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Unformatted text preview: Computer Vision : CISC 4/689 Corner Detection Basic idea: Find points where two edges meeti.e., high gradient in two directions Cornerness is undefined at a single pixel, because theres only one gradient per point Look at the gradient behavior over a small window Categories image windows based on gradient statistics Constant : Little or no brightness change Edge : Strong brightness change in single direction Flow : Parallel stripes Corner/spot : Strong brightness changes in orthogonal directions Computer Vision : CISC 4/689 Corner Detection: Analyzing Gradient Covariance Intuitively, in corner windows both I x and I y should be high Cant just set a threshold on them directly, because we want rotational invariance Analyze distribution of gradient components over a window to differentiate between types from previous slide: The two eigenvectors and eigenvalues 1 , 2 of C (Matlab: eig(C) ) encode the predominant directions and magnitudes of the gradient, respectively, within the window Corners are thus where min( 1 , 2 ) is over a threshold courtesy of Wolfram Computer Vision : CISC 4/689 Contents Harris Corner Detector Description Analysis Detectors Rotation invariant Scale invariant Affine invariant Descriptors Rotation invariant Scale invariant Affine invariant Computer Vision : CISC 4/689 Harris Detector: Mathematics [ ] 2 , ( , ) ( , ) ( , ) ( , ) x y E u v w x y I x u y v I x y = + + Change of intensity for the shift [ u,v ]: Intensity Shifted intensity Window function or Window function w(x,y) = Gaussian 1 in window, 0 outside Computer Vision : CISC 4/689 Harris Detector: Mathematics [ ] ( , ) , u E u v u v M v 2245 For small shifts [ u,v ] we have a bilinear approximation: 2 2 , ( , ) x x y x y x y y I I I M w x y I I I = where M is a 2 2 matrix computed from image derivatives: Computer Vision : CISC 4/689 Harris Detector: Mathematics [ ] ( , ) , u E u v u v M v 2245 Intensity change in shifting window: eigenvalue analysis 1 , 2 eigenvalues of M ( max )1/2 ( min )1/2 Ellipse E(u,v) = const If we try every possible orientation n , the max. change in intensity is 2 Computer Vision : CISC 4/689 Harris Detector: Mathematics 1 2 Corner 1 and 2 are large, 1 ~ 2 ; E increases in all directions 1 and 2 are small; E is almost constant in all directions Edge 1 >> 2 Edge 2 >> 1 Flat region Classification of image points using eigenvalues of M : Computer Vision : CISC 4/689 Harris Detector: Mathematics Measure of corner response: ( 29 2 det trace R M k M = 1 2 1 2 det trace M M = = + ( k empirical constant, k = 0.040.06) Computer Vision : CISC 4/689 Harris Detector: Mathematics 1 2 Corner Edge Edge Flat R depends only on...
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This note was uploaded on 01/12/2012 for the course ECE 618 taught by Professor Amini during the Spring '08 term at University of Louisville.
 Spring '08
 AMINI

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