Persistent Homology Apply in Digital Images

Abstract

Abstract We use the method of persistent homology and complex filter homology group calculation to study digital images. 2D digital images are composed of pixels, 3D images are composed of voxels. Both of them own a natural cubical construction. The complex cubical numbers are more suitable than simple, complex numbers in the field of digital images. At the same time, the way to compute simplicial complex can also apply to study cubical complex and its persistent homology. We construct a cubical complex of this space under different parameters, then calculate the homology of the cubical complex to obtain the persistent diagram, and use it to get the corresponding geometric structure message and the image’s topological characteristics. In the last, we discuss the application of persistent homology to image classification on the support vector machine and random forest method. KeywordsPersistent homologyCubical complexPersistence diagramImage classification