DIFFEOMORPHIC REGISTRATION FOR RETINOTOPIC MAPPING VIA QUASICONFORMAL MAPPING.

Human visual cortex is organized into several functional regions/areas. Identifying these visual areas of the human brain (i.e.

Surface Meshing with Curvature Convergence.

Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities.

Area-preservation mapping using optimal mass transport.

We present a novel area-preservation mapping/flattening method using the optimal mass transport technique, based on the Monge-Brenier theory. Our optimal transport map approach is rigorous and solid in theory, efficient and parallel in computation, yet general for various applications. By comparison with the conventional Monge-Kantorovich approach, our method reduces the number of variables from O(n2) to O(n), and converts the optimal mass transport problem to a convex optimization problem, which can now be efficiently carried out by Newton's method.

Conformal Magnifier: A Focus+Context Technique with Local Shape Preservation.

We present the conformal magnifier, a novel interactive focus+context visualization technique that magnifies a region of interest (ROI) using conformal mapping. Our framework supports the arbitrary shape design of magnifiers for the user to enlarge the ROI while globally deforming the context region without any cropping. By using the mathematically well-defined conformal mapping theory and algorithm, the ROI is magnified with local shape preservation (angle distortion minimization), while the transition area between the focus and context regions is deformed smoothly and continuously.

Interactive visibility retargeting in VR using conformal visualization.

In Virtual Reality, immersive systems such as the CAVE provide an important tool for the collaborative exploration of large 3D data. Unlike head-mounted displays, these systems are often only partially immersive due to space, access, or cost constraints. The resulting loss of visual information becomes a major obstacle for critical tasks that need to utilize the users' entire field of vision.

Volumetric Colon Wall Unfolding Using Harmonic Differentials.

Volumetric colon wall unfolding is a novel method for virtual colon analysis and visualization with valuable applications in virtual colonoscopy (VC) and computer-aided detection (CAD) systems. A volumetrically unfolded colon enables doctors to visualize the entire colon structure without occlusions due to haustral folds, and is critical for performing efficient and accurate texture analysis on the volumetric colon wall. Though conventional colon surface flattening has been employed for these uses, volumetric colon unfolding offers the advantages of providing the needed quantities of information with needed accuracy.

GPU-assisted computation of centroidal Voronoi tessellation.

Centroidal Voronoi tessellations (CVT) are widely used in computational science and engineering. The most commonly used method is Lloyd's method, and recently the L-BFGS method is shown to be faster than Lloyd's method for computing the CVT. However, these methods run on the CPU and are still too slow for many practical applications.

Ricci flow for 3D shape analysis.

Ricci flow is a powerful curvature flow method, which is invariant to rigid motion, scaling, isometric, and conformal deformations. We present the first application of surface Ricci flow in computer vision. Previous methods based on conformal geometry, which only handle 3D shapes with simple topology, are subsumed by the Ricci flow-based method, which handles surfaces with arbitrary topology.

Conformal geometry and its applications on 3D shape matching, recognition, and stitching.

Three-dimensional shape matching is a fundamental issue in computer vision with many applications such as shape registration, 3D object recognition, and classification. However, shape matching with noise, occlusion, and clutter is a challenging problem. In this paper, we analyze a family of quasi-conformal maps including harmonic maps, conformal maps, and least-squares conformal maps with regards to 3D shape matching.

Computing shortest cycles on discrete surfaces for acurate topological modifications of medical image isosurfaces.

Topological control over discrete isosurface is of primordial interest in medical applications, especially discrete model building for active contours. Previous attempts showed that the key point in acurately modifying topology was computation of shortest cycles on the surface of interest. This paper generalizes the shortest path algorithm to compute shortest cycles in a given homotopy class on a discrete surface with arbitrary topology.