In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford--Shah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We will give a numerical algorithm using finite differences. Finally, we will present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

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Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as \How many clusters are there?", "Which clustering method should be used?" and \How should outliers be handled?". We outline a general methodology for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology, a...

Motivation: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a 'good' clustering method and determining the 'correct' number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications.

In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient.

1 Funded by the O ce of Naval Research under contracts N00014-96-1-0192 and N00014-96-1-

We consider the problem of detecting features in spatial point processes in the presence of substantial clutter. One example is the detection of minefields using reconnaissance aircraft images that identify many objects that are not mines. Our solution uses K \Gammath nearest neighbor distances of points in the process to classify them as clutter or otherwise. The observed K \Gammath nearest neighbor distances are modeled as a mixture distribution, the parameters of which are estimated by a simple EM algorithm. This method allows for detection of generally shaped features, that need not be path connected. In the minefield example this method yields high detection and low false positive rates. Another application, to outlining seismic faults, is considered, with some success. The method works well in high dimensions. The method can also be used to produce very high breakdown-point robust estimators of a covariance matrix. KEY WORDS: Breakdown point; Edge effects; EM algorithm; Image ana...

MCLUST is a software package for cluster analysis written in Fortran and interfaced to the S-PLUS commercial software package1. It implements parameterized Gaussian hierarchical clustering algorithms [16, 1, 7] and the EM algorithm for parameterized Gaussian mixture models [5, 13, 3, 14] with the possible addition of a Poisson noise term. MCLUST also includes functions that combine hierarchical clustering, EM and the Bayesian Information Criterion (BIC) in a comprehensive clustering strategy [4, 8]. Methods of this type have shown promise in a number of practical applications, including character recognition [16], tissue segmentation [1], mine eld and seismic fault detection [4], identi cation of textile aws from images [2], and classi cation of astronomical data [3, 15]. Aweb page with related links can be found at

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