Singular value decomposition (SVD) is a technique for signal/image processing. Tomasi and Kanade (1992) proposed an SVD approach to the structure-from-motion problem. For the single object case, they devised a sequential algorithm so that it would be able to recover the scene in real time as the video images are taken. This is called a motion-shape estimation (MSE) problem. This paper evolves the single object MSE to multi-object MSE problem. Given a sequence of 2D video images of multiple moving objects, the problem is to track the 3D motion ofthe objects and reconstruct their 3D shapes. After selection of initial feature points (FPs), the SVD may be applied to a measurement matrix formed by the FPs sequentially tracked by a video system. The distribution of singular values would first reveal the information about the number of objects. Then, using an algebraic-based subspace clustering method, the FPs may be mapped onto their corresponding objects. Thereafter, the motion and shape may be estimated from a matrix factorization. Our method hinges upon the numerical effectiveness and stability of the SVD factorization.
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