Multiple Models Fitting as a Set Coverage Problem

This paper deals with the extraction of multiple models from noisy or outlier-contaminated data. We cast the multi-model fitting problem in terms of set coverage, deriving a simple and effective method that generalizes Ransac to multiple models and deals with intersecting structures and outliers in a straightforward and principled manner, while avoiding the typical shortcomings of sequential approaches and those of clustering. The method compares favorably against the state-of-the-art on simulated and publicly available real data-sets.

[1]  Tat-Jun Chin,et al.  The Random Cluster Model for robust geometric fitting , 2012, CVPR.

[2]  P. Torr Geometric motion segmentation and model selection , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  Venu Madhav Govindu,et al.  Efficient Higher-Order Clustering on the Grassmann Manifold , 2013, 2013 IEEE International Conference on Computer Vision.

[4]  Tat-Jun Chin,et al.  The Random Cluster Model for robust geometric fitting , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[5]  É. Vincent,et al.  Detecting planar homographies in an image pair , 2001, ISPA 2001. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis. In conjunction with 23rd International Conference on Information Technology Interfaces (IEEE Cat..

[6]  Andrea Fusiello,et al.  T-Linkage: A Continuous Relaxation of J-Linkage for Multi-model Fitting , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[7]  Philip H. S. Torr,et al.  Stochastic Motion Clustering , 1994, ECCV.

[8]  Yuri Boykov,et al.  Energy-Based Geometric Multi-model Fitting , 2012, International Journal of Computer Vision.

[9]  Kenichi Kanatani,et al.  Removing Mistracking of Multibody Motion Video Database Hopkins155 , 2013, BMVC.

[10]  Andrea Fusiello,et al.  Robust Multiple Structures Estimation with J-Linkage , 2008, ECCV.

[11]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Tat-Jun Chin,et al.  Robust fitting of multiple structures: The statistical learning approach , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[13]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[14]  B. S. Manjunath,et al.  The multiRANSAC algorithm and its application to detect planar homographies , 2005, IEEE International Conference on Image Processing 2005.

[15]  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.

[16]  Jon M. Kleinberg,et al.  An Impossibility Theorem for Clustering , 2002, NIPS.

[17]  Anton Osokin,et al.  Fast Approximate Energy Minimization with Label Costs , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  Tat-Jun Chin,et al.  Interacting Geometric Priors For Robust Multimodel Fitting , 2014, IEEE Transactions on Image Processing.

[19]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[20]  Erkki Oja,et al.  A new curve detection method: Randomized Hough transform (RHT) , 1990, Pattern Recognit. Lett..

[21]  Tat-Jun Chin,et al.  A global optimization approach to robust multi-model fitting , 2011, CVPR 2011.

[22]  Amnon Shashua,et al.  A unifying approach to hard and probabilistic clustering , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[23]  David Suter,et al.  Two-View Multibody Structure-and-Motion with Outliers through Model Selection , 2006, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Emmanuel J. Candès,et al.  Robust Subspace Clustering , 2013, ArXiv.

[25]  Hongdong Li,et al.  Two-View Motion Segmentation from Linear Programming Relaxation , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[26]  Pietro Perona,et al.  Beyond pairwise clustering , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[27]  Jan-Michael Frahm,et al.  USAC: A Universal Framework for Random Sample Consensus , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Jana Kosecka,et al.  Nonparametric Estimation of Multiple Structures with Outliers , 2006, WDV.

[29]  Peter Meer,et al.  Nonlinear Mean Shift for Clustering over Analytic Manifolds , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[30]  James H. Elder,et al.  Efficient Edge-Based Methods for Estimating Manhattan Frames in Urban Imagery , 2008, ECCV.

[31]  Brendan J. Frey,et al.  FLoSS: Facility location for subspace segmentation , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[32]  Venu Madhav Govindu,et al.  A tensor decomposition for geometric grouping and segmentation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[33]  Andrea Fusiello,et al.  Robust Multiple Model Fitting with Preference Analysis and Low-rank Approximation , 2015, BMVC.