Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm

The Progressive-X algorithm, Prog-X in short, is proposed for geometric multi-model fitting. The method interleaves sampling and consolidation of the current data interpretation via repetitive hypothesis proposal, fast rejection, and integration of the new hypothesis into the kept instance set by labeling energy minimization. Due to exploring the data progressively, the method has several beneficial properties compared with the state-of-the-art. First, a clear criterion, adopted from RANSAC, controls the termination and stops the algorithm when the probability of finding a new model with a reasonable number of inliers falls below a threshold. Second, Prog-X is an any-time algorithm. Thus, whenever is interrupted, e.g. due to a time limit, the returned instances cover real and, likely, the most dominant ones. The method is superior to the state-of-the-art in terms of accuracy in both synthetic experiments and on publicly available real-world datasets for homography, two-view motion, and motion segmentation.

[1]  Andrei Z. Broder,et al.  On the resemblance and containment of documents , 1997, Proceedings. Compression and Complexity of SEQUENCES 1997 (Cat. No.97TB100171).

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

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

[4]  Roberto Tron RenVidal.  A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms , 2007 .

[5]  Emilio L. Zapata,et al.  Lower order circle and ellipse Hough transform , 1997, Pattern Recognit..

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

[7]  Jiri Matas,et al.  Multi-Class Model Fitting by Energy Minimization and Mode-Seeking , 2017, ECCV.

[8]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

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

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

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

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

[13]  Paul Amayo,et al.  Geometric Multi-model Fitting with a Convex Relaxation Algorithm , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[14]  Vladimir Kolmogorov,et al.  An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision , 2001, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Lena Gorelick,et al.  Minimizing Energies with Hierarchical Costs , 2012, International Journal of Computer Vision.

[16]  Tat-Jun Chin,et al.  Interacting Geometric Priors For Robust Multi-Model Fitting (Supplementary Material) , 2014 .

[17]  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.

[18]  Yan Yan,et al.  Mode-Seeking on Hypergraphs for Robust Geometric Model Fitting , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[19]  Hiroshi Kawakami,et al.  Detection of Planar Regions with Uncalibrated Stereo using Distributions of Feature Points , 2004, BMVC.

[20]  Paul L. Rosin.  Ellipse fitting by accumulating five-point fits , 1993, Pattern Recognit. Lett..

[21]  Jiri Matas,et al.  Graph-Cut RANSAC , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[22]  Josef Kittler,et al.  A survey of the hough transform , 1988, Comput. Vis. Graph. Image Process..

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

[24]  Philip H. S. Torr,et al.  Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting , 2002, International Journal of Computer Vision.

[25]  VekslerOlga,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001 .

[26]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .

[27]  Andrea Fusiello,et al.  Multiple Models Fitting as a Set Coverage Problem , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[28]  Jiri Matas,et al.  Robust Detection of Lines Using the Progressive Probabilistic Hough Transform , 2000, Comput. Vis. Image Underst..

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

[30]  Yan Yan,et al.  Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  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..

[32]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

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

[34]  Slawomir J. Nasuto,et al.  NAPSAC: High Noise, High Dimensional Robust Estimation - it's in the Bag , 2002, BMVC.