This paper introduces a new approach for the joint alignment of a large collection of segmented images into the same system of coordinates while estimating at the same time an optimal common coordinate system. The atlas resulting from our group-wise alignment algorithm is obtained as the hidden variable of an Expectation-Maximization (EM) estimation. This is achieved by identifying the most consistent label across the collection of images at each voxel in the common frame of coordinates.
In an iterative process, each subject is iteratively aligned with the current probabilistic atlas until convergence of the estimated atlas is reached. Two different transformation models are successively applied in the alignment process: an affine transformation model and a dense non-rigid deformation field. The metric for both transformation models is the mutual information that is computed between the probabilistic atlas and each subject. This metric is optimized in the affine alignment step using a gradient based stochastic optimization (SPSA) and with a variational approach to estimate the non-rigid atlas to subject transformations.
A first advantage of our method is that the computational cost increases linearly with the number of subjects in the database. This method is therefore particularly suited for a large number of subjects. Another advantage is that, when computing the common coordinate system, the estimation algorithm identifies weights 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 atlas construction method on a population of 80 brain images segmented into 4 labels (background, white and gray matters and ventricles). First, the 80 subjects were aligned using affine and dense non-rigid deformation models. The results are visually assessed by examining how the population converges closer to a central tendency when the deformation model allows more degrees of freedom (from affine to dense non-rigid field). Second, the stability of the atlas construction procedure for various sizes of population was investigated by starting from a subset of the total population which was incrementally augmented until the total population of 80 subjects was reached. Third, the consistency 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 10 subjects. According to William's index, our reference choice performed favorably. Finally, the performance of our algorithm was quantified on a synthetic population of 10 subjects (generated using random B-Spline transformations) using a global overlap measure for each label. We also measured the robustness of this measure to the introduction of noisy subjects in the population.

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

The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination of the fractal dimension of a given volume only from the fractal measurement made on the projections or slice images given by medical imaging. This paper gives general results about the Minkowski dimensions and contents of projections and sections of a set. We also show with examples that they depend essentially on the directions of the planes and so there is - in general case - no relation between 3D and 2D fractal dimensions. This consideration is then illustrated with examples from synthetic models and from CT scan images of wrists. In conclusion, this study reveals that the quantitative characterization of an organic volume (in particular osseous) requires taking into account the whole volume, and not only some of its slices or projections.

Impairment of left ventricular contractility due to cardiovascular diseases is reflected in left ventricle (LV) motion patterns. An abnormal change of torsion or long axis shortening LV values can help with the diagnosis and follow-up of LV dysfunction. Tagged Magnetic Resonance (TMR) is a widely spread medical imaging modality that allows estimation of the myocardial tissue local deformation. In this work, we introduce a novel variational framework for extracting the left ventricle dynamics from TMR sequences. A bi-dimensional representation space of TMR images given by Gabor filter banks is defined. Tracking of the phases of the Gabor response is combined using a variational framework which regularizes the deformation field just at areas where the Gabor amplitude drops, while restoring the underlying motion otherwise. The clinical applicability of the proposed method is illustrated by extracting normality models of the ventricular torsion from 19 healthy subjects.

Detailed descriptions of cardiac geometry and architecture are necessary for examining and understanding structural changes to the myocardium that are the result of pathologies, for interpreting the results of experimental studies of propagation, and for use as a three-dimensional orthotropically anisotropic model for the computational reconstruction of propagation during arrhythmias. Diffusion tensor imaging (DTI) provides a means to reconstruct fibre and sheet orientation throughout the ventricles. We reconstruct and quantify canine cardiac architecture in selected regions of the left and right ventricular free walls and the inter-ventricular septum. Fibre inclination angle rotates smoothly through the wall in all regions, from positive in the endocardium to negative in the epicardium. However, fibre transverse and sheet angles show large variability in basal regions. Additionally, regions where two populations (positive and negative) of sheet structure merge are identified. From these data, we conclude that a single DTI-derived atlas model of ventricular architecture should be applicable to modelling propagation in wedges from the equatorial and apical left ventricle, and allow comparisons to experimental 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 whole ventricles will be required.

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