ECE468_7 - ECE 468 CS 519 Digital Image Processing...

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Prof. Sinisa Todorovic [email protected] ECE 468 / CS 519: Digital Image Processing Gradients, Harris Corners 1
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Image Gradient along X-axis I x ( x, y ) = I ( x + 1 , y ) - I ( x, y ) = 2 4 0 0 0 0 - 1 1 0 0 0 3 5 | {z } D x ( x,y ) I ( x, y ) 2
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Image Gradient along Y-axis = 2 4 0 0 0 0 - 1 0 0 1 0 3 5 | {z } D y ( x,y ) I ( x, y ) I y ( x, y ) = I ( x, y + 1) - I ( x, y ) 3
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Filtering Image Gradient convolution is associative w ( x, y ; σ ) I x ( x, y ) = w ( x, y ; σ ) D x ( x, y ) I ( x, y ) = [ w ( x, y ; σ ) D x ( x, y )] I ( x, y ) 4
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= [ D x ( x, y ) w ( x, y ; σ )] I ( x, y ) Filtering Image Gradient w ( x, y ; σ ) I x ( x, y ) = w ( x, y ; σ ) D x ( x, y ) I ( x, y ) = [ w ( x, y ; σ ) D x ( x, y )] I ( x, y ) convolution is commutative 5
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= [ D x ( x, y ) w ( x, y ; σ )] I ( x, y ) Filtering Image Gradient w ( x, y ; σ ) I x ( x, y ) = w ( x, y ; σ ) D x ( x, y ) I ( x, y ) = [ w ( x, y ; σ ) D x ( x, y )] I ( x, y ) = w x ( x, y ; σ ) I ( x, y ) derivative of the filter 6
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Weighted Image Gradient Image is discrete Gradient is approximate We always find the gradient of the filter ! w ( x, y ; σ ) I x ( x, y ) = w x ( x, y ; σ ) I ( x, y ) w ( x, y ; σ ) I y ( x, y ) = w y ( x, y ; σ ) I ( x, y ) 7
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Interest Points Harris corners 8
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Properties of Interest Points Locality -- robust to occlusion, noise Saliency -- rich visual cue Stable under affine transforms Distinctiveness -- differ across distinct objects Efficiency -- easy to compute 9
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Example of Detecting Harris Corners 10
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Harris Corner Detector homogeneous region no change in all directions edge no change along the edge corner change in all directions Source: Frolova, Simakov, Weizmann Institute scanning window 11
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