Zoltan Kato

A Markov random field image segmentation model for color textured images

Abstract We propose a Markov random field (MRF) image segmentation model, which aims at combining color and texture features. The theoretical framework relies on Bayesian estimation via combinatorial optimization (simulated annealing). The segmentation is obtained by classifying the pixels into different pixel classes. These classes are represented by multi-variate Gaussian distributions. Thus, the only hypothesis about the nature of the features is that an additive Gaussian noise model is suitable to describe the feature distribution belonging to a given class. Here, we use the perceptually uniform CIE-L * u * v * color values as color features and a set of Gabor filters as texture features. Gaussian parameters are either computed using a training data set or estimated from the input image. We also propose a parameter estimation method using the EM algorithm. Experimental results are provided to illustrate the performance of our method on both synthetic and natural color images.

Bayesian Image Classification Using Markov Random Fields

In this paper, we present three optimisation techniques, Deterministic Pseudo-Annealing (DPA), Game Strategy Approach (GSA), and Modified Metropolis Dynamics (MMD), in order to carry out image classification using a Markov random field model. For the first approach (DPA), the a posteriori probability of a tentative labelling is generalised to a continuous labelling. The merit function thus defined has the same maxima under constraints yielding probability vectors. Changing these constraints convexifies the merit function. The algorithm solves this unambiguous maximisation problem, and then tracks down the solution while the original constraints are restored yielding a good, even if suboptimal, solution to the original labelling assignment problem. In the second method (GSA), the maximisation problem of the a posteriori probability of the labelling is solved by an optimisation algorithm based on game theory. A non-cooperative n-person game with pure strategies is designed such that the set of Nash equilibrium points of the game is identical to the set of local maxima of the a posteriori probability of the labelling. The algorithm converges to a Nash equilibrium. The third method (MMD) is a modified version of the Metropolis algorithm: at each iteration the new state is chosen randomly, but the decision to accept it is purely deterministic. This is also a suboptimal technique but it is much faster than stochastic relaxation. These three methods have been implemented on a Connection Machine CM2. Experimental results are compared to those obtained by the Metropolis algorithm, the Gibbs sampler and ICM (Iterated Conditional Mode).

A Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification

In this paper, we are interested in massively parallel multiscale relaxation algorithms applied to image classification. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. First, we present a classical multiscale model which consists of a label pyramid and a whole observation field. The potential functions of coarser grids are derived by simple computations. The optimization problem is first solved at the higher scale by a parallel relaxation algorithm; then the next lower scale is initialized by a projection of the result. Second, we propose a hierarchical Markov random field model based on this classical model. We introduce new interactions between neighbor levels in the pyramid. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price. This model results in a relaxation algorithm with a new annealing scheme: the multitemperature annealing (MTA) scheme, which consists of associating higher temperatures to higher levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalization of the annealing theorem of S. Geman and D. Geman (IEEE Trans. Pattern Anal. Mach. Intell.6, 1984, 721–741).

Unsupervised parallel image classification using Markovian models

Abstract This paper deals with the problem of unsupervised classification of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing (SA), iterated conditional modes (ICM), etc). However, when the parameters are unknown, the problem becomes more difficult. One has to estimate the hidden label field parameters only from the observed image. Herein, we are interested in parameter estimation methods related to monogrid and hierarchical MRF models. The basic idea is similar to the expectation–maximization (EM) algorithm: we recursively look at the maximum a posteriori (MAP) estimate of the label field given the estimated parameters, then we look at the maximum likelihood (ML) estimate of the parameters given a tentative labeling obtained at the previous step. The only parameter supposed to be known is the number of classes, all the other parameters are estimated. The proposed algorithms have been implemented on a Connection Machine CM200. Comparative experiments have been performed on both noisy synthetic data and real images.

Color image segmentation and parameter estimation in a markovian framework

Abstract An unsupervised color image segmentation algorithm is presented, using a Markov random field (MRF) pixel classification model. We propose a new method to estimate initial mean vectors effectively even if the histogram does not have clearly distinguishable peaks. The only parameter supplied by the user is the number of classes.

