Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previ...Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previous work scattered in the topology and geometry literature, we rigorously present a theoretical basis for orientable polygonal surface representation from a modem point of view. Based on the presented basis, we propose a new combinatorial data structure that can guarantee the property of orientable 2-manifolds and is primal/dual efficient. Comparisons with other widely used data structures are also presented in terms of time and space efficiency.展开更多
Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping...Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping between highand low-dimensional space via a five-tuple model. Nonlinear dimensionality reduction based on manifold learning provides a feasible way for solving such a problem. We propose a novel globular neighborhood based locally linear embedding (GNLLE) algorithm using neighborhood update and an incremental neighbor search scheme, which not only can handle sparse datasets but also has strong anti-noise capability and good topological stability. Given that the distance measure adopted in nonlinear dimensionality reduction is usually based on pairwise similarity calculation, we also present a globular neighborhood and path clustering based locally linear embedding (GNPCLLE) algorithm based on path-based clustering. Due to its full consideration of correlations between image data, GNPCLLE can eliminate the distortion of the overall topological structure within the dataset on the manifold. Experimental results on two image sets show the effectiveness and efficiency of the proposed algorithms.展开更多
文摘Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previous work scattered in the topology and geometry literature, we rigorously present a theoretical basis for orientable polygonal surface representation from a modem point of view. Based on the presented basis, we propose a new combinatorial data structure that can guarantee the property of orientable 2-manifolds and is primal/dual efficient. Comparisons with other widely used data structures are also presented in terms of time and space efficiency.
基金Project (No 2008AA01Z132) supported by the National High-Tech Research and Development Program of China
文摘Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping between highand low-dimensional space via a five-tuple model. Nonlinear dimensionality reduction based on manifold learning provides a feasible way for solving such a problem. We propose a novel globular neighborhood based locally linear embedding (GNLLE) algorithm using neighborhood update and an incremental neighbor search scheme, which not only can handle sparse datasets but also has strong anti-noise capability and good topological stability. Given that the distance measure adopted in nonlinear dimensionality reduction is usually based on pairwise similarity calculation, we also present a globular neighborhood and path clustering based locally linear embedding (GNPCLLE) algorithm based on path-based clustering. Due to its full consideration of correlations between image data, GNPCLLE can eliminate the distortion of the overall topological structure within the dataset on the manifold. Experimental results on two image sets show the effectiveness and efficiency of the proposed algorithms.
