30 April 1992 Motion segmentation using singular value decomposition
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This paper presents a method for the segmentation of multiple motions in a scene using the singular value decomposition of a feature track matrix. It is shown that motions can be separated using the right singular vectors associated with the nonzero singular values. This is based on the relationship between the right singular vectors and the principal components of the covariance matrix of the tracks. Furthermore, under general assumptions, the number of numerically nonzero singular values can be used to determine the number of motions. This can be used to derive a relationship 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 and a study of the robustness of the method is given. The paper ends with a critical analysis of the approach.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Terrance E. Boult, Lisa Gottesfeld Brown, "Motion segmentation using singular value decomposition", Proc. SPIE 1611, Sensor Fusion IV: Control Paradigms and Data Structures, (30 April 1992); doi: 10.1117/12.57937; https://doi.org/10.1117/12.57937

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