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lec17_ransac_web

lec17_ransac_web - CS4670/5760 Computer Vision Kavita Bala...

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Lecture 17: RANSAC CS4670/5760: Computer Vision Kavita Bala

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Alignment Alignment: find parameters of model that maps one set of points to another Typically want to solve for a global transformation that accounts for *most* true correspondences Difficulties Noise (typically 1-3 pixels) Outliers (often 50%)
Least squares: find t to minimize To solve, form the normal equations Differentiate and equate to 0 to minimize

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Affine transformations Matrix form 2 n x 6 6 x 1 2 n x 1
Solving for homographies

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Solving for homographies
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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Recap: Two Common Optimization Problems Problem statement Solution Problem statement Solution (matlab) 1 s.t. minimize x x Ax A x T T T 0 o solution t lsq trivial - non Ax 1 .. 2 1 : ) eig( ] , [ v x A A v n T b Ax o solution t squares least b A x \ 2 minimize b Ax b A A A x T T 1

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Hybrid Image competition results Hall of Fame : 16sp/artifacts/pa1/hof.html
Runners Up

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Benjamin Siper, Sania Nagpal
Nadav Nehoran, Thomas Ilyevsky

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Daniel Donenfeld, Markus Salasoo
Joshua Chan, Jerica Huang

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Third Place
Aditi Jain, Ross Tannenbaum

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James Briggs, Vishwanathan Ramanathan
Second Place

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Aaron Ferber, Mateo Espinosa Zarlenga
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