Comparing vector fields across surfaces: interest for characterizing the orientations of cortical folds

Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the vector fields from the original surfaces onto a common domain. In this paper, we propose a framework to achieve this task by mapping the vector fields onto a common space, using some notions of differential geometry. The proposed framework enables the computation of statistics on vector fields. We demonstrate its interest in practice with an application on real data with a quantitative assessment of the reproducibility of curvature directions that describe the complex geometry of cortical folding patterns. The proposed framework is general and can be applied to different types of vector fields and surfaces, allowing for a large number of high potential applications in medical imaging.

Characterization of surface motion patterns in highly deformable soft tissue organs from dynamic Magnetic Resonance Imaging

In this work, we present a pipeline for characterization of bladder surface dynamics during deep respiratory movements from dynamic Magnetic Resonance Imaging (MRI). Dynamic MRI may capture temporal anatomical changes in soft tissue organs with high-contrast but the obtained sequences usually suffer from limited volume coverage which makes the high resolution reconstruction of organ shape trajectories a major challenge in temporal studies. For a compact shape representation, the reconstructed temporal data with full volume coverage are first used to establish a subject-specific dynamical 4D mesh sequences using the large deformation diffeomorphic metric mapping (LDDMM) framework. Then, we performed a statistical characterization of organ shape changes from mechanical parameters such as mesh elongations and distortions. Since shape space is curved, we have also used the intrinsic curvature changes as metric to quantify surface evolution. However, the numerical computation of curvature is strongly dependant on the surface parameterization (i.e. the mesh resolution). To cope with this dependency, we propose a non-parametric level set method to evaluate spatio-temporal surface evolution. Independent of parameterization and minimizing the length of the geodesic curves, it shrinks smoothly the surface curves towards a sphere by minimizing a Dirichlet energy. An Eulerian PDE approach is used for evaluation of surface dynamics from the curve-shortening flow. Results demonstrate the numerical stability of the derived descriptor throughout smooth continuous-time organ trajectories. Intercorrelations between individuals' motion patterns from different geometric features are computed using the Laplace-Beltrami Operator (LBO) eigenfunctions for spherical mapping.

A new geodesic-based feature for characterization of 3D shapes: application to soft tissue organ temporal deformations

In this paper, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of a bladder during a forced respiratory motion with a reduced number of 3D surface points: first, a set of equidistant points representing the vertices of quadrilateral mesh for the surface in the first time frame are tracked throughout a long dynamic MRI sequence using a Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. Second, a novel geometric feature which is invariant to scaling and rotation is proposed for characterizing the temporal organ deformations by employing an Eulerian Partial Differential Equations (PDEs) methodology. We demonstrate the robustness of our feature on both synthetic 3D shapes and realistic dynamic MRI data portraying the bladder deformation during forced respiratory motions. Promising results are obtained, showing that the proposed feature may be useful for several computer vision applications such as medical imaging, aerodynamics and robotics.

Fourier descriptors based on the structure of the human primary visual cortex with applications to object recognition

In this paper we propose a supervised object recognition method using new global features and inspired by the model of the human primary visual cortex V1 as the semidiscrete roto-translation group $SE(2,N) = \mathbb Z_N\rtimes \mathbb R^2$. The proposed technique is based on generalized Fourier descriptors on the latter group, which are invariant to natural geometric transformations (rotations, translations). These descriptors are then used to feed an SVM classifier. We have tested our method against the COIL-100 image database and the ORL face database, and compared it with other techniques based on traditional descriptors, global and local. The obtained results have shown that our approach looks extremely efficient and stable to noise, in presence of which it outperforms the other techniques analyzed in the paper.