Sylvain Faisan
Assistant Professor

Contents
Description of Activities
Decomposition of a signal sequence
We address the problem of decomposing a sequence of spectroscopic signals. Data are a series of signals modeled as a noisy sum of parametric peaks. We aim to estimate the peak parameters given that they change slowly between two contiguous signals. The key idea is to decompose the whole sequence rather than each signal independently. The problem is set within a Bayesian framework. The peaks with similar evolution are gathered into groups and a Markovian prior on the peak parameters of a same group is used to favor a smooth evolution of the peaks. In addition, the peak number and the group number are unknown and have to be estimated (the number of peaks in two contiguous signals change if peaks vanish). Therefore, the posterior distribution is sampled with a reversible jump Markov chain Monte Carlo algorithm.

Polarimetric Image Processing
We have proposed a new procedure to estimate polarization signatures for Stokes or Mueller images, while preserving sharp transitions. The procedure is based on nonlocal means (NLM) filtering, which is an efficient denoising algorithm that outperforms popular denoising methods regarding the preservation of sharp edges and fine texture details. The noise is filtered while yielding physically admissible Stokes vectors (or Mueller matrices) at each pixel location. The proposed joint filteringestimation procedure is expressed as a constrained optimization problem. Interestingly, we show that it can be equivalently seen as a two step method: a filtering stage based on the NLM approach followed by an estimation step ensuring physical admissibility. Ellipticity of the Stokes vectors estimated with the proposed approach (right) and by using the pseudoinverse (left) are presented.

Retinal Image Registration
We have proposed a new, robust and automated method for registering sequences of images acquired from scanning ophthalmoscopes. The method uses a multiscale Bspline representation of the deformation field to map images to each other and an hierarchical optimization method. We applied the method to video sequences acquired from different parts of the retina. In all cases, the registration was successful, even in the presence of large distortions from microsaccades, and the resulting deformation fields describe the fixational motion of the eye.

Comparing a subject to a statistical model
The goal of this project was to build a 3D statistical model that represents the location of clinically relevant regions of the skull. The landmark distribution which is estimated from 3D CT scans is modeled using a multivariate Gaussian Markov random field. The main contribution lies in a new way to characterize what constitutes an anomaly in a subject when it is compared to such a statistical model (which does not need to be a Gaussian Markov random field). Once global abnormality of the subject is detected, local anomalies are searched for by finding the smallest subset of landmarks whose well chosen displacement can render the subject normal according to the statistical model. S. Faisan, A new paradigm to compare a subject to a statistical model. Application to the detection of skull abnormalities . Pattern Recognition Letters, pp. 13091315, Vol. 33, Num. 10, doi:10.1016/j.patrec.2012.03.009, July 2012 
Warping a binary image... Simple, isn'it?
The estimation of onetoone mappings is one of the most intensively studied topics in the research field of nonrigid registration. Although the computation of such mappings can now be performed accurately and efficiently, the solutions for using them in the context of binary image deformation is much less satisfactory. In particular, warping a binary image with such transformations may alter its discrete topological properties if common resampling strategies are considered. In order to deal with this issue, this article proposes a method for warping such images according to continuous and bijective mappings, while preserving their discrete topological properties (i.e. their homotopy type). Results obtained in the context of atlasbased segmentation of complex anatomical structures highlight the advantages of the proposed approach. At left, you can see the skull template that is warped in the proposed application (left, middle: front and profile view of the template. Right: template visualized with its topological skeleton).

Functional MRI  Brain Mapping
Activation detection at voxel v is formulated in terms of temporal alignment between sequences of hemodynamic response onsets detected in the fMRI signal at v and in the spatial neighborhood of v, and the input sequence of stimuli or stimulus onsets (see Fig. a). The multiple event sequence alignment problem is solved within the probabilistic framework of hidden Markov multiple event sequence models (HMMESMs). It consists in hypothesizing about a set of valid scenarios that could explain the N observed HRO event sequences. A valid scenario (see Fig. b), relies on the combination of:
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