In this paper we propose a new method for quantification of the rate of brain tissue deformation of patients with neurode-generative diseases. Our method allows for generating intermediary (virtual) MR brain volumes from real scans. In addition, we introduce two new descriptor spaces: (i) joint brain tissue deformation displacement vector magnitude and Jacobian and (ii) joint polar angles of displacement vector. In order to conduct our analysis, we built a visualization environment that illustrates images and flows, and it quantifies parameters. Through the calculation of the parameters, of the intermediary MR volumes, we create N-fold information simulating the deformation process. While our method is suitable for every neurodegenerative disease, we empirically tested our scheme on patients with diagnosed Alzheimer's disease, mild cognitive impairment and normal controls from the ADNI database. We focus on regions containing either ventricles or hippocampus. A distinction between different subjects could clearly be made.

Segmentation of brain structures from MR images is crucial in understanding the disease progress, diagnosis, and treatment monitoring. Atlases, showing the expected locations of the structures, are commonly used to start and guide the segmentation process. In many cases, the quality of the atlas may have a significant effect in the final result. In the literature, commonly used atlases may be obtained from one subject's data, only from the healthy, or depict only certain structures that limit their accuracy. Anatomical variations, pathologies, imaging artifacts all could aggravate the problems related to application of atlases. In this paper, we propose to use multiple atlases that are sufficiently different from each other as much as possible to handle such problems. To this effect, we have built a library of atlases and computed their similarity values to each other. Our study showed that the existing atlases have varying levels of similarity for different structures.

This paper develops a recursive method for computing moments of 2D objects described by elliptic Fourier descriptors (EFD). Green's theorem is utilized to transform 2D surface integrals into 1D line integrals and EFD description is employed to derive recursions for moments computations. Experiments are performed to quantify the accuracy of our proposed method. Comparison with Bernstein-Bézier representations is also provided.

This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and intershape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm. We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance images. We present a set of 2-D and 3-D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy.

We propose a novel scheme for fusion between two types of modalities to support function-based classification. While the first modality targets functional classification from sounds registered at impact, the second one aims classification of objects in 3D images. Using audio one can answer functional questions such as what is the material the analyzed objects are built of, if the objects are full or hollow, if they are heavy, and if they are rigidly linked to their supports. Audio based signatures are used to label parts of the object under analysis. Different parts of any object can be partitioned in generic multi-level hierarchical descriptions of functional components. Functionality, in the visual modality reasoning scheme, is derived from a large set of geometric attributes and relationships between object parts. These geometric properties represent labeling signatures to the primitive and functional parts of the analyzed classes. The fusion between both of the modalities relies on a shared cooperation among audio and visual signatures of the functional and primitive parts. The scheme does not require a-priori knowledge about any class. We tested the proposed scheme on a database of about one thousand different 3D objects. The results show high accuracy in classification

This paper presents a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. This scheme derives a new differential scalar field for a given volumetric scalar field, which could easily be adapted to other differential properties. Moreover, this scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.

This paper presents a scheme to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. The proposed scheme is not only precise and insensitive to aliasing, but also provides a method to globally segment the images into volumetric regions that contain convex or concave {elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. This scheme, which derives a new differential scalar field for a given scalar field, could easily be adapted to other differential properties.

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tessellations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non-uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for that indeed different algorithms should be employed to compute the Gaussian and mean curvatures.