Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA

By René Vidal, Roberto Tron, Richard I. Hartley. International Journal of Computer Vision, 2008

441 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/322b3feffe79585c112c6a0d86c05909634ac7c5

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In Aerospace Engineering

In Computer Vision and Pattern Recognition

Citations in the corpus

Damped Newton algorithms for matrix factorization with missing data (2005, unknown): “Damped Newton with Line Search.”
Figure-ground segmentation improves handled object recognition in egocentric video (2010, background): “Sparse features are easier to track or match, and feature tracks are often used in motion segmentation (e.g. [9] [24] [28]).”
Low rank subspace clustering (LRSC) (2014, background): “It is shown in Vidal et al. (2008) that this matrix is such that Cij ¼ 0 when points i and j are in different subspaces, hence it can be used to build an affinity matrix.”
Estimating 3D shape from degenerate sequences with missing data (2009, methodology): “In figure 6 we show the performance of our (rigid factorization) algorithm against 4 state-of-the-art methods: BF-Buchanan&Fitzgibbon’s Damped Newton method[2], PF- power factorization [8,22] 3 , GA- Guerreiro&Aguiar EM (alternate) algorithm [6],Aanaes- Aanaes et al [1].”
A closed form solution to robust subspace estimation and clustering (2011, background): “As shown in [21], this matrix is such that Cij = 0 when points i and j are in different subspaces, hence it can be used to build an affinity matrix.”
Energy-Based Geometric Multi-model Fitting (2012, methodology): “The general geometric framework for (13) is to detect independent motions as hyperplanes, which is comparable to those for GPCA and RANSAC in Tron and Vidal (2007).”
Ieee Transactions on Pattern Analysis and Machine Intelligence Segmentation of Moving Objects by Long Term Video Analysis (2014, unknown): “While initially all these techniques were very sensitive to noise, more recent models have solved this problem [26], [68], [41], [53], [42], [74].”
A Continuous Occlusion Model for Road Scene Understanding (2016, methodology): “For moving objects, this is within the purview of motion segmentation, which has been approached through algebraic factorization methods [4, 27, 26], statistical methods [11, 9, 20] and clustering methods [31, 8].”
Subspace video stabilization (2011, methodology): “This important constraint has been used to help solve a number of problems in computer vision, including structure from motion [Tomasi and Kanade 1992], correspondence [Irani 2002], and motion segmentation [Vidal et al. 2008].”
Sparse subspace clustering (2009, background): “Subspace clustering is an important problem with numerous applications in image processing, e.g. image representation and compression [15] [29], and computer vision, e.g. image/motion/video segmentation [6] [16] [30] [28] [26].”
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit (2015, unknown): “In many computer vision applications, such as motion segmentation [10, 35, 28], hand written digit clustering [41] and face clustering [4, 21], data from different classes can be well approximated by a union of low dimensional sub-spaces.”
A Geometric Analysis of Subspace Clustering with Outliers (2011, unknown): “One such example is motion segmentation [45].”
A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degenerate and Non-degenerate (2006, methodology): “In practice, the number of trajectories can hardly satisfy GPCA’s requirement for it to handle more than 3 subspaces.”
Deep Subspace Clustering Networks (2017, methodology): “The resulting methods can then be roughly divided into three categories [42]: factorization methods [7, 17, 44, 29, 16], higher-order model based methods [49, 6, 33, 37], and self-expressiveness based methods [9, 24, 26, 46, 15, 12, 22, 52].”
Subspace Clustering (2011, methodology): “Also, let Q ¼ VV > 2 R N 3 N : ð5Þ As shown in [2] and [33], the matrix Q is such that Q jk ¼ 0 if points j and k are in different subspaces: (6) In the absence of noise, (6) can be used to obtain the segmentation of the data by applying spectral clustering to the eigenvectors of Q [7] (see the…”