In this paper, we present a novel method on surface partition from the perspective of approximation theory. Different from previous shape proxies, the ellipsoidal variance proxy is proposed to penalize the partition results falling into disconnected parts. On its support, the Principle Component Analysis (PCA) based energy is developed for asymptotic cluster aspect ratio and size control. We provide the theoretical explanation on how the minimization of the PCA-based energy leads to the optimal asymptotic behavior for approximation. Moreover, we show the partitions on densely sampled triangular meshes converge to the theoretic expectations. To evaluate the effectiveness of surface approximation, polygonal/triangular surface remeshing results are generated. The experimental results demonstrate the high approximation quality of our method.

This paper introduces a particle-based approach for anisotropic surface meshing. Given an input polygonal mesh endowed with a Riemannian metric and a specified number of vertices, the method generates a metric-adapted mesh. The main idea consists of mapping the anisotropic space into a higher dimensional isotropic one, called "embedding space". The vertices of the mesh are generated by uniformly sampling the surface in this higher dimensional embedding space, and the sampling is further regularized by optimizing an energy function with a quasi-Newton algorithm. All the computations can be re-expressed in terms of the dot product in the embedding space, and the Jacobian matrices of the mappings that connect different spaces. This transform makes it unnecessary to explicitly represent the coordinates in the embedding space, and also provides all necessary expressions of energy and forces for efficient computations. Through energy optimization, it naturally leads to the desired anisotropic particle distributions in the original space. The triangles are then generated by computing the Restricted Anisotropic Voronoi Diagram and its dual Delaunay triangulation. We compare our results qualitatively and quantitatively with the state-of-the-art in anisotropic surface meshing on several examples, using the standard measurement criteria.

A way of recognizing monosyllable Chinese words using the method of vector quantization (VQ) and a hidden Markov model (HMM) is described. The theories of vector quantization and hidden Markov models are reviewed and studied the way they are used in recognizing monosyllable Chinese speech. Special attention was paid to sample program in order to obtain as much information as possible. A test was conducted on a small vocabulary containing thirty monosyllable Chinese words which have exactly the same compound vowel. The classification accuracy obtained is about 85% compared with the traditional DTW (decoder timing waveform), method which is not more than 60%.>