Delaunay meshes (DM) are a special type of manifold triangle meshes --- where the local Delaunay condition holds everywhere --- and find important applications in digital geometry processing. This paper addresses the \yongjin{general} DM simplification problem: given an arbitrary manifold triangle mesh M with n vertices and the user-specified resolution m(< n), compute a Delaunay mesh M* with m vertices that has the least Hausdorff distance to M. To solve the problem, we abstract the simplification process using a 2D Cartesian grid model, in which each grid point corresponds to triangle meshes with a certain number of vertices and a simplification process is a monotonic path on the grid. We develop a novel differential-evolution-based method to compute a low-cost path, which leads to a high quality Delaunay mesh. Extensive evaluation shows that our method consistently outperforms the existing methods in terms of approximation error. In particular, our method is highly effective for small-scale CAD models and man-made objects with sharp features but less details. Moreover, our method is fully automatic and can preserve sharp features well and deal with models with multiple components, whereas the existing methods often fail.

This paper proposes a novel algorithm to extract feature landmarks on the vestibular system (VS), for the analysis of Adolescent Idiopathic Scoliosis (AIS) disease. AIS is a 3-D spinal deformity commonly occurred in adolescent girls with unclear etiology. One popular hypothesis was suggested to be the structural changes in the VS that induce the disturbed balance perception, and further cause the spinal deformity. The morphometry of VS to study the geometric differences between the healthy and AIS groups is of utmost importance. However, the VS is a genus-3 structure situated in the inner ear. The high-genus topology of the surface poses great challenge for shape analysis. In this work, we present a new method to compute exact geodesic loops on the VS. The resultant geodesic loops are in Euclidean metric, thus characterizing the intrinsic geometric properties of the VS based on the real background geometry. This leads to more accurate results than existing methods, such as the hyperbolic Ricci flow method. Furthermore, our method is fully automatic and highly efficient, e.g., one order of magnitude faster than. We applied our algorithm to the VS of normal and AIS subjects. The promising experimental results demonstrate the efficacy of our method and reveal more statistically significant shape difference in the VS between right-thoracic AIS and normal subjects.

This paper describes a high-resolution, real-time, three-dimensional shape measurement system using the modified two-plus-one phase-shifting algorithm. The data acquisition speed is as high as 60 frames/s with an image resolution of 640480 pixels per frame. Experiments demonstrated that the system was able to acquire the dynamic changing objects such as facial geometric shape changes when the subject is speaking, and the modified two-plus-one phase-shifting algorithm can further alleviate the error due to motion. Applications of this system include manufacturing, online inspection, medical imaging, compute vision, and computer graphics.

We develop a general approach that uses holomorphic 1-forms to parameterize anatomical surfaces with complex (possibly branching) topology. Rather than evolve the surface geometry to a plane or sphere, we instead use the fact that all orientable surfaces are Riemann surfaces and admit conformal structures, which induce special curvilinear coordinate systems on the surfaces. Based on Riemann surface structure, we can then canonically partition the surface into patches. Each of these patches can be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformal structures for several types of anatomical surfaces in MRI scans of the brain, including the cortex, hippocampus, and lateral ventricles. We found that the resulting parameterizations were consistent across

Computing discrete geodesic distance over triangle meshes is one of the fundamental problems in computational geometry and computer graphics. In this problem, an effective window pruning strategy can significantly affect the actual running time. Due to its importance, we conduct an in-depth study of window pruning operations in this paper, and produce an exhaustive list of scenarios where one window can make another window partially or completely redundant. To identify a maximal number of redundant windows using such pairwise cross checking, we propose a set of procedures to synchronize local window propagation within the same triangle by simultaneously propagating a collection of windows from one triangle edge to its two opposite edges. On the basis of such synchronized window propagation, we design a new geodesic computation algorithm based on a triangle-oriented region growing scheme. Our geodesic algorithm can remove most of the redundant windows at the earliest possible stage, thus significantly reducing computational cost and memory usage at later stages. In addition, by adopting triangles instead of windows as the primitive in propagation management, our algorithm significantly cuts down the data management overhead. As a result, it runs 4-15 times faster than MMP and ICH algorithms, 2-4 times faster than FWP-MMP and FWP-CH algorithms, and also incurs the least memory usage.