## Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories (2008)

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Venue: | In IEEE Conference on Computer Vision and Pattern Recognition |

Citations: | 32 - 4 self |

### BibTeX

@INPROCEEDINGS{Rao08motionsegmentation,

author = {Shankar R. Rao and Roberto Tron and René Vidal and Yi Ma},

title = {Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories},

booktitle = {In IEEE Conference on Computer Vision and Pattern Recognition},

year = {2008}

}

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### Abstract

We examine the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence. Using the affine camera model, this motion segmentation problem can be cast as the problem of segmenting samples drawn from a union of linear subspaces. Due to limitations of the tracker, occlusions and the presence of nonrigid objects in the scene, the obtained motion trajectories may contain grossly mistracked features, missing entries, or not correspond to any valid motion model. In this paper, we develop a robust subspace separation scheme that can deal with all of these practical issues in a unified framework. Our methods draw strong connections between lossy compression, rank minimization, and sparse representation. We test our methods extensively and compare their performance to several extant methods with experiments on the Hopkins 155 database. Our results are on par with stateof-the-art results, and in many cases exceed them. All MAT-LAB code and segmentation results are publicly available for peer evaluation at

### Citations

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Citation Context ...gmentation, that can roughly be grouped into three categories: factorizationbased, algebraic, and statistical. Many early attempts at motion segmentation attempt to directly factor Y according to (3) =-=[1, 7, 11, 12]-=-. To make such approaches tractable, the motions must be independent of one another, i.e. the pairwise intersection of the motion subspaces must be the zero vector. However, for most dynamic scenes wi... |

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Citation Context ...partially dependent on each other. This has motivated the development of algorithms designed to deal with dependent motions. Algebraic methods, such as Generalized Principal Component Analysis (GPCA) =-=[19]-=-, are generic subspace separation algorithms that do not place any restriction on the relative orientations of the motion subspaces. However, when a linear solution is used, the complexity of algebrai... |

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Citation Context ...enting each outlier as a separate group. Such small groups are also easily detectable. Figure 1. The motions sequences “1R2RC” (left), “arm” (center), and “cars10”(right) from the Hopkins155 database =-=[18]-=-. Experiments. For all of the experiments in Section 2, we choose three representative sequences from the Hopkins155 motion segmentation database [18] for testing: “1R2RC” (checkerboard), “arm” (artic... |

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1 | Example frames from three motion sequences with incomplete or corrupted trajectories. Sequences taken from [20]. trajectories that were marked as corrupted so that we may treat them as missing entries. We apply our ℓ1-based entry completion method to this - Figure |