Satellite image classification using a modified Metropolis dynamics

A pseudo-stochastic variation of the Metropolis dynamics for combinatorial optimization in image classification using Markov random fields is presented. At high temperature, the behavior of the algorithm is similar to the stochastic ones. However, if the temperature is less than a certain threshold, it becomes deterministic. The length of the pseudo-stochastic phase is controlled by a constant threshold used in the modified dynamics. The algorithm yields an approximate but usually good solution to the optimization problem. The algorithm runs on a connection machine. It is applied to the standard pixel classification problem; objective and subjective comparisons with other algorithms have been made.<<ETX>>

Image Segmentation Using Markov Random Field Model in Fully Parallel Cellular Network Architectures

Markovian approaches to early vision processes need a huge amount of computing power. These algorithms can usually be implemented on parallel computing structures. Herein, we show that the Markovian labeling approach can be implemented in fully parallel cellular network architectures, using simple functions and data representations. This makes possible to implement our model in parallel imaging VLSI chips.As an example, we have developed a simplified statistical image segmentation algorithm for the Cellular Neural/Nonlinear Networks Universal Machine (CNN-UM), which is a new image processing tool, containing thousands of cells with analog dynamics, local memories and processing units. The Modified Metropolis Dynamics (MMD) optimization method can be implemented into the raw analog architecture of the CNN-UM. We can introduce the whole pseudo-stochastic segmentation process in the CNN architecture using 8 memories/cell. We use simple arithmetic functions (addition, multiplication), equality-test between neighboring pixels and very simple nonlinear output functions (step, jigsaw). With this architecture, the proposed VLSI CNN chip can execute a pseudo-stochastic relaxation algorithm of about 100 iterations in about 100 ?s.In the suggested solution the segmentation is unsupervised, where a pixel-level statistical estimation model is used. We have tested different monogrid and multigrid architectures.In our CNN-UM model several complex preprocessing steps can be involved, such as texture-classification or anisotropic diffusion. With these preprocessing steps, our fully parallel cellular system may work as a high-level image segmentation machine, using only simple functions based on the close-neighborhood of a pixel.

Markov Random Fields in Image Segmentation

Markov Random Fields in Image Segmentation provides an introduction to the fundamentals of Markovian modeling in image segmentation as well as a brief overview of recent advances in the field. Segmentation is formulated within an image labeling framework, where the problem is reduced to assigning labels to pixels. In a probabilistic approach, label dependencies are modeled by Markov random fields (MRF) and an optimal labeling is determined by Bayesian estimation, in particular maximum a posteriori (MAP) estimation. The main advantage of MRF models is that prior information can be imposed locally through clique potentials. MRF models usually yield a non-convex energy function. The minimization of this function is crucial in order to find the most likely segmentation according to the MRF model. Classical optimization algorithms including simulated annealing and deterministic relaxation are treated along with more recent graph cut-based algorithms. The primary goal of this monograph is to demonstrate the basic steps to construct an easily applicable MRF segmentation model and further develop its multi-scale and hierarchical implementations as well as their combination in a multilayer model. Representative examples from remote sensing and biological imaging are analyzed in full detail to illustrate the applicability of these MRF models. Furthermore, a sample implementation of the most important segmentation algorithms is available as supplementary software. Markov Random Fields in Image Segmentation is an invaluable resource for every student, engineer, or researcher dealing with Markovian modeling for image segmentation.

Multiscale Markov random field models for parallel image classification

The authors consider multiscale Markov random field (MRF) models. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. A hierarchical model is proposed, which consists of a label pyramid and a whole observation field. The parameters of the coarse grid can be derived by simple computation from the finest grid. In the label pyramid, a new local interaction is introduced between two neighbor grids. This model gives a relaxation algorithm which can be run in parallel on the entire pyramid. The model allows propagation of local interactions more efficiently, giving estimates closer to the global optimum for deterministic as well as for stochastic relaxation schemes. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price.<<ETX>>

Segmentation of color images via reversible jump MCMC sampling

Reversible jump Markov chain Monte Carlo (RJMCMC) is a recent method which makes it possible to construct reversible Markov chain samplers that jump between parameter subspaces of different dimensionality. In this paper, we propose a new RJMCMC sampler for multivariate Gaussian mixture identification and we apply it to color image segmentation. For this purpose, we consider a first order Markov random field (MRF) model where the singleton energies derive from a multivariate Gaussian distribution and second order potentials favor similar classes in neighboring pixels. The proposed algorithm finds the most likely number of classes, their associated model parameters and generates a segmentation of the image by classifying the pixels into these classes. The estimation is done according to the Maximum A Posteriori (MAP) criterion. The algorithm has been validated on a database of real images with human segmented ground truth.