复杂几何对象的特征提取及分类和检索研究

For a complex object group comprising a plurality of 2D or 3D geometric objects, this proposal aims at conducting the following studies: (1) when a complex group is expressed as a single mathematical expression, how to eliminate the effects of the Gibbs phenomenon. (2) Given a large number of complex object groups, how to quantify the difference between them. (3) Since huge amonts of data will be involved when we proccess imformation of complex obeject groups, it is necessary to devlope effective and practical algorithm. How to design such kind of algorithm? (4) How to evaluate the actual effect of the research results of the previous three issues. The research results of these 4 problems have important practical value in object classification, pattern recognition and other fields. This proposal employs the discontinuous orthogonal complete function system, V-system, as a theoretical tool. The theorys of the V-system was proposed by the applicant, which was completed in the last National Natural Science Fund Project. Based on it, this proposal will focus on some distinctive characteristics of the V-system and continue in-depth study. First, the constructive definition of the multi-variable V-system will be proposed and corresponding algorithms will be developed. Then, successful experiment results will be provided by applying the theory and algorithem in the practical problems, such as trademark retrieval and model reuse. The main feature of this project is that the overall features of the complex object group will be paied special attention, and its innovation is that we use discontinuous function system, V-system, instead of cotinuous orthogonal function systems to solve the bottleneck problem of a complex object group having discontinuities. This proposal will mainly apply the theoretical results in trademark retrieval to evaluate its effect.

针对平面或立体的由多个几何对象构成的复杂群组，研究：1.在对复杂群组作整体数学表达时，怎样消除通常不可避免的Gibbs现象？2.面对大量的复杂群组，怎样给出群组间差别的量化标准？3.复杂群组的信息处理将面对巨量数据，怎样设计有效的实用算法？4.怎样检验前述3个问题的研究成果的实效？这4个问题在对象分类、模式识别等领域有重要的实用价值。本项研究的基本思想基于非连续正交完备函数V-系统的理论；V-系统的基础理论由申请人提出、并在上一个国家自然基金项目中完成，此为已有基础；本项目将聚焦V-系统的特殊性质进行深入研究，给出多变量V-系统的构造性定义与算法，紧密结合商标检索和模型重用的实际背景，提供具体实践检验的成功例证。本项目的特色首先表现在对复杂群组整体特征的关注，创新在于扬弃连续的正交函数系、而选用非连续的V-系统，解决复杂群组含有间断特性的瓶颈难点问题，并强调以商标检索来检验理论成果的实效。

理论上，完善了本项目的重要数学工具——V-系统的数学理论，得到了数学结构更加完善的V-多小波构造原理、以及V-多小波的存在性理论；应用上，主要致力于群组对象的特征表达及其分类检索，从相对简单的2D图像的特征提取，到复杂的3D模型群组的特征提取，展现了V-系统与经典正交函数系相比较的优势。.项目组共发表学术论文26篇（其中SCI收录5篇、EI收录12篇，核心期刊9篇）。.本项目搭建了比较完善的计算机工作平台，目前的平台无论是针对图像群组还是3D模型群组，处理起来都方便自如，能处理的3D网格数据量达到百万级。并针对2D商标检索和3D模型检索，提供了典型数据库的例证检测数据。研究成果具有鲜明的特色，充分体现了本课题的重要数学理论——V-系统的特点。.V-系统在复杂几何对象的特征提取及分类和检索中的相关应用研究，主要体现在下面几个方面：.①几何造型的2D、3D 整体表达与频谱分析。该项研究可用于几何对象的特征提取进而模式识别，已在多个通用数据库里得到有效性验证。.②在商标注册领域，提供商标查重的新途径。V-系统对复杂边界的商标图像的分类与识别有优势。.③数字图像的处理。包括图像消噪、图像增强、图像融合等，可以有效提高图像的质量。.④ 在3D模型的数字水印方面，提出一种鲁棒性较强的水印植入方案，是频域水印的一个突破。.⑤ 分形的频谱分析。借助V-系统可以对分形进行频谱分析，从另一个角度对自然现象进行刻画，并可用于某些自然现象的预警，是一项创新性研究。