This paper introduces a new approach for the joint alignment of a largecollection of segmented images into the same system of coordinates whileestimating at the same time an optimal common coordinate system. The atlasresulting from our group-wise alignment algorithm is obtained as the hiddenvariable of an Expectation-Maximization (EM) estimation. This is achievedby identifying the most consistent label across the collection of images at eachvoxel in the common frame of coordinates.
In an iterative process, each subject is iteratively aligned with the currentprobabilistic atlas until convergence of the estimated atlas is reached. Twodifferent transformation models are successively applied in the alignmentprocess: an affine transformation model and a dense non-rigiddeformation field. The metric for both transformation models is the mutualinformation that is computed between the probabilistic atlas and each subject.This metric is optimized in the affine alignment step using a gradient basedstochastic optimization (SPSA) and with a variational approach to estimate thenon-rigid atlas to subject transformations.
A first advantage of our method is that the computational cost increaseslinearly with the number of subjects in the database. This method is thereforeparticularly suited for a large number of subjects. Another advantage is that,when computing the common coordinate system, the estimation algorithm identifiesweights for each subject on the basis of the typicality of the segmentation.This makes the common coordinate system robust to outliers in the population.
Several experiments are presented in this paper to validate our atlasconstruction method on a population of 80 brain images segmented into 4 labels(background, white and gray matters and ventricles). First, the 80 subjects werealigned using affine and dense non-rigid deformation models. The results arevisually assessed by examining how the population converges closer toa central tendency when the deformation model allows more degrees of freedom(from affine to dense non-rigid field). Second, the stability of the atlasconstruction procedure for various sizes of population was investigated bystarting from a subset of the total population which was incrementallyaugmented until the total population of 80 subjects was reached. Third, theconsistency of our group-wise reference (hidden variable of the EM algorithm)was also compared to the choice of an arbitrary subject for a subset of 10subjects. According to William's index, our reference choiceperformed favorably. Finally, the performance of our algorithm was quantified ona synthetic population of 10 subjects (generated using random B-Splinetransformations) using a global overlap measure for each label. We also measuredthe robustness of this measure to the introduction of noisy subjects in thepopulation.

Multifractal analysis is known as a useful tool in signal analysis. However, themethods are often used without methodological validation. In this study, wepresent multidimensional models in order to validate multifractal analysismethods.

The inner knowledge of volumes from imagesis an ancient problem. This question becomes complicated when itconcerns quantization, as the case of any measurement and inparticular the calculation of fractal dimensions. Trabecular bonetissues have, like many natural elements, an architecture whichshows a fractal aspect. Many studies have already been developedaccording to this approach. The question which arises however is toknow to which extent it is possible to get an exact determination ofthe fractal dimension of a given volume only from the fractalmeasurement made on the projections or slice images given by medicalimaging. This paper gives general results about the Minkowskidimensions and contents of projections and sections of a set. Wealso show with examples that they depend essentially on thedirections of the planes and so there is - in general case - norelation between 3D and 2D fractal dimensions. This consideration isthen illustrated with examples from synthetic models and from CTscan images of wrists. In conclusion, this study reveals that thequantitative characterization of an organic volume (in particularosseous) requires taking into account the whole volume, and not onlysome of its slices or projections.

Impairment of left ventricular contractility due tocardiovascular diseases is reflected in left ventricle (LV) motionpatterns. An abnormal change of torsion or long axis shortening LVvalues can help with the diagnosis and follow-up of LVdysfunction. Tagged Magnetic Resonance (TMR) is a widely spreadmedical imaging modality that allows estimation of the myocardialtissue local deformation. In this work, we introduce a novelvariational framework for extracting the left ventricle dynamicsfrom TMR sequences. A bi-dimensional representation space of TMRimages given by Gabor filter banks is defined. Tracking of thephases of the Gabor response is combined using a variationalframework which regularizes the deformation field just at areaswhere the Gabor amplitude drops, while restoring the underlyingmotion otherwise. The clinical applicability of the proposedmethod is illustrated by extracting normality models of theventricular torsion from 19 healthy subjects.

Detailed descriptions of cardiacgeometry and architecture are necessary for examining andunderstanding structural changes to the myocardium that are theresult of pathologies, for interpreting the results ofexperimental studies of propagation, and for use as athree-dimensional orthotropically anisotropic model for thecomputational reconstruction of propagation during arrhythmias.Diffusion tensor imaging (DTI) provides a means to reconstructfibre and sheet orientation throughout the ventricles. Wereconstruct and quantify canine cardiac architecture in selectedregions of the left and right ventricular free walls and theinter-ventricular septum. Fibre inclination angle rotates smoothlythrough the wall in all regions, from positive in the endocardiumto negative in the epicardium. However, fibre transverse and sheetangles show large variability in basal regions. Additionally,regions where two populations (positive and negative) of sheetstructure merge are identified. From these data, we conclude thata single DTI-derived atlas model of ventricular architectureshould be applicable to modelling propagation in wedges from theequatorial and apical left ventricle, and allow comparisons toexperimental studies carried out in wedge preparations. However,due to inter-individual variability in basal regions, individual(rather than atlas) DTI models of basal wedges or of the wholeventricles will be required.

The image's restoration is an essential step in medical imaging.Several Filters are developped to remove noise, the most interestingare filters who permits to denoise the image preserving semanticallyimportant structures. One class of recent adaptive denoising methodsis the nonlinear Partial Differential Equations who knows currently asignificant success. This work deals with mathematical study for aproposed nonlinear evolution partial differential equation for imageprocessing. The existence and the uniqueness of the solution areestablished. Using a finite differences method we experiment thevalidity of the proposed model and we illustrate the efficiently ofthe method using some medical images. The Signal to Noise Ration(SNR) number is used to estimate the quality of the restoredimages.