Morse-theoretic topological modeling of 3D objects and applications

3D 对象的莫尔斯理论拓扑建模和应用

• 批准号: 311656-2008
• 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: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=480941
• 关键词: Morse; theoretic; topological; modeling; 3D

The importance of 3D object recognition is increasing rapidly in the field of computer graphics and multimedia communication due to the difficulty in processing information efficiently without its recognition. 3D objects consist of geometric and topological information, and their compact representation is an important step towards a variety of computer vision and graphics applications. One of the key mathematical tools used to study the topology of 3D objects is Morse theory, which studies the relationship between functions on a space and the shape of the space.

三维物体识别在计算机图形学和多媒体通信领域的重要性日益增加，因为不进行三维物体识别就难以有效地处理信息。三维对象由几何和拓扑信息组成，它们的紧凑表示是实现各种计算机视觉和图形应用的重要一步。用于研究三维物体拓扑结构的关键数学工具之一是莫尔斯理论，它研究空间上的函数与空间形状之间的关系。