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lec19_svm

# lec19_svm - CS6670 Computer Vision Noah Snavely Lecture 19...

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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
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
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
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?
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
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
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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lec19_svm - CS6670 Computer Vision Noah Snavely Lecture 19...

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