lec14

# lec14 - Lecture 14: October 11, 10 Exam 1, Oct 13, class...

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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 1 Lecture 14: October 11, 10 • Exam 1, Oct 13, class time – Close book, material covered listed in Oct 4 class slides • Last Class – Structure from motion sequence: affine cameras • Tomasi-Kanade Factorization algorithm – Factor data matrix into camera and point position matrices by using SVD • Affine to Euclidean (similarity) upgrade • Today’s objective –Examp le s – Reconstruction from projective (perspective) sequences

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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 2 Factorizing the measurement matrix Obtaining a factorization from SVD: Source: M. Hebert This decomposition minimizes |D-MS| 2
USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 3 Euclidean Upgrade from Multiple Views • Consider orthographic cameras • We want to find matrix Such that M i ^ = M i Q satisfies the constraints for an orthographic matrix (submatrix of M i ^ must be a rotation matrix) • This leads to constrains on elements of M i and C, given in eq. 12.12. Find a linear solution for matrix D= CC T (it is unfortunate that the book uses the same symbol as for the data matrix defined earlier). Then compute C (“square root of D” ) by “Cholesky decomposition”.

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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 4 Other Affine Cameras • Euclidean upgrade also possible for other affine cameras (weak perspective, para perspective) – Each class imposes some constraints on the elements of A
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## This note was uploaded on 11/23/2010 for the course CS 574 taught by Professor Ramnevatia during the Fall '10 term at USC.

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lec14 - Lecture 14: October 11, 10 Exam 1, Oct 13, class...

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