the input data associated with an input location, the input-data signals received during a row cycle representing the input data associated with the input locations in an input row, for processing the input data represented by the input-data signals applied thereto during a location cycle to generate output intensity signals representing the intensity of the image at an output location therein, the output intensity signals generated by the output-intensity means during a row cycle representing the intensity of the image at the output locations in an output row, therein, the output-intensity means generating the output intensity signals representing the intensity at the next output location (i) from the input data associated with the next input location if the validity signal associated with the next input location has the valid value and (ii) from the input data associated with a subsequent input location if the validity signal associated with the next input location has the invalid value, the output-intensity means generating the output intensity signals representing the intensities in the next output row (i) from the input data associated with the next input row if the bypass-row signal associated with the next input row has the no-bypass value and (ii) from the input data associated with a subsequent input row if the bypass-row signal associated with the next input row has the bypass value, the apparatus further including advancement means, adapted to receive a stall-in-column signal that assumes alternatively an advance value and a stall value, the advancement means operating in each location cycle to apply to the output-intensity means (a) when the stall-in-column signal assumes the stall value, input-data signals representing the input data associated with the input location whose data it applied during the previous location cycle and (b) when the stall-in-column signal assumes the advance value, input-data signals representing the input data associated with the next input location the advancement means further being adapted to receive a stall-in-row signal that alternatively assumes an advance value and a stall value, the advancement means operating in each row cycle to apply to the output-intensity means, (a) when the stall-in-row signal assumes the stall value, input-data signals representing the input data associated with the input location in the input row whose data it applied during the previous row cycle and, (b) when the stall-in-row signal assumes the advance value, input-data signals representing the input data associated with the input locations in the next input row, the scaling circuit comprising:

A. an X scaling engine operable alternatively in an expansion mode and in a reduction mode and including;

(i) X relative-position means, adapted to receive an X update signal representing an X update value, for storing the X update value as a relative-position quantity representing the difference in position between a given output location and a location boundary of the location neighborhood associated with a given input location and for producing an X relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output location is inside or outside the location neighborhood associated with the given input location;

(ii) X increment means, responsive to the X relative-position signal, for producing an X increment output, the X increment output that the X increment means produces when the X relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location representing (a) the amount by which the relative positions of the given input and output locations will change if only the given output location is advanced by one location when the X scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output locations will change if only the given input location is advanced by one location when the X scaling engine is in its reduction mode, the X increment output representing, when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location, the amount by which the relative positions of the given input and output locations will change if the give input and output locations are both advanced by one location;

(iii) an X adder responsive to the X increment and relative-position signals for generating and applying to the X relative-position means as the X update signal a signal representing the sum of the quantities represented by the X increment and relative-position signals;

(iv) X stall-in-column-signal means responsive to the X relative-position signal for generating and applying to the advancement means a stall-in-column signal that;

(a) assumes the advance value whenever the X scaling engine is in its reduction mode; and

(b) whenever the X scaling engine is in its expansion mode, assumes the advance value when the X relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the stall value when the X relative-position signal indicates that the given output location is outside the neighborhood of the given input location; and

(v) validity-signal means responsive to the X relative-position signal for generating a validity signal that;

(a) assumes the valid value whenever the X scaling engine is in the expansion mode; and

(b) whenever the X scaling engine is in the reduction mode, assumes the valid value when the relative-position signal indicates that the given output location is within the location neighborhood associated with the given input location and assumes the invalid value when the relative-position signal indicates that the given output location is outside the location neighborhood associated with the given input location; and

B. a Y scaling engine operable alternatively in an expansion mode and in a reduction mode and including;

(i) Y relative-position means, adapted to receive a Y update signal representing a Y update value, for storing the Y update value as a relative-position quantity representing the difference in position between a given output row and a row boundary of the row neighborhood associated with a given input row and for producing a Y relative-position signal representing the stored relative-position quantity and thereby indicating whether the given output row is inside or outside the row neighborhood associated with the given input row;

(ii) Y increment means, responsive to the Y relative-position signal, for producing a Y increment output, the Y increment output that the Y increment means produces when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row representing (a) the amount by which the relative positions of the given input and output rows will change if only the given output row is advanced by one row when the Y scaling engine is in its expansion mode and (b) the amount by which the relative positions of the given input and output rows will change if only the given input row is advanced by one row when the Y scaling engine is in its reduction mode, the Y increment output representing, when the Y relative-position signal indicates that the given output row is within the row neighborhood of the given input row, the amount by which the relative positions of the given input and output rows will change if the given input and output rows are both advanced by one row;

(iii) a Y adder responsive to the Y increment and relative-position signals for generating and applying to the relative-position means as the Y update signal a signal representing the sum of the quantities represented by the Y increment and relative-position signals;

(iv) Y stall-in-row-signal means responsive to the Y relative-position signal for generating and applying to the advancement means a stall-in-row signal that;

(a) assumes the advance value whenever the Y scaling engine is in its reduction mode; and

(b) whenever the Y scaling engine is in its expansion mode, assumes the advance value when the Y relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the stall value when the Y relative-position signal indicates that the given output row is outside the row neighborhood associated with the given input row; and

(v) bypass-row-signal means responsive to the Y relative-position signal for generating a bypass-row signal that;

(a) assumes the no-bypass value whenever the Y scaling engine is in the expansion mode; and

(b) whenever the Y scaling engine is in the reduction mode, assumes the no-bypass value when the relative-position signal indicates that the given output row is within the row neighborhood associated with the given input row and assumes the bypass value when the relative-position signal indicates that the given output row is outside the neighborhood associated with the given input row.