Presentation08 - Computer Vision Lecture #8 Hossam...

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Computer Vision Lecture #8 Hossam Abdelmunim 1 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical and Computer Engineering Department, University of Louisville, Louisville, KY, USA ECE619/645 – Spring 2011
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Homogeneous (projective) representation of lines A 2D line ax + by + c = 0 is represented by the homogeneous vector below (projective line): L=(a, b, c) T
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Some properties involving points and lines: The point p=(x,y,1) T lies on the line (L) iff: p T L=0 Two points p and q defines a line L: L=p X q Two lines L and m can define a point p: p = L X m
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Examples
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Examples
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The equation p r T F p l = 0 represents a line equation as shown before. This is the epipolar line in the right image. This line is represented by u r =F p l . So it can be written as p r T u r =0 or u r T p r =0. The epipole e r belongs to this line of course: u r T e r =0 This will lead to: p l T F T e r =0
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This note was uploaded on 01/12/2012 for the course ECE 618 taught by Professor Amini during the Spring '08 term at University of Louisville.

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Presentation08 - Computer Vision Lecture #8 Hossam...

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