L5(Stereo)

# L5(Stereo) - Preliminary Sldies Introduction to Computer...

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Spring 2006 Stereo 1 Introduction to Computer Vision CS / ECE 181B Tuesday, April 27, 2006 Multiple view geometry and stereo Ack: M. Turk and M. Pollefeys Preliminary Sldies Spring 2006 Stereo 2 Seeing in 3D • Humans can perceive depth, shape, etc. – 3D properties of the world – How do we do it? • We use many cues – Oculomotor convergence/divergence – Accomodation (changing focus) – Motion parallax (changing viewpoint) – Monocular depth cues Occlusion, perspective, texture gradients, shading, size – Binocular disparity (stereo) • How can computers perceive depth?

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Spring 2006 Stereo 3 Spring 2006 Stereo 4
Spring 2006 Stereo 5 Multiple views and depth Spring 2006 Stereo 6 Why multiple views? • A camera projects the 3D world into 2D images • This is not always a problem – humans can figure out a lot from a 2D view!

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Spring 2006 Stereo 7 Why multiple views? • But precise 3D information (distance, depth, shape, curvature, etc.) is difficult or impossible to obtain from a single view • In order to measure distances, sizes, angles, etc. we need multiple views (and calibrated cameras!) – Monocular binocular trinocular… C 1 C 2 C 3 Spring 2006 Stereo 8 Multiple view geometry C 1 C 2 • Two big questions for multiple view geometry problems: – Which are possible? – Which are most likely? • There are many possible configurations of scene points that could have created corresponding points in multiple views
Spring 2006 Stereo 9 Questions Correspondence geometry: Given an image point x in the first view, how does this constrain the position of the corresponding point x’ in the second image? Camera geometry (motion): Given a set of corresponding image points {x i _x’ i }, i=1,…,n, what are the cameras P and P’ for the two views? Scene geometry (structure): Given corresponding image points x i _x’ i and cameras P, P’, what is the position of (their pre-image) X in space? M. Pollefeys Spring 2006 Stereo 10 Two-view geometry C 1 C 2 Epipolar line Not necessarily along a row of the image p • The epipolar geometry is defined by the origins of the camera coordinate frames, the scene point P , and the locations of the image planes

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Spring 2006 Stereo 11 C,C’,x,x’ and X are coplanar Epipolar geometry Spring 2006 Stereo 12 What if only C,C’,x are known? Epipolar Geometry
Spring 2006 Stereo 13 All points on π project on l and l’ Epipolar Geometry Spring 2006 Stereo 14 Family of planes π and lines l and l’ Intersection in e and e’ Epipolar Geometry

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Spring 2006 Stereo 15 epipoles e,e’ = intersection of baseline with image plane = projection of projection center in other image = vanishing point of camera motion direction
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## This note was uploaded on 12/29/2011 for the course ECE 181b taught by Professor Staff during the Fall '08 term at UCSB.

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L5(Stereo) - Preliminary Sldies Introduction to Computer...

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