Multidimensional Texture Analysis for Unsupervised Pattern Classification

Clustering techniques aim to regroup a set of multidimensional observations, represented as data points scattered through a N-dimensional data space, into groups, or clusters, according to their similarities or dissimilarities. Each point corresponds to a vector of observed features measured on the objects to be classified. Among the different approaches that have been developed for cluster analysis [Jain et al., 1999; Theodoridis & Koutroumbas, 2003; Tran et al., 2005; Xu & Wunsch, 2005; Filipone et al., 2008], we consider the statistical approach [Devijver & Kittler, 1983]. In this framework, many clustering procedures have been proposed, based on the analysis of the underlying probability density function (pdf). The high density of data points within the clusters gives rise to modal regions corresponding to the modes of the pdf that are separated by valleys of low densities [Parzen, 1962]. Independently from cluster analysis, a large amount of research effort is devoted to image segmentation. Starting from an unstructured collection of pixels, we generally agree about the different regions constituting an image due to our visual grouping capabilities. The most important factors that lead to this perceptual grouping are similarity, proximity and connectedness. More precisely, segmentation can be considered as a partitioning scheme such that: Every pixel of the image must belong to a region, The regions must be composed of contiguous pixels, The pixels constituting a region must share a given property of similarity. These three conditions can be easily adapted to the clustering process. Indeed, each data point must be assigned to a cluster, and the clusters must be composed of neighbouring data points since the points assigned to the same cluster must share some properties of similarity. Considering this analogy between segmentation and clustering, several image segmentation procedures based on the gray-level function analysis have been successfully adapted to detect the modes or to seek the valleys of the pdf for pattern classification purpose [BotteLecocq et al., 2007]. In this framework, the underlying pdf is generally estimated on a regular discrete array of sampling points [Postaire & Vasseur, 1982]. The idea of using a pdf estimation for mode O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m