Random wavelet series based on a tree-indexed Markov chain

We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a tree-indexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby performing their multifractal analysis. We also show that almost every sample path displays an oscillating singularity at almost every point and that the points at which a sample path has at most a given Holder exponent form a set with large intersection.Comment: 25 page

Image Document Categorization using Hidden Tree Markov Models and Structured Representations

. Categorization is an important problem in image document processing and is often a preliminary step for solving subsequent tasks such as recognition, understanding, and information extraction. In this paper the problem is formulated in the framework of concept learning and each category corresponds to the set of image documents with similar physical structure. We propose a solution based on two algorithmic ideas. First, we transform the image document into a structured representation based on X-Y trees. Compared to \at" or vector-based feature extraction techniques, structured representations allow us to preserve important relationships between image sub-constituents. Second, we introduce a novel probabilistic architecture that extends hidden Markov models for learning probability distributions de ned on spaces of labeled trees