测地线中心Voronoi网格：理论、算法与应用
Geodesic Centroidal Voronoi Tessellations: Theories, Algorithms and Applications
摘要：
目前，数字媒体的大数据（包括图像、视频和3D图形模型）通常被建模为嵌入在高维特征空间中的低维流形网格。本文总结了近年来我们在流形网格上的测地线质心Voronoi网格（GCVTs）的研究工作。我们表明，GCVT可以找到一个广泛的有趣的应用在计算机视觉和图形，由于效率的搜索，定位和索引固有的这些内在的几何结构。然后，我们提出了具有挑战性的问题，如何建立GCVTs的组合结构，并建立其时间和空间复杂度，包括理论和算法的结果。
英文摘要：
Nowadays, big data of digital media (including images, videos and 3D graphical models) are frequently modeled as low-dimensional manifold meshes embedded in a high-dimensional feature space. In this paper, we summarized our recent work on geodesic centroidal Voronoi tessellations(GCVTs), which are intrinsic geometric structures on manifold meshes. We show that GCVT can find a widely range of interesting applications in computer vision and graphics, due to the efficiency of search, location and indexing inherent in these intrinsic geometric structures. Then we present the challenging issues of how to build the combinatorial structures of GCVTs and establish their time and space complexities, including both theoretical and algorithmic results.
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