Digital topology

Digital topology

Persistent homology of images

Published in Rodrigo Rojas Moraleda, Nektarios A. Valous, Wei Xiong, Niels Halama, Computational Topology for Biomedical Image and Data Analysis, 2019

Rodrigo Rojas Moraleda, Nektarios A. Valous, Wei Xiong, Niels Halama

Here, the aim is to provide a definition of the concept of connected components [13]. A simple model of the digital plane is to treat the set of all points in R2 as having integer coordinates. The concepts of digital topology and geometry are concerned with topological and geometrical properties of subsets of the digital plane (digital sets). In the context of image processing, the digital plane is a mathematical model of black and white elements; the set of black points S and the complement set of white points CS. Given a point P=(m,n)⊤∈Z2 then the 8-neighbors of P are points with integer coordinates (k,l)⊤ such that max (| m − k|, | n − l|) ≤ 1. A practical notation for the 8-neighbors of P is shown in Table 2.1.

Automatic method to calculate the storage volume of refrigerator assembly based on binary voxel images

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Published in Journal of the Chinese Institute of Engineers, 2021

Jianhui Fu, Yoongho Jung, Jin Wang, Guodong Lu, Wei Wang, Xinwei Zhang

To generate a closed voxel boundary, all holes in each part and gaps between adjacent parts of the refrigerator assembly are filled on the basis of a binary image. For the sake of clarity, we first review some notation for digital topology. Then, we introduce the method of filling holes and gaps based on the topological properties of the binary image.

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Persistent homology of images

Automatic method to calculate the storage volume of refrigerator assembly based on binary voxel images