Cécile Hardouin

Mixed-State Auto-Models and Motion Texture Modeling

In image motion analysis as well as for several application fields like daily pluviometry data modeling, observations contain two components of different nature. A first part is made with discrete values accounting for some symbolic information and a second part records a continuous (real-valued) measurement. We call such type of observations “mixed-state observations”. In this work we introduce a generalization of Besags auto-models to deal with mixed-state observations at each site of a lattice. A careful construction as well as important properties of the model will be given. A special class of positive Gaussian mixed-state auto-models is proposed for the analysis of motion textures from video sequences. This model is first explored via simulations. We then apply it to real images of dynamic natural scenes.

Test de différence de contrastes et somme pondérée de khi-deux

After recalling the framework of minimum-contrast estimation, its consistency and its asymptotic normality, we highlight the fact that these results do not require any stationarity or ergodicity assumptions. The asymptotic distribution of the underlying contrast difference test is a weighted sum of independent chi-square variables having one degree of freedom each. We illustrate these results in three contexts: (1) a nonhomogeneous Markov chain with likelihood contrast; (2) a Markov field with coding, pseudolikelihood or likelihood contrasts; (3) a not necessarily Gaussian time series with Whittles contrast. In contexts (2) and (3), we compare experimentally the power of the likelihood-ratio test with those of other contrast-difference tests.

Two-scale spatial models for binary data

A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified, and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the background. The background behaviour is captured through a hidden Gaussian process after a logit transformation on its Bernoulli success probabilities. The likelihood is then the product of the (conditional) autologistic probability distribution and the hidden Gaussian–Bernoulli process. The parameters of the new model come from both spatial scales. A series of simulations illustrates the spatial-dependence properties of the model and likelihood-based methods are used to estimate its parameters. Presence–absence data of corn borers in the roots of corn plants are used to illustrate how the model is fitted.