MAGSAC: Marginalizing Sample Consensus

A method called, sigma-consensus, is proposed to eliminate the need for a user-defined inlier-outlier threshold in RANSAC. Instead of estimating the noise sigma, it is marginalized over a range of noise scales. The optimized model is obtained by weighted least-squares fitting where the weights come from the marginalization over sigma of the point likelihoods of being inliers. A new quality function is proposed not requiring sigma and, thus, a set of inliers to determine the model quality. Also, a new termination criterion for RANSAC is built on the proposed marginalization approach. Applying sigma-consensus, MAGSAC is proposed with no need for a user-defined sigma and improving the accuracy of robust estimation significantly. It is superior to the state-of-the-art in terms of geometric accuracy on publicly available real-world datasets for epipolar geometry (F and E) and homography estimation. In addition, applying sigma-consensus only once as a post-processing step to the RANSAC output always improved the model quality on a wide range of vision problems without noticeable deterioration in processing time, adding a few milliseconds.

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

[2]  David G. Lowe,et al.  Object recognition from local scale-invariant features , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[3]  Jean-Michel Morel,et al.  Accurate Motion Estimation through Random Sample Aggregated Consensus , 2017, ArXiv.

[4]  Jiri Matas,et al.  Locally Optimized RANSAC , 2003, DAGM-Symposium.

[5]  Jiri Matas,et al.  Epipolar geometry estimation via RANSAC benefits from the oriented epipolar constraint , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[6]  Jiri Matas,et al.  Matching with PROSAC - progressive sample consensus , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[7]  Philip H. S. Torr,et al.  Outlier detection and motion segmentation , 1993, Other Conferences.

[8]  Andrew Zisserman,et al.  MLESAC: A New Robust Estimator with Application to Estimating Image Geometry , 2000, Comput. Vis. Image Underst..

[9]  Jiri Matas,et al.  Optimal Randomized RANSAC , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[11]  Jiri Matas,et al.  Robust wide-baseline stereo from maximally stable extremal regions , 2004, Image Vis. Comput..

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

[13]  Jiri Matas,et al.  Robust wide-baseline stereo from maximally stable extremal regions , 2004, Image Vis. Comput..

[14]  Lionel Moisan,et al.  Automatic Homographic Registration of a Pair of Images, with A Contrario Elimination of Outliers , 2012, Image Process. Line.

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

[16]  Jiri Matas,et al.  Fixing the Locally Optimized RANSAC , 2012, BMVC.

[17]  Charles V. Stewart,et al.  MINPRAN: A New Robust Estimator for Computer Vision , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

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

[19]  Matthew Turk,et al.  EVSAC: Accelerating Hypotheses Generation by Modeling Matching Scores with Extreme Value Theory , 2013, 2013 IEEE International Conference on Computer Vision.

[20]  Sven J. Dickinson,et al.  Incremental model-based estimation using geometric constraints , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Naima Kaabouch,et al.  A survey on image mosaicing techniques , 2016, J. Vis. Commun. Image Represent..

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

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

[24]  Andrew Zisserman,et al.  Wide baseline stereo matching , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[25]  C. Strecha,et al.  Wide-baseline stereo from multiple views: A probabilistic account , 2004, CVPR 2004.

[26]  Andrew Zisserman,et al.  Robust Detection of Degenerate Configurations while Estimating the Fundamental Matrix , 1998, Comput. Vis. Image Underst..

[27]  Jiri Matas,et al.  MODS: Fast and robust method for two-view matching , 2015, Comput. Vis. Image Underst..

[28]  Tamás Szirányi,et al.  Change Detection in Optical Aerial Images by a Multilayer Conditional Mixed Markov Model , 2009, IEEE Transactions on Geoscience and Remote Sensing.

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

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