Approximate Minimum Homology Basis for 3D Image and Its Application in Medical Image Segmentation
Jisui Huang, Na Lei, Ke Chen, Yuxue Ren, Zhenchang Wang, Yuanyuan Shang · 2022 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) · 2022
3D medical images consist of voxels with points, edges, faces, and volumes. A fascinating question is how to compute the shortest basis of the first homology group of a 3D image. The fastest time complexity known for this question is O($n^{\omega}+n^{2}$g), where n is the size of voxels and $\omega \lt$ 2.3728639 is a quantity so that two n×n matrices can be multiplied in O($n^{\omega}$) time. But it is still slow in practical applications. We first construct a hexahedral mesh of an arbitrary domain of a 3D image and second propose an approximate algorithm with time complexity O($n^{\omega}$) to calculate the minimal homology basis for the 3D images. Experiments show that our approximate algorithm is very close to the exact algorithm. We demonstrate the effectiveness of our algorithm in segmenting the semicircular canals, the organ with complex topology.