Otsu's binarization method is one of the most popular image-thresholding methods; Student's t -test is one of the most widely-used statistical tests to compare two groups. This paper aims to stress the equivalence between Otsu's binarization method and the search for an optimal threshold that provides the largest absolute Student's t-statistic. It is then naturally demonstrated that the extension of Otsu's binarization method to multi-level thresholding is equivalent to the search for optimal thresholds that provide the largest F -statistic through one-way analysis of variance (ANOVA). Furthermore, general equivalences between some parametric image-thresholding methods and the search for optimal thresholds with the largest likelihood-ratio test statistics are briefly discussed.

This paper presents a novel application of simultaneous autoregressive models to the synthesis of magnetic material images. The effects of using either symmetric or non-symmetric neighbour sets upon the visual and statistical properties of the resulting synthesised images are investigated. The use of a neighbour set whose shape corresponds to the orientations and coarseness of the texture allows the generation of synthetic images of good quality. Also, the size of such a neighbour set is usually smaller than that of the symmetric set required to reach similar modelling accuracy, thereby minimising the computational effort.

Versions of the Gibbs sampler are derived for the analysis of data from the hidden Markov mesh random fields sometimes used in image analysis. This provides a numerical approach to the otherwise intractable Bayesian analysis of these problems. Detailed formulation is provided for particular examples based on Devijver's Markov mesh model (1988), and the BUGS package is used to do the computations. Theoretical aspects are discussed and a numerical study, based on image analysis, is reported.

Methods are reviewed for choosing regularized restorations in image processing. In particular, a method developed by Galatsanos and Katsaggelos (see ibid., vol.1, p.322-336, 1992) is given a Bayesian interpretation and is compared with other Bayesian and non-Bayesian alternatives. A small illustrative example is provided and a complement is provided for the discussion of noise variance estimation of Galatsanos et al.

The definition of the usual Boltzmann machine is extended to allow for neurons with polytomous (multicategory) rather than simply binary responses. Updating rules are defined along with the associated stationary distributions, and an alternating minimization method is described for the purposes of training. Emphasis is placed on the relevance of statistical ideas, including polytomous logistic regression, the iterative proportional fitting procedure and the EM algorithm.

Markov random fields are typically used as priors in Bayesian image restoration methods to represent spatial information in the image. Commonly used Markov random fields are not in fact capable of representing the moderate-to-large scale clustering present in naturally occurring images and can also be time consuming to simulate, requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge. Markov mesh models, a causal subclass of Markov random fields, are, however, readily simulated. We describe an empirical study of simulated realizations from various models used in the literature, and we introduce some new mesh-type models. We conclude, however, that while large-scale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations. It is emphasized that the results do not detract from the use of Markov random fields as representers of local spatial properties, which is their main purpose in the implementation of Bayesian statistical approaches to image analysis. Brief allusion is made to the issue of parameter estimation.>

Bayesian methods for recovering a 2-D surface are discussed. It is assumed that there is a textural image that can be modeled by a Markov random field and that the original surface is composed of different surfaces, each of which is associated with one textural state. Both parametric and nonparametric methods are used to enforce smoothness of these surfaces. Iterative procedures are examined for simultaneous restoration of the textural image and estimation of underlying parameters. From the estimated textural image and the estimated parameters, an estimate for the original surface is obtained. Two illustrative examples are presented.>

The method of regularization is portrayed as providing a compromise between fidelity to the data and smoothness, with the tradeoff being determined by a scalar smoothing parameter. Various ways of choosing this parameter are discussed in the case of quadratic regularization criteria. They are compared algebraically, and their statistical properties are comparatively assessed from the results of all extensive simulation study based on simple images.>

It was previously proved by Bailey and Jain that the asymptotic classification error rate of the (unweighted) k-nearest neighbor (k-NN) rule is lower than that of any weighted k-NN rule. Equations are developed for the classification error rate of a test sample when the number of training samples is finite, and it is argued intuitively that a weighted rule may then in some cases achieve a lower error rate than the unweighted rule. This conclusion is confirmed by analytically solving a particular simple problem, and as an illustration, experimental results are presented that were obtained using a generalized form of a weighting function proposed by Dudani.

In the above correspondence1 a maximum likelihood method is proposed for ``estimating'' class memberships and underlying statistical parameters, within the context of distribution mixtures. In the present comment it is pointed out that biases are incurred in parameter estimation, that the class memberships and parameters are conceptually different, and therefore that the so-called standard mixture likelihood is to be preferred. Also in the correspondence,1 Akaike's information criterion (AIC) is used to choose the number of classes in the mixture. Here a brief theoretical caveat is issued.