Texture analysis is one of the fundamental issues of Image Processing, which has many applications in medical imaging. In this project, texture analysis issues are tackled from a probabilistic view point, considering the image as a realization of a random field whose properties reflect those of the texture formation. Hence, the project is resolutely located at the intersection of Image Processing and Probability Theory. We propose to federate under the topic of Texture analysis several multidisciplinary teams of researchers which will share their complementary contributions. We will work with random modeling of textures. These models contain some parameters which are used to characterize the textural aspect of images and extract some medical information from images. For example, the fractal analysis has been applied either to mammography for the characterization of the breast density, the classification of breast types and the assessment of cancer risks or to bone radiographs for the characterization of the bone architecture and the evaluation of the osteoporotic fracture risk. Actually the project focuses on those two medical applications, which have a major importance to Public Health: the breast cancer and the osteo-articular diseases. For this purpose, it includes two partners from the health domain: the unit INSERM-ERI-20 of the Gustave Roussy Institute in Villejuif and the team INSERM U658 of the Regional Hospital of Orleans. The activity of the team INSERM U 658 is devoted to the characterization of bone tissue and the quality of bone architecture using imagery. Its main goal is to supplement the densitometry used in clinical practice for measuring the bone mass with a texture analysis of bone images which would give relevant information about the trabecular microarchitecture. The unit INSERM ERI-20 has an expertise in the epidemiology of the breast cancer. Its work is based on the survey data E3N, which results from a large cohort study involving 100 000 female volunteers. Using an updated database, the goal is to answer a range of challenging issues concerning the medical aspect of mammograms. For both medical partners, the tasks can be broadly grouped into several steps: (1) construction of databases, (2) modelization of images and definition of relevant indices computed from images, (3) test, validation and result exploitation. The previous applications raise a methodological problem which is at the forefront of our project: How to characterize relevantly the appearance of radiographs (mammograms or bone radiographs)' We will use the analysis of texture to address this issue. The approach we follow consists in (1) proposing random models for the modeling of radiological images and (2) using the estimated parameters of models for the construction of indices which characterize the textural aspect of images. Due to the anisotropic nature of bone radiographs and mammograms, the modeling of these images is a difficult mathematical task. The theoretical study of anisotropic models raises numerous challenges which have to be taken up for succeeding in model applications. First, it is necessary to define mathematically the anisotropy and to know how to apprehend it through models. For many anisotropic models, it also remains to develop strategies for estimating model parameters and testing the adequacy of models to data. In addition, it still remains to design techniques for simulating accurately the defined random fields. Hence, the main part of the project will be devoted to the mathematical study of these methodological issues. It involves researchers in Probability Theory and Image Processing gathered through the two mathematical teams : MAP5, CNRS UMR 8145 from University Paris Descartes and LTCI, CNRS UMR 5141 from the School of Telecommunications in Paris.