基于三维流形连续框架的三维数据场建模与分析新方法

项目名称： 基于三维流形连续框架的三维数据场建模与分析新方法

项目编号： No.61272032

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 方美娥

作者单位： 杭州电子科技大学

项目金额： 60万元

中文摘要： 如何有效分析和利用海量的三维数据是21世纪最具挑战性的科学问题之一。传统的基于线性插值框架的可视化与拓扑分析方法是分片线性流形上的建模与分析，需存储的数据量大，能挖掘的信息的精度和广度均非常有限，本项目提出三维数据场建模与分析的新框架，主要研究工作如下： 1.引入微分算子多项式，建立拟插值三维数据场的Box样条连续模型，实现比已有方法更高精度的、二阶连续可微的、真正三维意义上的建模方法，并构造自适应局部加细采样网格上的重建核，实现三维数据场的高效压缩； 2.在连续模型框架下，运用三维流形上的Morse-Smale复形理论及微分几何与拓扑分析手段，形成一整套挖掘三维数据场整体拓扑和各层次的精细几何结构的有效方法，并探究基于本质几何量的新方法； 3.将新框架下的建模与分析方法应用于蛋白质分子场，探寻活性位点，计算与分析蛋白质分子三维结构中重要的功能结构及其几何属性。

中文关键词： 3D标量场；C2连续框架；Box样条建模；拟插值算子；可视化与拓扑分析

英文摘要： How to effectively analyze and utilize 3D data fields is one of the most challenging scientific problems in the visualization domain in 21st century. Traditional visualization and topology analysis methods are based on the linear interpolation framework which belongs to piecewise linear manifold. It needs too much memory space, while both the accuracy and the width of information it can dig are very limited. In this project, we propose a new framework to model and analyze 3D data fields. Main research works will include: 1. By introducing a polynomial differential operator, we build a continuous quasi- interpolation framework with box splines of global C2 smoothness, which makes 2D-based analysis more accurate and 3D-based analysis like differential geometry in the large possible. Based on this, we further construct reconstruction basis functions upon adaptively refining meshes so as to effectively compress 3D data fields; 2. Under the proposed continuous framework, we apply the Morse-smale theory and all kinds of tools of differential geometry and topology analysis on 3D-manifold to obtain a set of effective method for digging the topology in whole and refined geometric structures of 3D data fields. Furthermore, we try to find essential geometry terms of 3D-manifold and construct new analytical methods. 3. App

英文关键词： 3D scalar fields；C2-continuous frame；modeling by box-splines；quasi-interpolation operator；visualization and topology analysis