TY - GEN
T1 - Incorporating constraints and prior knowledge into factorization algorithms - An application to 3D recovery
AU - Gruber, Amit
AU - Weiss, Yair
PY - 2006
Y1 - 2006
N2 - Matrix factorization is a fundamental building block in many computer vision and machine learning algorithms. In this work we focus on the problem of "structure from motion" in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations. This problem may be reduced to a low rank factorization problem. When all the 2D locations are known, singular value decomposition yields a least squares factorization of the measurements matrix. In realistic scenarios this assumption does not hold: some of the data is missing, the measurements have correlated noise, and the scene may contain multiple objects. Under these conditions, most existing factorization algorithms fail while human perception is relatively unchanged. In this work we present an EM algorithm for matrix factorization that takes advantage of prior information and imposes strict constraints on the resulting matrix factors. We present results on challenging sequences.
AB - Matrix factorization is a fundamental building block in many computer vision and machine learning algorithms. In this work we focus on the problem of "structure from motion" in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations. This problem may be reduced to a low rank factorization problem. When all the 2D locations are known, singular value decomposition yields a least squares factorization of the measurements matrix. In realistic scenarios this assumption does not hold: some of the data is missing, the measurements have correlated noise, and the scene may contain multiple objects. Under these conditions, most existing factorization algorithms fail while human perception is relatively unchanged. In this work we present an EM algorithm for matrix factorization that takes advantage of prior information and imposes strict constraints on the resulting matrix factors. We present results on challenging sequences.
UR - http://www.scopus.com/inward/record.url?scp=33745816026&partnerID=8YFLogxK
U2 - 10.1007/11752790_10
DO - 10.1007/11752790_10
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AN - SCOPUS:33745816026
SN - 3540341374
SN - 9783540341376
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 151
EP - 162
BT - Subspace, Latent Structure and Feature Selection - Statistical and Optimization Perspectives Workshop, SLSFS 2005, Revised Selected Papers
T2 - Subspace, Latent Structure and Feature Selection - Statistical and Optimization Perspectives Workshop, SLSFS 2005
Y2 - 23 February 2005 through 25 February 2005
ER -