The underlying aim of this research is to investigate the mathematical descriptions of homogeneous textures in digital images for the purpose of segmentation and recognition. The research covers the problem of testing these mathematical descriptions by using them to generate synthetic realisations of the homogeneous texture for subjective and analytical comparisons with the source texture from which they were derived. The application of this research is in analysing satellite or airborne images of the Earth's surface. In particular, Synthetic Aperture Radar (SAR) images often exhibit regions of homogeneous texture, which if segmented, could facilitate terrain classification. In this thesis we present noncausal, nonparametric, multiscale, Markov random field (MRF) models for recognising and synthesising texture. The models have the ability to capture the characteristics of, and to synthesise, a wide variety of textures, varying from the highly structured to the stochastic. For texture synthesis, we introduce our own novel multiscale approach incorporating a new concept of local annealing. This allows us to use large neighbourhood systems to model complex natural textures with high order statistical characteristics. The new multiscale texture synthesis algorithm also produces synthetic textures with few, if any, phase discontinuities. The power of our modelling technique is evident in that only a small source image is required to synthesise representative examples of the source texture, even when the texture contains long-range characteristics. We also show how the high-dimensional model of the texture may be modelled with lower dimensional statistics without compromising the integrity of the representation. We then show how these models -- which are able to capture most of the unique characteristics of a texture -- can be for the ``open-ended'' problem of recognising textures embedded in a scene containing previously unseen textures. Whilst this technique was developed for the practical application of recognising different terrain types from Synthetic Aperture Radar (SAR) images, it has applications in other image processing tasks requiring texture recognition.

Les neurones sensoriels réagissent à des stimuli externes en émettant des séquences de potentiels d’action (“spikes”). Ces spikes transmettent collectivement de l’information sur le stimulus en formant des motifs spatio-temporels qui constituent le code neural. On observe expérimentalement que ces motifs se produisent de façon irrégulière, mais avec une structure qui peut être mise en évidence par l’utilisation de descriptions probabilistes et de méthodes statistiques. Cependant, la caractérisation statistique des données expérimentales présente plusieurs contraintes majeures: en dehors de celles qui sont inhérentes aux statistiques empiriques comme la taille de l’échantillonnage, ‘le’ modèle statistique sous-jacent est inconnu. Dans cette thèse, nous abordons le problème d’un point de vue complémentaire à l’approche expérimentale. Nous nous intéressons à des modèles neuro-mimétiques permettant d’étudier la statistique collective des potentiels d’action et la façon dont elle dépend de l’architecture et l’histoire du réseau ainsi que du stimulus. Nous considérons tout d’abord un modèle de type Intègre-et-Tire à conductance incluant synapses électriques et chimiques. Nous montrons que la statistique des potentiels d’action est caractérisée par une distribution non stationnaire et de mémoire infinie, compatible avec les probabilités conditionnelles (left interval-specification), qui est non-nulle et continue, donc une distribution de Gibbs. Nous présentons ensuite une méthode qui permet d’unifier les modèles dits d’entropie maximale spatio-temporelle (dont la mesure invariante est une distribution de Gibbs dans le sens de Bowen) et les modèles neuro-mimétiques, en fou / Sensory neurons respond to external stimulus using sequences of action potentials (“spikes”). They convey collectively to the brain information about the stimulus using spatio-temporal patterns of spikes (spike trains), that constitute a “neural code”. Since spikes patterns occur irregularly (yet highly structured) both within and over repeated trials, it is reasonable to characterize them using statistical methods and probabilistic descriptions. However, the statistical characterization of experimental data presents several major constraints: apart from those inherent to empirical statistics like finite size sampling, ‘the’ underlying statistical model is unknown. In this thesis we adopt a complementary approach to experiments. We consider neuromimetic models allowing the study of collective spike trains statistics and how it depends on network architecture and history, as well as on the stimulus. First, we consider a conductance-based Integrate-and-Fire model with chemical and electric synapses. We show that the spike train statistics is characterized by non-stationary, infinite memory, distribution consistent with conditional probabilities (Left interval specifications), which is continuous and non null, thus a Gibbs distribution. Then, we present a novel method that allows us to unify spatio-temporal Maximum Entropy models (whose invariant measure are Gibbs distributions in the Bowen sense) and neuro-mimetic models, providing a solid ground towards biophysical explanation of spatio-temporal correlations observed in experimental data. Finally, using these tools, we discuss the stimulus response of retinal ganglion cells, and the possible generalization of the co