A unified framework for isotropic meshing based on narrowband Euclidean distance transformation

In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing highquality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient,and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-ofthe-art techniques, but is significantly faster than conventional CPU-based implementations.

A Normalization Method of Moment Invariants for 3D Objects on Different Manifolds

3D objects can be stored in computer of different describing ways, such as point set, polyline, polygonal surface and Euclidean distance map. Moment invariants of different orders may have the different magnitude. A method for normalizing moments of 3D objects is proposed, which can set the values of moments of different orders roughly in the same range and be applied to different 3D data formats universally. Then accurate computation of moments for several objects is presented and experiments show that this kind of normalization is very useful for moment invariants in 3D objects analysis and recognition.

EDT Method for Multiple Labelled Objects Subject to Tied Distances

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches aligned with real-world applications.The Euclidean distance transform(EDT)has fared well in both cases,providing a sound theoretical basis for a number of applications,such as median axis transform,fractal analysis,skeletonization,and Voronoi diagrams.Despite its wide applicability,the discrete form of the EDT includes interesting properties that have not yet been fully exploited in the literature.In this paper,we are particularly interested in the properties of 1)working with multiple objects/labels;and 2)identifying and counting equidistant pixels/voxels from certain points of interest.In some domains(such as dataset classification,texture,and complexity analysis),the result of applying the EDT transform with different objects,and their respective tied distances,may compromise the performance.In this sense,we propose an efficient modification in the method presented in[1],which leads to a novel approach for computing the distance transform in a space with multiple objects,and for counting equidistant pixels/voxels.