In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is

This paper describes a Graphics Processing Unit (GPU)-assisted real-time three-dimensional shape measurement system. Our experiments demonstrated that the absolute coordinates calculation and rendering speed of a GPU is more than four times faster than that of a dual CPU workstation with the same graphics card. By implementing the GPU into our system, we realized simultaneous absolute coordinate acquisition, reconstruction and display at 30 frames per second with a resolution of approximately 266K points per frame. Moreover, a 2+1 phase-shifting algorithm was employed to alleviate the measurement error caused by motion. Applications of the system include medical imaging, manufacturing, entertainment, and security.

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.

Parameterizations of manifolds are widely applied to the fields of numerical partial differential equations and computer graphics. To this end, in recent years several efficient and reliable numerical algorithms have been developed by different research groups for the computation of triangular and tetrahedral mesh parameterizations. However, it is still challenging when the topology of manifolds is nontrivial, e.g., the 3-manifold of a topological solid torus. In this paper, we propose a novel volumetric stretch energy minimization algorithm for volume-preserving parameterizations of toroidal polyhedra with a single boundary being mapped to a standard torus. In addition, the algorithm can also be used to compute the equiareal mapping between a genus-one closed surface and the standard torus. Numerical experiments indicate that the developed algorithm is effective and performs well on the bijectivity of the mapping. Applications on manifold registrations and partitions are demonstrated to show the robustness of our algorithms.

Surface parameterizations have been widely applied in the computer-aided design for the geometric processing tasks of surface registration, remeshing, texture mapping, and so on. In this paper, we present an efficient balanced energy minimization (BEM) algorithm for the computation of simply connected open surface parameterizations with balanced angle and area distortions. The existence of a nontrivial accumulation function of the BEM algorithm is guaranteed under some mild conditions and the limiting function is shown to be one-to-one. Comparisons of the BEM algorithm with the angle- and the area-preserving parameterizations show that the angular distortion is close to that of the angle-preserving parameterization while the area distortion is significantly improved. An application of the BEM on the Chinese virtual broadcasting technique is demonstrated thereafter, which is consisted of surface remeshing, registration, and morphing.