Methods and apparatus for generating a projection of an image

• US 6,381,375 B1
• Filed: 04/06/1998
• Issued: 04/30/2002
• Est. Priority Date: 02/20/1998
• Status: Expired due to Term

• Current Assignee: Cognex Corporation, Russ Weinzimmer
• Original Assignee: Cognex Corporation
• Inventors: Reyzin, Igor
• Primary Examiner(s): Mehta, Bhavesh
• Assistant Examiner(s): PATEL, KANJIBHAI B
• Application Number:
  US09/055,543
• Time in Patent Office: 1,485 Days
• Field of Search: 382/276, 382/277, 382/293, 382/295, 382/296, 382/300, 345/648, 345/649, 345/672, 345/651, 345/659, 345/647
• US Class Current: 382/276
• CPC Class Codes: G06T 3/00 Geometric image transformations in the plane of the image

Abstract

Novel methods for generating a projection of an image according to the invention concurrently rotate, scale, translate, skew, shear, or otherwise transform the image via a sequence of two one-dimensional transformations. A first intermediate image is generated via affine transformation of the source along a first axis. The intermediate image is then subjected to affine transformation along a second axis, e.g., perpendicular to the first. A projection of the resultant image is generated along a selected one of the first or second axes by summing pixel intensities in corresponding rows (or columns) or by summing counts of pixels whose intensities are above or below a threshold.

Claims

1. An image processing method for generating a projection of a source image, the method comprising the steps of:

A. generating an intermediate image by a first affine transformation of the source image along a first axis relative to the source image, wherein said first transformation is executed by the steps of (1) selecting a plurality of coordinates for the intermediate image and (2) calculating for each of those selected coordinate a corresponding coordinate in the source image;

B. generating a destination image by a second affine transformation of the intermediate image along a second axis relative to the source image wherein said second transformation is executed by the steps of (1) selecting a plurality of coordinates for destination image and (2) calculating for each of those selected coordinates a corresponding coordinate in the intermediate image; and

C. generating a projection of the destination image along a selected one of the first and second axes.

2. A method according to claim 1, wherein step (C) comprises any of the steps of:

A. generating a projection along an x-axis of the destination image by any of the steps of;

i. summing intensities of pixels in the destination image in successive columns along the x-axis, or

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive columns along the x-axis, and

B. generating a projection along a y-axis of the destination image by any of the steps of;

i. summing intensities of pixels in the destination image in successive rows along the y-axis, or

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive rows of the destination image.

3. A method according to claim 1, wherein step (A) comprises

i. defining a mapping between coordinates in the intermediate image and those in the source image;

and

ii. determining a pixel intensity for at least a selected coordinate in the intermediate image as a function of intensities of one or more pixels in a vicinity of a coordinate in the source image to which the selected coordinate maps.

4. A method according to claim 1, wherein step (B) comprises

i. defining a mapping between coordinates in the destination image and those in the intermediate image;

and

ii. determining a pixel intensity for at least a selected coordinate in the destination image as a function of intensities of one or more pixels in a vicinity of a coordinate in the intermediate image to which the selected coordinate maps.

5. A method according to claim 1, wherein the first axis and the second axis are a y-axis and an x-axis, respectively.

6. A method according to claim 1, wherein

step (A) comprises generating the intermediate image by affine transformation of the source image, along the first axis, in accord with a partial transformation matrix L;

step (3) comprises generating the destination image by affine transformation of the intermediate image, along the second axis, in accord with a partial transformation matrix U; and

where L and U are decompositions of a transformation matrix M, such that M=L·

U.

7. A method according to claim 6, wherein the partial transformation matrix L is in accord with the relation $L=\left[\begin{array}{cc}{l}_{11}& 0\\ l_{21}& l_{22}\end{array}\right]$

wherein l₁₁, l₂₁ and l₂₂ are parameters of L and wherein l₁₁=1.

8. A method according to claim 6, wherein the partial transformation matrix U is in accord with the relation $U=\left[\begin{array}{cc}{u}_{11}& u_{12}\\ 0& u_{22}\end{array}\right]$

wherein u₁₁, u₁₂ and u₂₂ are parameters of U and wherein u₂₂=1.

9. An image processing method for generating a projection of a source image, the method comprising the steps of

A. generating an intermediate image by affine transformation of the source image along a first axis, such generating step including

i. defining a mapping between coordinates in the intermediate image and coordinates in the source image, wherein said step of defining the mapping includes the steps of (1) selecting a plurality of coordinates for the intermediate image and (2) calculating for each of those selected coordinates a corresponding coordinate in the source image, wherein each of the selected coordinates of the intermediate image has a pair of integer coordinates and each of the corresponding coordinates of the source image has at least one integer coordinate,

ii. determining a pixel intensity for each selected coordinate in the intermediate image as a function of intensities of one or more pixels in a vicinity of the corresponding coordinate in the source image to which the selected coordinate maps, the pixel intensity being determined without interpolation in more than one dimension,

B. generating a destination image by affine transformation of the intermediate image along a second axis, such generating step including

i. defining a mapping between coordinates in the destination image and coordinates in the intermediate image, wherein said step of defining the mapping includes the steps of (1) selecting a plurality of coordinates for the destination image and (2) calculating for each of those selected coordinates a corresponding coordinate in the intermediate image, wherein each of the selected coordinates of the intermediate image has a pair of integer coordinates and each of the corresponding coordinates of the source image has at least one integer coordinate,

ii. determining a pixel intensity for at least a selected coordinate in the destination image as a function of intensities of one or more pixels in a vicinity of a coordinate in the intermediate image to which the selected coordinate maps, the pixel intensity being determined without interpolation in more than one dimension, and

C. generating an image processing projection of the destination image along a selected one of the first and second axes.

10. A method according to claim 9, wherein step (C) comprises any of

A. generating an image processing projection along an x-axis of the destination image by any of

i. summing intensities of pixels in the distinction image in successive columns along the x-axis, and

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive columns along the x-axis, and

B. generating an image processing projection along a y-axis of the destination image by any of

i. summing intensities of pixels in the destination image in successive rows along the y-axis, and

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive rows of the destination image.

