持续同调在图像分类和识别中的应用  

Application of persistent homology to image classification and recognition

作　　者：张景亮 鞠先孟 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2017年第4期494-508,共15页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11371093)

摘　　要：运用持续同调和单纯复形同调群计算的方法对图像做定性分析.将彩色数字图像看作为5维欧氏空间的一个子空间,构造出这个空间在不同参数下的单纯复形;然后,通过计算单纯复形的同调得到相应的条形码,从而基于该条形码来获取图像的拓扑特征以及相应的几何结构信息;最后,探讨了将持续同调应用在图像的分类和识别工作中的可行性.In this paper, we use the idea of persistent homology and the knowledge of algebraic topology to do the qualitative analysis of the digital image. We regard a digital image as a subspace of a 5 dimensional Euclidean space, and then construct a series of simpliciM complexes under different parameters. After that, we can get a barcode through computing the homology of simplicial complexes. The characteristic of geometry and topology can be got from the barcode. In the end, we discuss that whether the topological invariance features are helpful to image identification and classification.

关 键 词：持续同调 计算几何 条形码 贝蒂数 图像分类和识别 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]