Local Variation as a Statistical Hypothesis Test

The goal of image oversegmentation is to divide an image into several pieces, each of which should ideally be part of an object. One of the simplest and yet most effective oversegmentation algorithms is known as local variation (LV) Felzenszwalb and Huttenlocher in Efficient graph-based image segmentation. IJCV 59(2):167–181 (2004). In this work, we study this algorithm and show that algorithms similar to LV can be devised by applying different statistical models and decisions, thus providing further theoretical justification and a well-founded explanation for the unexpected high performance of the LV approach. Some of these algorithms are based on statistics of natural images and on a hypothesis testing decision; we denote these algorithms probabilistic local variation (pLV). The best pLV algorithm, which relies on censored estimation, presents state-of-the-art results while keeping the same computational complexity of the LV algorithm.

[1]  Yong Jae Lee,et al.  Predicting Important Objects for Egocentric Video Summarization , 2015, International Journal of Computer Vision.

[2]  C. Lawrence Zitnick,et al.  Fast Edge Detection Using Structured Forests , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Fernand Meyer,et al.  Topographic distance and watershed lines , 1994, Signal Process..

[4]  Thomas Deselaers,et al.  Measuring the Objectness of Image Windows , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[6]  Gregory Shakhnarovich,et al.  Image Segmentation by Cascaded Region Agglomeration , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[7]  Anuj Srivastava,et al.  Probability Models for Clutter in Natural Images , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  R. Larsen,et al.  An introduction to mathematical statistics and its applications (2nd edition) , by R. J. Larsen and M. L. Marx. Pp 630. £17·95. 1987. ISBN 13-487166-9 (Prentice-Hall) , 1987, The Mathematical Gazette.

[9]  Eero P. Simoncelli,et al.  On Advances in Statistical Modeling of Natural Images , 2004, Journal of Mathematical Imaging and Vision.

[10]  C. V. Jawahar,et al.  Blocks That Shout: Distinctive Parts for Scene Classification , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[11]  Camille Couprie,et al.  Learning Hierarchical Features for Scene Labeling , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  David Mumford,et al.  Statistics of natural images and models , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[13]  Richard Ruggles,et al.  An Empirical Approach to Economic Intelligence in World War II , 1947 .

[14]  Sven J. Dickinson,et al.  TurboPixels: Fast Superpixels Using Geometric Flows , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Pierre Moulin,et al.  Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors , 1999, IEEE Trans. Inf. Theory.

[16]  Paul A. Viola,et al.  A Non-Parametric Multi-Scale Statistical Model for Natural Images , 1997, NIPS.

[17]  Rama Chellappa,et al.  Entropy rate superpixel segmentation , 2011, CVPR 2011.

[18]  Pascal Fua,et al.  SLIC Superpixels Compared to State-of-the-Art Superpixel Methods , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Eric J. Pauwels,et al.  Image Segmentation by Nonparametric Clustering Based on the Kolmogorov-Smirnov Distance , 2000, ECCV.

[20]  Michael Lindenbaum,et al.  Learning High-Density Regions for a Generalized Kolmogorov-Smirnov Test in High-Dimensional Data , 2012, NIPS.

[21]  Alexei A. Efros,et al.  Scene Semantics from Long-Term Observation of People , 2012, ECCV.

[22]  Christoph Schnörr,et al.  Natural Image Statistics for Natural Image Segmentation , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[23]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Michael Baltaxe,et al.  Probabilistic Local Variation Segmentation , 2014 .

[25]  Jitendra Malik,et al.  Learning a classification model for segmentation , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[26]  GouldStephen,et al.  Multi-Class Segmentation with Relative Location Prior , 2008 .

[27]  Jonathan T. Barron,et al.  Multiscale Combinatorial Grouping , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[28]  Antonio Criminisi,et al.  TextonBoost for Image Understanding: Multi-Class Object Recognition and Segmentation by Jointly Modeling Texture, Layout, and Context , 2007, International Journal of Computer Vision.

[29]  David Zhang,et al.  Automatic Image Segmentation by Dynamic Region Merging , 2010, IEEE Transactions on Image Processing.

[30]  Stephen Gould,et al.  Multi-Class Segmentation with Relative Location Prior , 2008, International Journal of Computer Vision.

[31]  Alexei A. Efros,et al.  Recovering Surface Layout from an Image , 2007, International Journal of Computer Vision.

[32]  Daniel P. Huttenlocher,et al.  Efficient Graph-Based Image Segmentation , 2004, International Journal of Computer Vision.

[33]  Amir Rosenfeld,et al.  Extracting foreground masks towards object recognition , 2011, 2011 International Conference on Computer Vision.

[34]  R. H. Myers,et al.  Probability and Statistics for Engineers and Scientists , 1978 .

[35]  Raymond H. Myers,et al.  Probability and Statistics for Engineers and Scientists. , 1973 .

[36]  Sebastian Nowozin,et al.  Higher-Order Correlation Clustering for Image Segmentation , 2011, NIPS.

[37]  Ricardo Cabral,et al.  Piecewise Planar and Compact Floorplan Reconstruction from Images , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[38]  Jitendra Malik,et al.  Learning to detect natural image boundaries using local brightness, color, and texture cues , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[39]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[40]  Jitendra Malik,et al.  A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[41]  Charless C. Fowlkes,et al.  Contour Detection and Hierarchical Image Segmentation , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.