lec19_svm - CS6670: Computer Vision Noah Snavely Lecture...

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Lecture 19: Single-view modeling CS6670: Computer Vision Noah Snavely
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Announcements Project 3: Eigenfaces due tomorrow, November 11 at 11:59pm Quiz on Thursday, first 10 minutes of class
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Announcements Final projects Feedback in the next few days Midterm reports due November 24 Final presentations tentatively scheduled for the final exam period: Wed, December 16, 7:00 PM - 9:30 PM
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Multi-view geometry We’ve talked about two views And many views What can we tell about geometry from one view? 0
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Projective geometry Readings Mundy, J.L. and Zisserman, A., Geometric Invariance in Computer Vision, Appendix: Projective Geometry for Machine Vision, MIT Press, Cambridge, MA, 1992, (read 23.1 - 23.5, 23.10) available online: http://www.cs.cmu.edu/~ph/869/papers/zisser-mundy.pdf Ames Room
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Projective geometry—what’s it good for? Uses of projective geometry • Drawing • Measurements • Mathematics for projection • Undistorting images • Camera pose estimation • Object recognition Paolo Uccello
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Applications of projective geometry Vermeer’s Music Lesson Reconstructions by Criminisi et al.
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1 2 3 4 1 2 3 4 Measurements on planes Approach: unwarp then measure What kind of warp is this?
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Image rectification To unwarp (rectify) an image solve for homography H given p and p’ solve equations of the form: w p’ = Hp – linear in unknowns: w and coefficients of H – H is defined up to an arbitrary scale factor – how many points are necessary to solve for H ? p p’
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Solving for homographies
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Solving for homographies
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Solving for homographies Defines a least squares problem: Since is only defined up to scale, solve for unit vector Solution: = eigenvector of with smallest eigenvalue Works with 4 or more points 2n × 9 9 2n
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l Point and line duality A line l is a homogeneous 3-vector It is to every point (ray) p on the line: l p =0 p 1 p 2
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This note was uploaded on 09/27/2010 for the course CS 667 at Cornell University (Engineering School).

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lec19_svm - CS6670: Computer Vision Noah Snavely Lecture...

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