11. A method according to claim 9, wherein at least of the defining steps includes determining at least selected ones of the mapping iteratively.

12. A method according to claim 11, wherein defining step (B)(i) comprises determining mappings between coordinates in the intermediate image and

13. A method according to claim 12, wherein the defining step comprises determining mappings between coordinates in the source image and those of the intermediate image in accord with the relations

 

x_s[i+1,j]=x_s[i,j]+1

14. A method according to claim 12, wherein the defining step comprises determining mappings between coordinates in the source image and those of the intermediate image in accord with the relations

15. A method according to claim 12, wherein the defining step comprises determining mappings between coordinates in the source image and those of the intermediate image in accord with the relations

16. A method according to claim 12, wherein the defining step comprises determining mappings between coordinates in the source image and those of the intermediate image in accord with the relations

17. An image processing method for generating a projection of a source image, the method comprising the steps of:

A. generating an intermediate image by a general affine transformation of the source image along a first axis relative to the source image, said transformation mapping coordinates having two integer coordinate values in the intermediate image to respective coordinates in the source image, the general affine transformation concurrently effecting at least two transformations selected from a group of transformations including concurrently rotating, scaling, translating, skewing, and shearing,

B. generating a destination image by the general affine transformation of the intermediate image along a second axis relative to the source image; and

C. generating an image processing projection of the destination image along a selected one of the first and second axes.

18. A method according to claim 17, wherein step (C) comprises any of the steps of:

A. generating a projection along an x-axis of the destination image by any of the steps of;

i. summing intensities of pixels in the destination image in successive columns along the x-axis, or

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive columns along the x-axis, and

B. generating a projection along a y-axis of the destination image by any of the steps of;

i. summing intensities of pixels in the destination image in successive rows along the y-axis, or

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive rows of the destination image.

19. An image processing method for generating an image processing projection of a source image, the method comprising the steps of:

A. generating an intermediate image by a first affine transformation of the source image along a first axis relative to the source image, wherein said first affine transformation is executed by the steps of (1) selecting a plurality of coordinates for the intermediate image and (2) calculating for each of those selected coordinate a corresponding coordinate in the source image, where each of the selected coordinates of the intermediate image has a pair of integer coordinates and each of the corresponding coordinates of the source image has at least one integer coordinate,

B. generating a destination image by a second affine transformation of the intermediate image along a second axis relative to the source image wherein said second affine transformation is executed by the steps of (1) selecting a plurality of coordinates for destination image and (2) calculating for each of those selected coordinates a corresponding coordinate in the intermediate image, where each of the selected coordinates of the destination image has a pair of integer coordinates and each of the corresponding coordinates of the intermediate image having at least one integer coordinate; and

C. generating an image processing projection of the destination image along a selected one of the first and second axes.

20. A method according to claim 19, wherein step (C) comprises any of the steps of:

A. generating an image processing projection along an x-axis of the destination image by any of the steps of;

i. summing intensities of pixels in the destination image in successive columns along the x-axis, or

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive columns along the x-axis, and

B. generating an image processing projection along a y-axis of the destination image by any of the steps of;

i. summing intensities of pixels in the destination image in successive rows along the y-axis, or

ii. summing counts of pixels in the destination image with intensities any of above and below a selected threshold in successive rows of the destination image.

21. A method according to claim 19, wherein step (A) comprises

i. defining a mapping between coordinates in the intermediate image and those in the source image;

and

ii. determining a pixel intensity for at least a selected coordinate in the intermediate image as a function of intensities of one or more pixels in a vicinity of a coordinate in the source image to which the selected coordinate maps.

22. A method according to claim 19, wherein step (B) comprises

i. defining a mapping between coordinates in the destination image and those in the intermediate image;

and

ii. determining a pixel intensity for at least a selected coordinate in the destination image as a function of intensities of one or more pixels in a vicinity of a coordinate in the intermediate image to which the selected coordinate maps.

23. A method according to claim 19, wherein the first axis and the second axis are a y-axis and an x-axis, respectively.

24. A method according to claim 19, wherein

step (A) comprises generating the intermediate image by affine transformation of the source image, along the first axis, in accord with a partial transformation matrix L;

step (B) comprises generating the destination image by affine transformation of the intermediate image, along the second axis, in accord with a partial transformation matrix U; and

where L and U are decompositions of a transformation matrix M, such that M=L·

U.

25. A method according to claim 24, wherein the partial transformation matrix L is in accord with the relation $L=\left[\begin{array}{cc}{l}_{11}& 0\\ l_{21}& l_{22}\end{array}\right]$

wherein l₁₁, l₂₁ and l₂₂ are parameters of L and wherein l₁₁=1.

26. A method according to claim 25, wherein the partial transformation matrix U is in accord with the relation $U=\left[\begin{array}{cc}{u}_{11}& u_{12}\\ 0& u_{22}\end{array}\right]$

wherein u₁₁, u₁₂ and u₂₂ are parameters of U and wherein u₂₂=1.