Fast bilinear extrapolation of 3D ising field partition function. application to fMRI image analysis.

Symmetric ising models define the simplest discrete Markov random fields that can be used for segmentation purpose. Unsupervised segmentation requires an automatic setting of the temperature parameter of ising fields. To this end, partition function (PF) estimation becomes a key issue. In this paper, we present a bilinear extrapolation technique for a fast PF estimation of 3D ising field. The proposed method is a two-step procedure that applies to the context where multiple 3D ising fields are involved over different objects (eg, brain regions) of different size and topology. First, a small set of reference PFs is accurately estimated using path sampling. Second, the large remaining set of PFs is computed using a temperature-dependent bilinear extrapolation technique. It is shown that our approach is accurate and computationally efficient to account for topological fluctuations of ising fields on regular and irregular graphs. A convincing application to joint detection-estimation of brain activity in functional MRI is also presented.