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Unformatted text preview: CMPEN454, PSU Robert Collins Lecture 15: Generalized Stereo: Epipolar Geometry CMPEN454, PSU Robert Collins Generalized Stereo Key idea: Any two images showing an overlapping view of the world can be treated as a stereo pair... ... we just have to figure out how the two views are related. Some of the most beautiful math in vision concerns describing how multiple views are related, geometrically. CMPEN454, PSU Robert Collins Recall: Epipolar Constraint Important Stereo Vision Concept: Given a point in the left image, we dont have to search the whole right image for a corresponding point. The epipolar constraint reduces the search space to a onedimensional line. CMPEN454, PSU Robert Collins Review : Simple Stereo System Left camera Right camera z x y z x y T x Same Y Coord! Epipolar line P Equation relating depth and disparity baseline disparity depth CMPEN454, PSU Robert Collins Review: Epipolar Constraint Corresponding features are constrained to lie along conjugate epipolar lines (on the same row in the case of our simple setup). CMPEN454, PSU Robert Collins General Stereo O 2 O 1 z 1 z 2 x 1 y 1 y 2 x 2 C 1 C 2 In general, the cameras may be related by In general, the cameras may be related by an arbitrary transformation (R,T) an arbitrary transformation (R,T) In general, intrinsic camera parameters In general, intrinsic camera parameters may be different, and even unknown may be different, and even unknown Epipolar Epipolar Matrix Matrix Fundamental Matrix Fundamental Matrix CMPEN454, PSU Robert Collins EPIPOLAR GEOMETRY CMPEN454, PSU Robert Collins Epipolar Geometry e r e l O r p r P p l O...
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