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Derivation of Epipolar Line

asked 2012-11-03 03:55:46 -0500

rotating_image gravatar image

Hi i have this mathematical doubt about derivation of epipolar lines...in a book i read the following..image description image description

i cannot understand how the cross product of e' x x' giving the epipolar line l'...please can any one explain the maths or refer me to some reference...my google search and vector geometry classes not helping yet..!!

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answered 2012-12-31 10:33:21 -0500

waqarshahid gravatar image

You can read the following,it details the proof which you require that how cross product result in the line containing them

http://undergraduate.csse.uwa.edu.au/units/CITS4240/Lectures/lectsvr.pdf

regards waqar

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Thanks waqar for useful reference.

So, in the figure in question, if e' and x' are represented in homogenous coordinates then their cross-product will represent a normal to the plane which passes through e',x' and origin (0,0,0) of homogenous coordinate system. And intersection between this plane and Z=W, where e'=(x1,y1,W) and x'=(x2,y2,W), will be the line l' hence l' can be represented as cross product of e' and x'.

pranav gravatar imagepranav ( 2013-01-02 06:21:03 -0500 )edit

Thanks for your comment as it preserves some knowledge. The original slides are not available anymore...

SR gravatar imageSR ( 2015-05-05 16:36:50 -0500 )edit
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Asked: 2012-11-03 03:55:46 -0500

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Last updated: Dec 31 '12