Enhanced Local Subspace Affinity for feature-based motion segmentation

We present a new motion segmentation algorithm: the Enhanced Local Subspace Affinity (ELSA). Unlike Local Subspace Affinity, ELSA is robust in a variety of conditions even without manual tuning of its parameters. This result is achieved thanks to two improvements. The first is a new model selection technique for the estimation of the trajectory matrix rank. The second is an estimation of the number of motions based on the analysis of the eigenvalue spectrum of the Symmetric Normalized Laplacian matrix. Results using the Hopkins155 database and synthetic sequences are presented and compared with state of the art techniques.

[1]  Angel D. Sappa,et al.  Rank estimation in 3D multibody motion segmentation , 2008 .

[2]  Naoyuki Ichimura,et al.  Motion segmentation based on feature selection from shape matrix , 2000, Systems and Computers in Japan.

[3]  René Vidal,et al.  Clustering and dimensionality reduction on Riemannian manifolds , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[4]  René Vidal,et al.  Segmenting Motions of Different Types by Unsupervised Manifold Clustering , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[5]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[6]  Touradj Ebrahimi,et al.  Tracking video objects in cluttered background , 2005, IEEE Transactions on Circuits and Systems for Video Technology.

[7]  René Vidal,et al.  Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[8]  Joachim M. Buhmann,et al.  Seeing the Objects Behind the Dots: Recognition in Videos from a Moving Camera , 2009, International Journal of Computer Vision.

[9]  Lihi Zelnik-Manor,et al.  Degeneracies, dependencies and their implications in multi-body and multi-sequence factorizations , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[10]  Yair Weiss,et al.  Incorporating Non-motion Cues into 3D Motion Segmentation , 2006, ECCV.

[11]  Takeo Kanade,et al.  A Multibody Factorization Method for Independently Moving Objects , 1998, International Journal of Computer Vision.

[12]  K. Kanatani,et al.  Estimating the Number of Independent Motions for Multibody Motion Segmentation , 2002 .

[13]  Kerfichi Kanatani,et al.  Statistical Optimization and Geometric Visual Inference , 1997, AFPAC.

[14]  P. Koev,et al.  On the largest principal angle between random subspaces , 2006 .

[15]  Kenichi Kanatani,et al.  Geometric Structure of Degeneracy for Multi-body Motion Segmentation , 2004, ECCV Workshop SMVP.

[16]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[17]  René Vidal,et al.  Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[18]  Guangliang Chen,et al.  Spectral Curvature Clustering (SCC) , 2009, International Journal of Computer Vision.

[19]  Namrata Vaswani,et al.  Tracking Deforming Objects Using Particle Filtering for Geometric Active Contours , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Andrew Zisserman,et al.  Learning Layered Motion Segmentations of Video , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[21]  Thomas S. Huang,et al.  Recovering Articulated Motion with a Hierarchical Factorization Method , 2003, Gesture Workshop.

[22]  Rustam Stolkin,et al.  An EM/E-MRF algorithm for adaptive model based tracking in extremely poor visibility , 2008, Image Vis. Comput..

[23]  René Vidal,et al.  Motion Segmentation with Missing Data Using PowerFactorization and GPCA , 2004, CVPR.

[24]  Unai Bidarte,et al.  Hardware implementation of optical flow constraint equation using FPGAs , 2005, Comput. Vis. Image Underst..

[25]  Gérard G. Medioni,et al.  Inferring Segmented Dense Motion Layers Using 5D Tensor Voting , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Patrick Pérez,et al.  Detection and segmentation of moving objects in complex scenes , 2009, Comput. Vis. Image Underst..

[27]  U. Feige,et al.  Spectral Graph Theory , 2015 .

[28]  René Vidal,et al.  Projective Factorization of Multiple Rigid-Body Motions , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[29]  Marc Pollefeys,et al.  A Factorization-Based Approach for Articulated Nonrigid Shape, Motion and Kinematic Chain Recovery From Video , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Liangpei Zhang,et al.  A MAP Approach for Joint Motion Estimation, Segmentation, and Super Resolution , 2007, IEEE Transactions on Image Processing.

[31]  Lawrence K. Saul,et al.  Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold , 2003, J. Mach. Learn. Res..

[32]  Takeo Kanade,et al.  Shape and motion from image streams under orthography: a factorization method , 1992, International Journal of Computer Vision.

[33]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[34]  John Wright,et al.  Segmentation of Multivariate Mixed Data via Lossy Data Coding and Compression , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[35]  J. Cheeger A lower bound for the smallest eigenvalue of the Laplacian , 1969 .

[36]  Alessio Del Bue,et al.  Non-rigid metric reconstruction from perspective cameras , 2010, Image Vis. Comput..

[37]  Joaquim Salvi,et al.  Rank estimation of trajectory matrix in motion segmentation , 2009 .

[38]  Jing Xiao,et al.  Multi-view AAM fitting and camera calibration , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[39]  Bijoy K. Ghosh,et al.  Spatio-temporal continuous wavelet transforms for motion-based segmentation in real image sequences , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[40]  Gene H. Golub,et al.  Numerical methods for computing angles between linear subspaces , 1971, Milestones in Matrix Computation.

[41]  L. Ambrosio,et al.  Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .

[42]  Joaquim Salvi,et al.  New Trends in Motion Segmentation , 2009 .

[43]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

[44]  Merico E. Argentati,et al.  Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates , 2001, SIAM J. Sci. Comput..

[45]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[46]  M. Naderi Think globally... , 2004, HIV prevention plus!.

[47]  Ehsan Elhamifar,et al.  Sparse subspace clustering , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[48]  Kenichi Kanatani,et al.  Motion segmentation by subspace separation and model selection , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[49]  René Vidal,et al.  A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[50]  Marc Pollefeys,et al.  A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degenerate and Non-degenerate , 2006, ECCV.

[51]  David J. Kriegman,et al.  Clustering appearances of objects under varying illumination conditions , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[52]  Yair Weiss,et al.  Multibody factorization with uncertainty and missing data using the EM algorithm , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[53]  Andrea Fusiello,et al.  Segmentation and tracking of multiple video objects , 2007, Pattern Recognit..

[54]  Daniel Cremers,et al.  Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation , 2005, International Journal of Computer Vision.

[55]  Laurenz Wiskott,et al.  Segmentation from Motion: Combining Gabor- and Mallat-Wavelets to Overcome Aperture and Correspondence Problem , 1997, CAIP.

[56]  Yair Weiss,et al.  Factorization with Uncertainty and Missing Data: Exploiting Temporal Coherence , 2003, NIPS.

[57]  N. Otsu A threshold selection method from gray level histograms , 1979 .

[58]  João Paulo Costeira,et al.  Subspace segmentation with outliers: A grassmannian approach to the maximum consensus subspace , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.