NDLI: Factorization with Uncertainty

Content Provider	Springer Nature Link
Author	Anandan, P. Irani, Michal
Copyright Year	2002
Abstract	Factorization using Singular Value Decomposition (SVD) is often used for recovering 3D shape and motion from feature correspondences across multiple views. SVD is powerful at finding the global solution to the associated least-square-error minimization problem. However, this is the correct error to minimize only when the x and y positional errors in the features are uncorrelated and identically distributed. But this is rarely the case in real data. Uncertainty in feature position depends on the underlying spatial intensity structure in the image, which has strong directionality to it. Hence, the proper measure to minimize is covariance-weighted squared-error (or the Mahalanobis distance). In this paper, we describe a new approach to covariance-weighted factorization, which can factor noisy feature correspondences with high degree of directional uncertainty into structure and motion. Our approach is based on transforming the raw-data into a covariance-weighted data space, where the components of noise in the different directions are uncorrelated and identically distributed. Applying SVD to the transformed data now minimizes a meaningful objective function in this new data space. This is followed by a linear but suboptimal second step to recover the shape and motion in the original data space. We empirically show that our algorithm gives very good results for varying degrees of directional uncertainty. In particular, we show that unlike other SVD-based factorization algorithms, our method does not degrade with increase in directionality of uncertainty, even in the extreme when only normal-flow data is available. It thus provides a unified approach for treating corner-like points together with points along linear structures in the image.
Starting Page	101
Ending Page	116
Page Count	16
File Format	PDF
ISSN	09205691
Journal	International Journal of Computer Vision
Volume Number	49
Issue Number	2-3
e-ISSN	15731405
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2002-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Artificial Intelligence (incl. Robotics) Computer Imaging, Graphics and Computer Vision Image Processing Automation and Robotics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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