The proposed research focuses on statistical aspects of two classes of image models: Gibbs random fields (GRFs) on discrete lattices (Part I) and deformable templates on continuous domains (Part II). For the first class, the purpose is to fit a GRF which generates images with analytical and visual characteristics similar to those of natural textures. This includes parameter estimation and model selection: the former is an inference problem of estimating the unknown parameter (maybe high dimensional) contained in the energy function that induces the GRF; the latter is a multiple decision problem of choosing an energy function from a finite set of candidates. Some complicated issues, such as possible long-range dependence and indirect observations, will also be considered. The second class is studied in the context of object detection from laser radar sensors. The particular objects considered are human faces in an unconstrained environment. The face detection is formulated as a Bayesian inference problem, which consists of the prior (shape models), the likelihood (data models) and the algorithms (simulation from the posterior and inference based on the posterior). In particular, the simulation will be carried out by jump-diffusion processes and the inference is to identify the number of object(s) corresponding to the maximal posterior probability. Texture is a dominant feature in representation of various kinds of images. The first part of the proposed research attempts to render textures from statistical point of view. For instance, wood grain shows strong directional tendency but sand patterns appear isotropic and random. Such a difference can be represented in images created by computer graphics using different parameters for the same model. The second part of the proposed research will try to answer the questions "Is there any specific object in the picture?" "If yes, how many?" Here a model-based approach is taken which not only provides an swers to those questions based on the observed images but also quantifies the chance associated with each answer. Therefore, we should seek answers that are more likely (with greater chance) to be correct.
