This work is undertaken in the context of hierarchical stochastic models for the resolution of discrete inverse problems from low level vision. Some of these models lie on the nodes of a quadtree which leads to non-iterative inference procedures. Nevertheless, if they circumvent the algorithmic drawbacks of grid-based models (computational load and/or great dependance on the initialization), they admit modeling shortcomings (cumbersome and somehow artificial). We investigate a new hierarchical stochastic model which benefits from both the spatial and hierarchical prior modeling. The independence graph is based on a tree which has been pollarded with nodes at the coarsest resolution exhibiting a grid-based interaction structure. For this class of model, we address the critical problem of parameter estimation. To this end, we derive an EM algorithm on the hybrid structure which mixes an exact EM algorithm on each subtree and a low cost Gibbs EM algorithm on the coarse spatial grid. Experiments on a synthetic image and multispectral satellite images are reported.

This work takes place in the context of hierarchical stochastic models for the resolution of discrete inverse problems from low level vision. We investigate a new hybrid hierarchical structure: a Markov random field attached to the nodes of a truncated tree. It thus combines causal hierarchical prior on trees with a non-causal spatial prior at the coarsest level. We address the problem of computing posterior marginals with such a prior structure. This is performed using non-iterative two-sweep marginalizations on trees, combined with a low cost Gibbs sampler in between the two sweeps. Posterior marginals are thus obtained in a semi-iterative way. They are then used to infer unknown variables according to the IMPM estimator. This is illustrated by experiments on synthetic data and on multispectral satellite images.

This paper deals with hierarchical Markov random field models. We propose to introduce new hierarchical models based on a hybrid structure which combines a spatial grid of a reduced size at the coarsest level with sub-trees appended below it, down to the finest level. These models circumvent the algorithmic drawbacks of grid-based models (computational load and/or great dependance on the initialization) and the modeling drawbacks of tree-based approaches (cumbersome and somehow artificial structure). The hybrid structure leads to algorithms that mix a non-iterative inference on sub-trees with an iterative deterministic inference at the top of the structure. Experiments on a synthetic image demonstrate the gains provided in terms of both computational efficiency and the quality of results. Then experiments on real aerial images illustrate the ability of hybrid models to perform the multiresolution and multispectral image fusion.