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Factorization-based segmentation of motions

Factorization-based segmentation of motions,10.1109/WVM.1991.212809,Terrance E. Boult,Lisa Gottesfeld Brown Vision

Factorization-based segmentation of motions   (Citations: 62)
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The authors address the problem of motion segmentation using the singular value decomposition of a feature track matrix. It is shown that, under general assumptions, the number of numerically nonzero singular values can be used to determine the number of motions. Furthermore, motions can be separated using the right singular vectors associated with the nonzero singular values. A relationship is derived between a good segmentation, the number of nonzero singular values in the input and the sum of the number of nonzero singular values in the segments. The approach is demonstrated on real and synthetic examples. The paper ends with a critical analysis of the approach
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    • ...In these cases, the segmentation process can be approached by considering the objects as moving in 3-D space , and this approach has motivated several works in 3-D motion segmentation [1]–[6]...

    Luciano Silva da Silvaet al. Video Segmentation Based on Motion Coherence of Particles in a Video S...

    • ...The basic approach behind several early methods exploited the observation that the trajectories associated with each motion lie in a subspace of dimension four or less [1, 4]. Factorization approaches [4, 7, 8] provided an elegant framework to partition the matrix M directly into maximally rank deficient submatrices M i . However, these approaches were shown to degrade when the motions were not independent, or the input point tracks were ...

    Anil M. Cheriyadatet al. Nonnegative matrix factorization of partial track data for motion segm...

    • ...Motion segmentation from multiple views has been studied mostly in the case of affine cameras, because in this case the trajectories associated with each motion live in a linear subspace of dimension four or less (Boult and Brown 1991; Tomasi and Kanade 1992) (see Sect...
    • ...2.1). This subspace constraint was used by Boult and Brown (1991) to propose a multiframe 3-D motion segmentation algorithm based on thresholding the leading singular vector of the matrix of point trajectories W. Costeira and Kanade (CK) (Costeira and Kanade 1998) extended this approach by thresholding the entries of the so-called shape interaction matrix Q .T his matrix is built from the singular value decomposition (SVD)...

    René Vidalet al. Multiframe Motion Segmentation with Missing Data Using PowerFactorizat...

    • ...Early motion segmentation techniques based on the factorization method are proposed in [2], [10], which iteratively generate hypotheses of segmentation and verify them...

    Jingyu Yanet al. A Factorization-Based Approach for Articulated Nonrigid Shape, Motion ...

    • ...The only existing works on multiframe 3D motion segmentation are for points moving on a line in three perspective views [22], for multiple translating objects from line correspondences in three perspective views [23], and for rigid-body motions in three or more affine views [1], [2], [5], [9], [10], [15], [17], [18], [27], [35], [36]...

    René Vidalet al. Three-View Multibody Structure from Motion

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