基于持久同调的三维模型检索方法  

3D model retrieval method based on persistent homology

作　　者：况立群[1] 李丽[1] 幸嘉诚 谌钟毓 韩燮[1] KUANG Li-qun;LI Li;XING Jia-cheng;CHEN Zhong-yu;HAN Xie(School of Data Science and Technology,North University of China,Taiyuan 030051,China;School of Software,Nanchang University,Nanchang 330047,China;School of Software,East China Jiaotong University,Nanchang 330013,China)

机构地区：[1]中北大学大数据学院,山西太原030051 [2]南昌大学软件学院,江西南昌330047 [3]华东交通大学软件学院,江西南昌330013

出　　处：《计算机工程与设计》2020年第6期1773-1778,共6页Computer Engineering and Design

基　　金：国家自然科学基金项目(61672473);山西省重点研发计划基金项目(201803D121081)。

摘　　要：针对现有拓扑检索方法难以应用于无明显骨架结构的三维模型等问题,提出基于持久同调的三维模型检索方法。运用代数拓扑中的持久同调理论,从不同尺度范围上发现三维模型中的稳定拓扑不变量,捕获其全生命周期的变化,以持久性图作为特征描述子,通过度量持久性图间的相似性实现三维模型检索。实验结果表明,将持久同调应用于三维模型检索,能更准确地提取任意拓扑结构的三维模型的特征,提高了检索的有效性和准确性。Aiming at the problem that existing topological retrieval methods are difficult to apply to the 3D models without ob-vious skeleton structure,a 3D model retrieval method based on persistent homology was proposed.Persistent homology theory in algebraic topology was used to find stable topological invariants in 3D models from different scales,changes in its full life cycle were captured and the persistence diagram was used as the feature descriptor.The 3D model retrieval was realized by measuring the similarity between the persistence diagrams.Experimental results show that applying the persistent homology to 3D model retrieval can extract the features of the 3D models with arbitrary topologies more accurately,and improve the validity and accuracy of the retrieval.

关 键 词：三维模型检索 单纯复形 持久同调 持久性图 相似性度量 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]