Sub-Markov Random Walk for Image Segmentation

A novel sub-Markov random walk (subRW) algorithm with label prior is proposed for seeded image segmentation, which can be interpreted as a traditional random walker on a graph with added auxiliary nodes. Under this explanation, we unify the proposed subRW and other popular random walk (RW) algorithms. This unifying view will make it possible for transferring intrinsic findings between different RW algorithms, and offer new ideas for designing novel RW algorithms by adding or changing auxiliary nodes. To verify the second benefit, we design a new subRW algorithm with label prior to solve the segmentation problem of objects with thin and elongated parts. The experimental results on both synthetic and natural images with twigs demonstrate that the proposed subRW method outperforms previous RW algorithms for seeded image segmentation.

[1]  Leo Grady,et al.  Isoperimetric graph partitioning for image segmentation , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Ulrike von Luxburg,et al.  Hitting and commute times in large graphs are often misleading , 2010, 1003.1266.

[3]  Gregory F. Lawler,et al.  Random Walk: A Modern Introduction , 2010 .

[4]  Sang Uk Lee,et al.  Generative Image Segmentation Using Random Walks with Restart , 2008, ECCV.

[5]  Shih-Fu Chang,et al.  Learning with Partially Absorbing Random Walks , 2012, NIPS.

[6]  Jeff A. Bilmes,et al.  Submodularity beyond submodular energies: Coupling edges in graph cuts , 2011, CVPR 2011.

[7]  Deepu Rajan,et al.  Random Walks on Graphs for Salient Object Detection in Images , 2010, IEEE Transactions on Image Processing.

[8]  Gareth Funka-Lea,et al.  Multi-label Image Segmentation for Medical Applications Based on Graph-Theoretic Electrical Potentials , 2004, ECCV Workshops CVAMIA and MMBIA.

[9]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[10]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[11]  Camille Couprie,et al.  Power Watershed: A Unifying Graph-Based Optimization Framework , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Edwin R. Hancock,et al.  Clustering and Embedding Using Commute Times , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Luc Van Gool,et al.  Segmentation Using SubMarkov Random Walk , 2014, EMMCVPR.

[14]  Pushmeet Kohli,et al.  A Principled Deep Random Field Model for Image Segmentation , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Tommi S. Jaakkola,et al.  Partially labeled classification with Markov random walks , 2001, NIPS.

[16]  Dragomir R. Radev,et al.  DivRank: the interplay of prestige and diversity in information networks , 2010, KDD.

[17]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[18]  Leo Grady,et al.  Discrete Calculus - Applied Analysis on Graphs for Computational Science , 2010 .

[19]  Masatsugu Kidode,et al.  A Random Walk Procedure for Texture Discrimination , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Leo Grady,et al.  Random Walks for Image Segmentation , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Wolfgang Nejdl,et al.  An adaptive teleportation random walk model for learning social tag relevance , 2014, SIGIR.

[22]  Leo Grady,et al.  A Seeded Image Segmentation Framework Unifying Graph Cuts And Random Walker Which Yields A New Algorithm , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[23]  Christos Faloutsos,et al.  Fast Random Walk with Restart and Its Applications , 2006, Sixth International Conference on Data Mining (ICDM'06).

[24]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[25]  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.

[26]  Kwanghoon Sohn,et al.  A Generalized Random Walk With Restart and its Application in Depth Up-Sampling and Interactive Segmentation , 2013, IEEE Transactions on Image Processing.

[27]  Helen C. Shen,et al.  Linear Neighborhood Propagation and Its Applications , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Bernhard Schölkopf,et al.  Learning from Labeled and Unlabeled Data Using Random Walks , 2004, DAGM-Symposium.

[29]  Christos Faloutsos,et al.  Automatic multimedia cross-modal correlation discovery , 2004, KDD.

[30]  Leo Grady,et al.  Fast approximate Random Walker segmentation using eigenvector precomputation , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[31]  Vincent Lepetit,et al.  Multiscale Centerline Detection by Learning a Scale-Space Distance Transform , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[32]  Xuelong Li,et al.  Lazy Random Walks for Superpixel Segmentation , 2014, IEEE Transactions on Image Processing.

[33]  Jack J. Dongarra,et al.  Solving linear systems on vector and shared memory computers , 1990 .

[34]  Aude Billard,et al.  On Learning, Representing, and Generalizing a Task in a Humanoid Robot , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[35]  Zoubin Ghahramani,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[36]  Bernhard Schölkopf,et al.  Learning with Local and Global Consistency , 2003, NIPS.

[37]  U. Feige,et al.  Spectral Graph Theory , 2015 .

[38]  Bernhard Schölkopf,et al.  A kernel view of the dimensionality reduction of manifolds , 2004, ICML.

[39]  Marco Gori,et al.  Exact and approximate graph matching using random walks , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[40]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[41]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[42]  Leo Grady,et al.  Multilabel random walker image segmentation using prior models , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[43]  François Fouss,et al.  Random-Walk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation , 2007, IEEE Transactions on Knowledge and Data Engineering.