Change detection is of paramount importance in medical imaging, serving as a non-invasive quantifiable powerful tool in diagnosis and in assessment of the outcome of treatment of tumors. We present a new quantitative method for detecting changes in volumetric medical data and in clustering of anatomical structures, based on assessment of volumetric distortions that are required in order to deform a test three-dimensional medical dataset segment onto its previously-acquired reference, or a given prototype in the case clustering. Unlike the voxel-based classical techniques of shape comparison, our algorithm operates on tetrahedral meshes and can, therefore be applied on both closed, simply-connected, surfaces and in volumetric domains with more sophisticated boundaries.

Mesh parameterization is one of the fundamental operations in computer graphics (CG) and computeraided design (CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible (ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties (angle and area) of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.

Curvature is a fundamental component in differential geometry. It is used extensively in signal, image and shape processing, as a feature and in segmentation flows and regularization processes. In this paper we extend the notion of curvature in two ways. First, we present the Menger curvature which goes beyond classical curves and Riemannian manifolds to general metric spaces and is rigorously defined on a variety of discrete settings. We further extend the curvature to become a non-local entity using an adaptive, non-local integration measure, allowing curvature to be computed in a robust manner. Examples on natural and textural images highlight potential applications of these new concepts.

Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's “thin triangle condition”, which is tightly related to core congestion and route reliability. In this work we analyze the discrete Ricci curvature of the Internet, defined by Ollivier [1], Lin et al. [2], etc. Ricci curvature measures whether local distances diverge or converge. It is a more local measure which allows us to understand the distribution of curvatures in the network. We show by various Internet data sets that the distribution of Ricci cuvature is spread out, suggesting the network topology to be non-homogenous. We also show that the Ricci curvature has interesting connections to both local measures such as node degree and clustering coefficient, global measures such as betweenness centrality and network connectivity, as well as auxilary attributes such as geographical distances. These observations add to the richness of geometric structures in complex network theory.

We present a new program tool intended to increase the feedback received from students during interactive synchronous sessions. It works in a semicontinuous, nonobtrusive way, giving information about predefined parameters. The results are monitored online by the instructor and the data is logged for further evaluation. Instructors using the program have reported a significant change of their perceived level of interaction with the students. The better feedback allows them more adaptability to the student needs, without interrupting the flow of the session. The program is independent of the conferencing environment and runs in parallel with it.