Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation

International audienceIn this work, we present a novel multiscale texture model, and a related algorithm for the unsupervised segmentation of color images. Elementary textures are characterized by their spatial interactions with neighboring regions along selected directions. Such interactions are modeled in turn by means of a set of Markov chains, one for each direction, whose parameters are collected in a feature vector that synthetically describes the texture. Based on the feature vectors, the texture are then recursively merged, giving rise to larger and more complex textures, which appear at different scales of observation: accordingly, the model is named Hierarchical Multiple Markov Chain (H-MMC). The Texture Fragmentation and Reconstruction (TFR) algorithm, addresses the unsupervised segmen- tation problem based on the H-MMC model. The “fragmentation” step allows one to find the elementary textures of the model, while the “reconstruction” step defines the hierarchical image segmentation based on a probabilistic measure (texture score) which takes into account both region scale and inter-region interactions. The performance of the proposed method was assessed through the Prague segmentation benchmark, based on mosaics of real natural textures, and also tested on real-world natural and remote sensing images

Hybrid Approaches for MRF Optimization: Combination of Stochastic and Deterministic Methods

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2014. 2. 이경무.Markov Random Field (MRF) models are of fundamental importance in computer vision. Many vision problems have been successfully formulated in MRF optimization. They include stereo matching, segmentation, denoising, and inpainting, to mention just a few. To solve them effectively, numerous algorithms have been developed. Although many of them produce good results for relatively easy problems, they are still unsatisfactory when it comes to more difficult MRF problems such as non-submodular energy functions, strongly coupled MRFs, and high-order clique potentials. In this dissertation, several optimization methods are proposed. The main idea of proposed methods is to combine stochastic and deterministic optimization methods. Stochastic methods encourage more exploration in the solution space. On the other hand, deterministic methods enable more efficient exploitation. By combining those two approaches, it is able to obtain better solution. To this end, two stochastic methodologies are exploited for the framework of combination: Markov chain Monte Carlo (MCMC) and stochastic approximation. First methodology is the MCMC. Based on MCMC framework, population based MCMC (Pop-MCMC), MCMC with General Deterministic algorithms (MCMC-GD), and fusion move driven MCMC (MCMC-F) are proposed. Although MCMC provides an elegant framework of which global convergence is provable, it has the slow convergence rate. To overcome, population-based framework and combination with deterministic methods are used. It thereby enables global moves by exchanging information between samples, which in turn, leads to faster mixing rate. In the view of optimization, it means that we can reach a lower energy state rapidly. Second methodology is the stochastic approximation. In stochastic approximation, the objective function for optimization is approximated in stochastic way. To apply this approach to MRF optimization, graph approximation scheme is proposed for the approximation of the energy function. By using this scheme, it alleviates the problem of non-submodularity and partial labeling. This stochastic approach framework is combined with graph cuts which is very efficient algorithm for easy MRF optimizations. By this combination, fusion with graph approximation-based proposals (GA-fusion) is developed. Extensive experiments support that the proposed algorithms are effective across different classes of energy functions. The proposed algorithms are applied in many different computer vision applications including stereo matching, photo montage, inpaining, image deconvolution, and texture restoration. Those algorithms are further analyzed on synthetic MRF problems while varying the difficulties of the problems as well as the parameters for each algorithm.1 Introduction 1 1.1 Markov random eld . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 MRF and Gibbs distribution . . . . . . . . . . . . . . . . . . 1 1.1.2 MAP estimation and energy minimization . . . . . . . . . . . 2 1.1.3 MRF formulation for computer vision problems . . . . . . . . 3 1.2 Optimizing energy function . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Markov chain Monte Carlo . . . . . . . . . . . . . . . . . . . 7 1.2.2 Stochastic approximation . . . . . . . . . . . . . . . . . . . . 8 1.3 combination of stochastic and deterministic methods . . . . . . . . . 9 1.4 Outline of dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Population-based MCMC 13 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1 Swendsen-Wang Cuts . . . . . . . . . . . . . . . . . . . . . . 16 2.2.2 Population-based MCMC . . . . . . . . . . . . . . . . . . . . 19 2.3 Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4.1 Segment-based stereo matching . . . . . . . . . . . . . . . . . 31 2.4.2 Parameter analysis . . . . . . . . . . . . . . . . . . . . . . . . 41 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3 MCMC Combined with General Deterministic Methods 47 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.3 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3.1 Population-based sampling framework for MCMC-GD . . . . 53 3.3.2 Kernel design . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.1 Analysis on synthetic MRF problems . . . . . . . . . . . . . . 60 3.4.2 Results on real problems . . . . . . . . . . . . . . . . . . . . . 75 3.4.3 Alternative approach: parallel anchor generation . . . . . . . 78 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4 Fusion Move Driven MCMC 89 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.2.1 Sampling-based optimization . . . . . . . . . . . . . . . . . . 91 4.2.2 MCMC combined with fusion move . . . . . . . . . . . . . . . 92 4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5 Fusion with Graph Approximation 101 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.2 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2.1 Graph cuts-based move-making algorithm . . . . . . . . . . . 104 5.2.2 Proposals for fusion approach . . . . . . . . . . . . . . . . . . 106 5.3 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.3.1 Stochastic approximation . . . . . . . . . . . . . . . . . . . . 107 5.3.2 Graph approximation . . . . . . . . . . . . . . . . . . . . . . 108 5.3.3 Overall algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.3.4 Characteristics of approximated function . . . . . . . . . . . 110 5.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.1 Image deconvolution . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.2 Binary texture restoration . . . . . . . . . . . . . . . . . . . . 115 5.4.3 Analysis on synthetic problems . . . . . . . . . . . . . . . . . 118 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6 Conclusion 127 6.1 Summary and contribution of the dissertation . . . . . . . . . . . . . 127 6.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 6.2.1 MCMC without detailed balance . . . . . . . . . . . . . . . . 128 6.2.2 Stochastic approximation for higher-order MRF model . . . . 130 Bibliography 131 국문초록 141Docto

Multigrid and Multi-level Swendsen-Wang Cuts for Hierarchic Graph Partition

Many vision tasks can be formulated as partitioning an adjacency graph through optimizing a Bayesian posterior probability p defined on the partition-space. In this paper two approaches are proposed to generalize the SwendsenWang cut algorithm[1] for sampling p. The first method is called multigrid SW-cut which runs SW-cut within a sequence of local "attentional" windows and thus simulates conditional probabilities of p in the partition space. The second method is called multi-level SW-cut which projects the adjacency graph into a hierarchical representation with each vertex in the high level graph corresponding to a subgraph at the low level, and runs SW-cut at each level. Thus it simulates conditional probabilities of p at the higher level. Both methods are shown to observe the detailed balance equation and thus provide flexibilities in sampling the posterior probability p. We demonstrate the algorithms in image and motion segmentation with three levels (see Fig.1), and compare the speed improvement of the proposed methods

Pattern Recognition

A wealth of advanced pattern recognition algorithms are emerging from the interdiscipline between technologies of effective visual features and the human-brain cognition process. Effective visual features are made possible through the rapid developments in appropriate sensor equipments, novel filter designs, and viable information processing architectures. While the understanding of human-brain cognition process broadens the way in which the computer can perform pattern recognition tasks. The present book is intended to collect representative researches around the globe focusing on low-level vision, filter design, features and image descriptors, data mining and analysis, and biologically inspired algorithms. The 27 chapters coved in this book disclose recent advances and new ideas in promoting the techniques, technology and applications of pattern recognition