A spectral geometric framework for 3D shape analysis and applications

用于 3D 形状分析和应用的光谱几何框架

• 批准号: 311656-2013
• 负责人: BenHamza, Abdessamad
• 金额: $ 1.46万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=548470
• 关键词: spectral; geometric; framework; 3D; shape

In light of the prodigious popularity of 3D gaming and entertainment, vast databases of 3D models are distributed freely or commercially on the Internet. The availability and widespread usage of such repositories, coupled with the need to explore 3D shapes in depth as well as in breadth, has sparked the need to search these vast data collections, retrieve the most relevant selections, and permit them to be effectively reused. This research program seeks to develop a unified theoretical and computational framework for the design of novel invariant shape descriptors to facilitate comparison and differentiation between shapes or parts of a shape. The main idea is that spectral geometry provides relationships between geometric structures of manifolds and spectra of canonically defined differential operators, while Morse theory gives a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. By combining these theories, this project will study how shape processing, signature extraction, and matching algorithms interact to determine overall shape retrieval system performance. Furthermore, to gain greater insight into my own expertise in algorithmic development for 3D shape analysis, I will focus on translating the theoretical results into realistic practical applications. The goal of this project is to investigate the design and analysis of novel shape descriptors, and also to build on some of our existing work along this direction. In particular, we aim to (i) Formalize both the design and analysis of shape signatures by introducing more sound concepts from spectral geometry and Morse theory; (ii) Develop a theoretically rigorous and computationally feasible methodology for 3D object recognition; and (iii) Explore the use of these signatures in other applications, including animation and multimedia security. The shape signatures that will be investigated in this project provide a new way to look at the shape analysis problem by understanding the intrinsic geometry of a 3D shape. The outcome will be important contributions to the state-of-the-art techniques for 3D shape analysis, and will also have a profound impact on a slew of computer vision, graphics, and multimedia applications.

鉴于 3D 游戏和娱乐的极大普及，大量 3D 模型数据库在互联网上免费或商业分发。此类存储库的可用性和广泛使用，再加上深入和广度探索 3D 形状的需要，引发了搜索这些庞大数据集合、检索最相关的选择并允许有效重用它们的需求。该研究项目旨在开发一个统一的理论和计算框架，用于设计新颖的不变形状描述符，以促进形状或形状部分之间的比较和区分。主要思想是谱几何提供了流形的几何结构和规范定义的微分算子的谱之间的关系，而莫尔斯理论通过研究流形上的可微函数，给出了分析流形拓扑的非常直接的方法。通过结合这些理论，该项目将研究形状处理、签名提取和匹配算法如何相互作用以确定形状检索系统的整体性能。此外，为了更深入地了解我自己在 3D 形状分析算法开发方面的专业知识，我将专注于将理论结果转化为现实的实际应用。该项目的目标是研究新型形状描述符的设计和分析，并建立在我们沿着这个方向的一些现有工作的基础上。具体来说，我们的目标是（i）通过引入来自谱几何和莫尔斯理论的更多声音概念来形式化形状特征的设计和分析； (ii) 开发理论上严格且计算上可行的 3D 物体识别方法； (iii) 探索这些签名在其他应用中的使用，包括动画和多媒体安全。本项目将研究的形状特征通过了解 3D 形状的内在几何形状，提供了一种看待形状分析问题的新方法。其成果将为 3D 形状分析的最先进技术做出重要贡献，并且还将对一系列计算机视觉、图形和多媒体应用产生深远的影响。