Efficient convolutions using polynomial covers
First Claim
Patent Images
1. An image processing arrangement for comparing a first image (ƒ
- (x)) to a second image (g(x)), the arrangement comprisinga first quantizer for receiving as an input the first image and generating an approximation thereof defined as a polynomial first image cover having a predetermined degree d.sub.ƒ
, said first cover defined by a plurality of non-overlapping cover regions ci ;
a second quantizer for receiving as an input the second image and generating an approximation thereof defined as a polynomial second image cover having a predetermined degree dg, said second cover defined by a plurality of non-overlapping cover regions ci ;
a first differentiator receiving as an input the first polynomial of degree d.sub.ƒ
and differentiating said first polynomial d.sub.ƒ
+1 times to generate an impulse response representation of said first image;
a second differentiator receiving as an input the second polynomial of degree dg and differentiating said second polynomial dg +1 times to generate an impulse response representation of said second image;
a convolver responsive to the first and second impulse response representations for summing said impulse functions to generate a convolution representation of said first and second images; and
an integrator responsive to the convolution output from the convolver for integrating said convolution ((d.sub.ƒ
+1+dg+1)=d.sub.ƒ
+dg +2) times to generate as an output the pattern information related to the first and second images.
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Abstract
Signal processing and pattern recognition is efficiently accomplished by using a plurality of low degree polynomials to approximate the images. The polynomials are then differentiated to obtain impulse functions. The impulse functions may be easily and efficiently convolved and the convolution subsequently integrated to extract the desired signal information.
130 Citations
31 Claims
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1. An image processing arrangement for comparing a first image (ƒ
- (x)) to a second image (g(x)), the arrangement comprising
a first quantizer for receiving as an input the first image and generating an approximation thereof defined as a polynomial first image cover having a predetermined degree d.sub.ƒ
, said first cover defined by a plurality of non-overlapping cover regions ci ;a second quantizer for receiving as an input the second image and generating an approximation thereof defined as a polynomial second image cover having a predetermined degree dg, said second cover defined by a plurality of non-overlapping cover regions ci ; a first differentiator receiving as an input the first polynomial of degree d.sub.ƒ
and differentiating said first polynomial d.sub.ƒ
+1 times to generate an impulse response representation of said first image;a second differentiator receiving as an input the second polynomial of degree dg and differentiating said second polynomial dg +1 times to generate an impulse response representation of said second image; a convolver responsive to the first and second impulse response representations for summing said impulse functions to generate a convolution representation of said first and second images; and an integrator responsive to the convolution output from the convolver for integrating said convolution ((d.sub.ƒ
+1+dg+1)=d.sub.ƒ
+dg +2) times to generate as an output the pattern information related to the first and second images. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
- (x)) to a second image (g(x)), the arrangement comprising
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10. A method of extracting signal information from a pair of images, the pair of images defined by a first image ƒ
- (x) and a second image g(x), the method comprising the steps of;
a) quantizing each image by defining a cover for each image comprising a series of low degree polynomials of degree d.sub.ƒ
and dg, respectively, said quantized representations defined as F(x) and G(x), respectively;b) differentiating each quantized representation, the first quantized representation F(x) differentiated d.sub.ƒ
+1 times and the second quantized representation G(x) differentiated dg +1 times, each differentiating generating an impulse response representation of each image, to form F'"'"'(x) and G'"'"'(x), respectively;c) convolving the impulse response representations of F'"'"'(x) and G'"'"'(x) to generated F'"'"'(x)*G'"'"'(x); and d) integrating the convolution F'"'"'(x)*G'"'"'(x) (d.sub.ƒ
+1+dg+1) times to generate as an output the pattern information related to the first and second images. - View Dependent Claims (11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
- (x) and a second image g(x), the method comprising the steps of;
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21. An image processing arrangement for comparing a first image (ƒ
- (x)) to a second image (g(x)), the first image being larger than the second image and the second image defined a plurality of separate impulse functions for each pixel within said second image, the arrangement comprising
a quantizer for receiving as an input the first image and generating an approximation thereof defined as a polynomial image cover having a predetermined degree d.sub.ƒ
, said first cover defined by a plurality of non-overlapping cover regions ci ;a differentiator receiving as an input the polynomial of degree d.sub.ƒ
and differentiating said polynomial d.sub.ƒ
+1 times to generate an impulse response representation of said first image;a convolver responsive to the impulse response representation of said first image generated by said differentiator and the plurality of separate impulse functions of said second image for summing said impulse functions to generate a convolution representation of said first and second images; and an integrator responsive to the convolution output from the convolver for integrating said convolution (d.sub.ƒ
+1) times to generate as an output the pattern information related to the first and second images. - View Dependent Claims (22, 23, 24, 25)
- (x)) to a second image (g(x)), the first image being larger than the second image and the second image defined a plurality of separate impulse functions for each pixel within said second image, the arrangement comprising
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26. A method of extracting signal information from a pair of images, the pair of images defined by a first image ƒ
- (x) and a second image g(x), the second image being smaller than the first image and represented by a plurality of impulse functions for each pixel within said second image, the method comprising the steps of;
a) quantizing the first image by defining a cover for said first image comprising a series of low degree polynomials of degree d.sub.ƒ
, said quantized representation defined as F(x), respectively;b) differentiating said quantized representation d.sub.ƒ
+1 times to generate an impulse response representation of said first image, defined as F'"'"'(x);c) convolving the impulse response representation F'"'"'(x) with the plurality of impulse functions of the second image to generate F'"'"'(x)*g(x); and d) integrating the convolution F'"'"'(x)*g(x) (d.sub.ƒ
+1) times to generate as an output the pattern information related to the first and second images. - View Dependent Claims (27, 28, 29, 30, 31)
- (x) and a second image g(x), the second image being smaller than the first image and represented by a plurality of impulse functions for each pixel within said second image, the method comprising the steps of;
Specification