The authors empirically compare three algorithms for segmenting simple, noisy images: simulated annealing (SA), iterated conditional modes (ICM), and maximizer of the posterior marginals (MPM). All use Markov random field (MRF) models to include prior contextual information. The comparison is based on artificial binary images which are degraded by Gaussian noise. Robustness is tested with correlated noise and with object and background textured. The ICM algorithm is evaluated when the degradation and model parameters must be estimated, in both supervised and unsupervised modes and on two real images. The results are assessed by visual inspection and through a numerical criterion. It is concluded that contextual information from MRF models improves segmentation when the number of categories and the degradation model are known and that parameters can be effectively estimated. None of the three algorithms is consistently best, but the ICM algorithm is the most robust. The energy of the a posteriori distribution is not always minimized at the best segmentation.>

The authors examine two important problems, estimation and goodness of fit, in modeling binary single-texture images by discrete Markov random fields. A methodology for comparing parameter estimators is proposed and applied to evaluate four estimation procedures. The classes of models considered are four-parameter Derin-Elliot models and four-parameter autobinomial models with second-order neighborhoods. A Min- chi /sup 2/ estimator is proposed and shown to outperform estimators described in the literature. The methodology is based on a hardcore sampling process over the parameter space and a Wilcoxon rank-sum statistic. A static for assessing the goodness of fit between a specific model and an arbitrary texture image is also proposed and used in a Monte Carlo ranking test. The statistic is experimentally validated on synthetic textures. Experiments on natural textures suggest that second-order binary models do not fit natural textures well.>

The design of a pattern recognition system requires careful attention to error estimation. The error rate is the most important descriptor of a classifier's performance. The commonly used estimates of error rate are based on the holdout method, the resubstitution method, and the leave-one-out method. All suffer either from large bias or large variance and their sample distributions are not known. Bootstrapping refers to a class of procedures that resample given data by computer. It permits determining the statistical properties of an estimator when very little is known about the underlying distribution and no additional samples are available. Since its publication in the last decade, the bootstrap technique has been successfully applied to many statistical estimations and inference problems. However, it has not been exploited in the design of pattern recognition systems. We report results on the application of several bootstrap techniques in estimating the error rate of 1-NN and quadratic classifiers. Our experiments show that, in most cases, the confidence interval of a bootstrap estimator of classification error is smaller than that of the leave-one-out estimator. The error of 1-NN, quadratic, and Fisher classifiers are estimated for several real data sets.

This paper formulates the problem encountered in the first stage of two-stage, binary template matching as a set of hypotheses to be tested, including a hypothesis of ``no object.'' Two new statistics R and G are proposed, based on a likelihood ratio, and are compared to the sum of absolute differences and a correlation measure by analytical approximations and Monte Carlo experiments. Statistical power and a measure of sensitivity to the true location of the object are the criteria. Parameters are the numbers of 1's in object and image, subtemplate size, and parameters reflecting intensity distortion between template and object. One of the proposed statistics R is much more computationally intensive than the other G. Although R is more powerful than G and the other statistics, G is generally more sensitive to the true object location. Statistic G is also more powerful than the sum of absolute differences and correlation. All statistics are robust to incomplete knowledge of distortion parameters. Experiments on Landsat images confirm the sensitivity of G and recommend it for application in the first stage.

An error is corrected in an expression, for misclassification probability with dichotomous (binary) random variables, and the perils of dichotomous feature extraction are exhibited.

A number of linear and nonlinear mapping algorithms for the projection of patterns from a high-dimensional space to two dimensions are available. These two-dimensional representations allow quick visual observation of a data set. A combination of two popular mapping algorithms-Sammon's mean-square error technique and the triangulation method-is proposed to overcome the limitations in the individual algorithms. Some factors which describe the goodness of a projection are described, and a comparison is made of six of these algorithms by running them on four data sets. The results obtained support the use of the proposed algorithm.

A single modification to a mode-seeking clustering algorithm proposed by Koontz, Narendra, and Fukunaga is shown to generate a novel clustering and to provide an indication of cluster stability. The modified method should provide better clusterings for ``uniform, touching'' clusters than the original, although the original should work better than the modified method for ``touching Gaussian'' clusters. Suitable ranges for the clustering parameters of both methods are investigated. Since the modification requires changing only one line of the original algorithm, two clusterings can be obtained for the price of one coding.

The intrinsic dimensionality of a set of patterns is important in determining an appropriate number of features for representing the data and whether a reasonable two- or three-dimensional representation of the data exists. We propose an intuitively appealing, noniterative estimator for intrinsic dimensionality which is based on nearneighbor information. We give plausible arguments supporting the consistency of this estimator. The method works well in identifying the true dimensionality for a variety of artificial data sets and is fairly insensitive to the number of samples and to the algorithmic parameters. Comparisons between this new method and the global eigenvalue approach demonstrate the utility of our estimator.