Algorithmic Riemannian Geometry for a Statistical Analysis of Images

Florida State University, Tallahassee FL

Investigators

Abstract

ALGORITHMIC RIEMANNIAN GEOMETRY FOR A STATISTICAL ANALYSIS OF IMAGES Abstract This project is concerned with the investigation of novel algorithmic representations of images and geometrical signal processing techniques for the automated analysis of image content. The investigators develop a new framework for an appearance-based analysis of imaged objects in terms of their shapes and textures using methods and tools derived from differential geometry and statistics. A statistical formulation is of the essence due to the large variability of shapes and textures frequently encountered in imagery of interest. The use of differential geometric methods in image processing is still incipient, but very promising, as solid evidence exists that such methodology is particularly well suited for the study of multidimensional, nonlinear features such as shapes and textures. In recent years, the investigators have developed a statistical shape analysis program; shapes are viewed as elements of a shape space whose geometry is exploited for shape analysis. The investigators treat textures in a similar manner by creating a Riemannian manifold of textures and integrate both representations into a single shape-texture model for the algorithmic analysis of image content. Images are decomposed into their spectral components and local spectral histograms are treated as elements of an infinite-dimensional statistical manifold equipped with a geometric structure induced by non-parametric Fisher information. Differential geometric constructs are utilized to develop algorithms for: (i) statistical inferences and learning of shape-texture features; (ii) Bayesian detection and recognition of objects using shape-texture priors; (iii) dimensionality reduction techniques for efficient processing.