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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?
Stereo Constraints (Review) 1 Image plane Focal plane M p p’ 2 Epipolar Line Epipole

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Epipolar Constraint (Review)
From Geometry to Algebra (Review) O O’ P p p’

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From Geometry to Algebra (Review) O O’ P p p’
Linear Constraint: Should be able to express as matrix multiplication.

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The Essential Matrix (Review)
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
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
Motion Models (Review) + - - - Z Y X T T T Z Y X Z Y X 1 1 1 α β

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