The modeling and segmentation of images by MRF's (Markov random fields) is treated. These are two-dimensional noncausal Markovian stochastic processes. Two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of C MRF's. The algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology. A doubly stochastic representation is used in image modeling. Here, a Gaussian MRF is used to model textures in visible light and infrared images, and an autobinary (or autoternary, etc.) MRF to model a priori information about the local geometry of textured image regions. For image segmentation, the true texture class regions are treated either as a priori completely unknown or as a realization of a binary (or ternary, etc.) MRF. In the former case, image segmentation is realized as true maximum likelihood estimation. In the latter case, it is realized as true maximum a posteriori likelihood segmentation. In addition to providing a mathematically correct means for introducing geometric structure, the autobinary (or ternary, etc.) MRF can be used in a generative mode to generate image geometries and artificial images, and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters. The first segmentation algorithm is hierarchical and uses a pyramid-like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region.

Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields

A new image segmentation algorithm is presented, based on recursive Bayes smoothing of images modeled by Markov random fields and corrupted by independent additive noise. The Bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel, given the total noisy image, in a recursive way. The a posteriori distribution together with a criterion of optimality then determine a Bayes estimate of the scene. The algorithm presented is an extension of a 1-D Bayes smoothing algorithm to 2-D and it gives the optimum Bayes estimate for the scene value at each pixel. Computational concerns in 2-D, however, necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm. In particular, the scene (noiseless image) is modeled as a Markov mesh random field, a special class of Markov random fields, and the Bayes smoothing algorithm is applied on overlapping strips (horizontal/vertical) of the image consisting of several rows (columns). It is assumed that the signal (scene values) vector sequence along the strip is a vector Markov chain. Since signal correlation in one of the dimensions is not fully used along the edges of the strip, estimates are generated only along the middle sections of the strips. The overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image. The Bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel (discrete) or continuous random variables.

Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields

The purpose of this paper is to present new image coding schemes based on a predictive vector quantization (PVQ) approach. The predictive part of the encoder is used to partially remove redundancy, and the VQ part further removes the residual redundancy and selects good quantization levels for the global waveform. Two implementations of this coding approach have been devised, namely, sliding block PVQ and block tree PVQ. Simulations on real images show significant improvement over the conventional DPCM and tree codes using these new techniques. The strong robustness property of these coding schemes is also experimentally demonstrated.

Predictive Vector Quantization of Images

In this paper, two-dimensional stochastic linear models are used in developing algorithms for image analysis such as classification, segmentation, and object detection in images characterized by textured backgrounds. These models generate two-dimensional random processes as outputs to which statistical inference procedures can naturally be applied. A common thread throughout our algorithms is the interpretation of the inference procedures in terms of linear prediction residuals. This interpretation leads to statistical tests more insightful than the original tests and makes the procedures computationally tractable. This paper also examines a computational structure tailored to one of the algorithms. In particular, we describe a processor based on systolic arrays that realizes the object detection algorithm developed in the paper.

Statistical model-based algorithms for image analysis

A method for modeling images of natural terrain is developed and applied to the segmentation of aerial photographic data. An underlying stochastic structure based on linear filtering concepts provides a means of modeling the terrain in local areas of the image. Superimposed on this is a Markov random field that describes transitions from regions of one terrain type to another. Maximum likelihood and maximum a posteriori estimation are applied to estimate regions of similar terrain. Results of application to digitized aerial photographs are presented and discussed.

An estimation-theoretic approach to terrain image segmentation

A two-dimensional recursive algorithm based upon the use of multiple models is described for the problem of nonstationary image processing. Of importance is the doubly stochastic representation resulting from the modelling of the transition of the apriori probabilities.

R. Mediavilla

Papers

Recursive image estimation: A multiple model approach

Multiple Models for Nonstationary Image Estimation