TheoryandPracticeofProjectiveRectification

TheoryandPracticeofProjectiveRectification - Theory and...

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Theory and Practice of Projective Rectification Richard I. Hartley Presented by Yinghua Hu
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Goal Apply 2D projective transformations on a pair of stereo images so that the epipolar lines in resulting images match and are parallel to the x-axis.
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Stereo Constraints Epipolar Geometry 1 Image plane Focal plane M u u’ 2 Epipolar Line Epipole
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Before rectification
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Epipolar lines
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After rectification
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Some terms Cofactor matrix A * A * A = AA * =det(A)I If A is an invertible matrix, A * ≈(A T ) -1 Skew symmetrix matrix Given a vector t = (t x , t y , t z ) T [t] × = [ 0 -t z t y t z 0 -t x - t y t x 0 ] [t] × s = t×s
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Fundamental matrix x’ T Fx = 0
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Some Properties F is the fundamental matrix corresponding to an ordered pair of images (J, J’) and p and p’ are the epipoles, then F T is the fundamental matrix corresponding to images (J’, J) F=[p’] × M=M * [p] × , M is non-singular and not unique Fp=0 and p’ T F=0
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Outline of the algorithm Identify image-to-image matches u i ↔ u i ’ between the two images.
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