Simultaneous Sampling and Multi-Structure Fitting with Adaptive Reversible Jump MCMC

Multi-structure model fitting has traditionally taken a two-stage approach: First, sample a (large) number of model hypotheses, then select the subset of hypotheses that optimise a joint fitting and model selection criterion. This disjoint two-stage approach is arguably suboptimal and inefficient — if the random sampling did not retrieve a good set of hypotheses, the optimised outcome will not represent a good fit. To overcome this weakness we propose a new multi-structure fitting approach based on Reversible Jump MCMC. Instrumental in raising the effectiveness of our method is an adaptive hypothesis generator, whose proposal distribution is learned incrementally and online. We prove that this adaptive proposal satisfies the diminishing adaptation property crucial for ensuring ergodicity in MCMC. Our method effectively conducts hypothesis sampling and optimisation simultaneously, and yields superior computational efficiency over previous two-stage methods.

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

[2]  Philip H. S. Torr,et al.  IMPSAC: Synthesis of Importance Sampling and Random Sample Consensus , 2000, ECCV.

[3]  Nando de Freitas,et al.  An Introduction to MCMC for Machine Learning , 2004, Machine Learning.

[4]  Gareth O. Roberts,et al.  Examples of Adaptive MCMC , 2009 .

[5]  Dale Schuurmans,et al.  Convex Relaxation of Mixture Regression with Efficient Algorithms , 2009, NIPS.

[6]  Tat-Jun Chin,et al.  Accelerated Hypothesis Generation for Multi-structure Robust Fitting , 2010, ECCV.

[7]  Chu-Song Chen,et al.  Two-View Motion Segmentation by Mixtures of Dirichlet Process with Model Selection and Outlier Removal , 2007, 2007 IEEE 11th International Conference on Computer Vision.

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

[9]  Andrew Zisserman,et al.  Multiple View Geometry , 1999 .

[10]  Christophe Andrieu,et al.  A tutorial on adaptive MCMC , 2008, Stat. Comput..

[11]  Lixin Fan,et al.  Adaptive Sample Consensus for Efficient Random Optimization , 2009, ISVC.

[12]  H. Akaike.  A new look at the statistical model identification , 1974 .

[13]  Richard I. Hartley,et al.  In Defense of the Eight-Point Algorithm , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Tat-Jun Chin,et al.  Dynamic and hierarchical multi-structure geometric model fitting , 2011, 2011 International Conference on Computer Vision.

[15]  David J. Nott,et al.  Adaptive sampling for Bayesian variable selection , 2005 .

[16]  S. Brooks,et al.  Classical model selection via simulated annealing , 2003, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[17]  Nando de Freitas,et al.  Robust Full Bayesian Learning for Radial Basis Networks , 2001, Neural Computation.

[18]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

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

[20]  Padhraic Smyth,et al.  Trajectory clustering with mixtures of regression models , 1999, KDD '99.

[21]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

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

[23]  J. Rosenthal,et al.  Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms , 2007, Journal of Applied Probability.

[24]  Ninad Thakoor,et al.  Branch-and-bound hypothesis selection for two-view multiple structure and motion segmentation , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[25]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

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

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

[28]  P. Giordani,et al.  Adaptive Independent Metropolis–Hastings by Fast Estimation of Mixtures of Normals , 2008, 0801.1864.

[29]  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..

[30]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.