Computational geometry for polygonal reconfiguration, pattern analysis and recognition and music information retrieval

用于多边形重构、模式分析和识别以及音乐信息检索的计算几何

• 批准号: 9293-2009
• 负责人: Toussaint, Godfried
• 金额: $ 2.19万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=450457
• 关键词: Computational; geometry; polygonal; reconfiguration; pattern

The proposed research aims to develop efficient algorithms for solving geometric problems that arise in the following areas. (1) The exploration of algorithms for the reconfiguration of different types of linkages in 2 and 3 dimensional space, under various restrictions on the types of motions allowed. Another goal is to explore under what conditions linkages are "stuck" in the sense that they cannot be reconfigured to a flat convex configuration. These results are relevant, not only to robotics, but to protein folding in molecular biology. (2) One of the most promising approaches to pattern recognition is the nearest-neighbor decision rule (also referred to as instance-based learning). It is proposed to improve the space and time efficiency of state-of-the-art nearest neighbor rule algorithms, by incorporating proximity graphs. A second objective is to develop new measures of string similarity and polygonal chain similarity for pattern recognition problems. (3) It is proposed to explore the application of computational geometric tools to problems that arise in music information retrieval and music theory. These problems range from measuring the similarity of rhythms and melodies, to performing cluster and phylogenetic analyses of families of rhythms, with the goal of obtaining a deeper understanding of both, music theory and practical applications to music information retrieval. (4) Traditionally the scientific analysis of textiles has been carried out on several physical structural levels of the fabrics. However, a scientific analysis of the geometric structure of the patterns that appear on the textiles has been largely ignored. We propose a new approach to the scientific study of textiles that breaks with this tradition: the phylogenetic analysis of geometric patterns that decorate the textiles. At the heart of our approach is the design of a measure of dissimilarity between two textile patterns, that mimics the way in which biologists measure the dissimilarity between two DNA molecular sequences, i.e., the minimum number of mutations (simple local and global transformations) required to transform one textile pattern into the other. This research will have an impact of image-based search on the internet, as well as textile retrieval systems for use in museums and libraries.

拟议的研究旨在开发有效的算法来解决以下领域出现的几何问题。(1)在允许的运动类型的各种限制下，探索二维和三维空间中不同类型连杆机构的重新配置算法。另一个目标是探索在什么条件下的联系是“卡住”的意义上，他们不能重新配置为一个平面凸配置。这些结果不仅与机器人学有关，而且与分子生物学中的蛋白质折叠有关。(2)最有前途的模式识别方法之一是最近邻决策规则（也称为基于实例的学习）。它提出了提高空间和时间效率的国家的最先进的近邻规则算法，通过将邻近图。第二个目标是开发新的措施，字符串相似性和多边形链相似性的模式识别问题。(3)建议探讨计算几何工具的应用，出现在音乐信息检索和音乐理论的问题。这些问题的范围从测量的节奏和旋律的相似性，进行聚类和系统发育分析的节奏的家庭，以获得更深入的了解，音乐理论和音乐信息检索的实际应用的目标。(4)传统上，纺织品的科学分析是在织物的几个物理结构层面上进行的。然而，对出现在纺织品上的图案的几何结构的科学分析在很大程度上被忽视了。我们提出了一种新的方法来科学研究的纺织品，打破了这一传统：系统发育分析的几何图案装饰的纺织品。我们方法的核心是设计两种纺织品图案之间的相异性的测量方法，该方法模仿生物学家测量两种DNA分子序列之间的相异性的方式，即，将一种纺织图案转换成另一种所需的最小数量的突变（简单的局部和全局变换）。这项研究将对互联网上基于图像的搜索以及博物馆和图书馆使用的纺织品检索系统产生影响。