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lecture24 - Multi-View Geometry(Cont Stereo...

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Multi-View Geometry (Cont.)
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Stereo Constraints (Review) p p’ ? Given p in left image, where can the corresponding point p’ in right image be?
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Stereo Constraints (Review) 1 Image plane Focal plane M p p’ 2 Epipolar Line Epipole
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Epipolar Constraint (Review)
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From Geometry to Algebra (Review) O O’ P p p’
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From Geometry to Algebra (Review) O O’ P p p’
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Linear Constraint: Should be able to express as matrix multiplication.
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The Essential Matrix (Review)
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The Essential Matrix Based on the Relative Geometry of the Cameras Assumes Cameras are calibrated (i.e., intrinsic parameters are known) Relates image of point in one camera to a second camera (points in camera coordinate system). Is defined up to scale 5 independent parameters
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The Essential Matrix Similarly p is the epipolar line corresponding to p in the right camera T ε
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The Essential Matrix ε [ ] 0 e R = = × t e e’ Essential Matrix is singular with rank 2 Similarly, ε [ ] [ ] 0 = - = = × × e t R e t R e T T T T
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Small Motions and Epipolar Constraint
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Motion Models (Review) + - - - Z Y X T T T Z Y X Z Y X 1 1 1 α β
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