Fig. 5
From: Topological data analysis in medical imaging: current state of the art
Numerous ways to compute PH from radiographic images. a An example 3D slice from a CT scan showing a lung tumor. The red box shows the lung tumor. The segmented tumor pixels are highlighted in white to distinguish them from their CT pixel values, which may be better seen in the following two images. b The same slice of the CT scan image only showing the tumor pixels that have been segmented. c A point cloud illustrating the tumor surface by stacking the tumor contours of all the 2D CT scan slices. d (i) Persistence diagrams derived from sublevel filtration of a 3D tumor image; image b showing a 2D slice. Three persistence diagrams are displayed. Each of the three dimensions of the topological hole under consideration has an unique diagram (H0/0-dim: connected components, H1/1-dim: cycles, and H2/2-dim: voids). (ii) The persistence diagrams, of which a 2D slice is shown in b, were generated by sublevel filtering the 3D tumor image with adjacent boundary box pixels. (iii) The lightly drawn persistence diagrams for the Vietoris–Rips filtering of the tumor surface-representing point cloud in c. e This is the persistent barcode extracted from the PH (H0/0-dim: connected components, H1/1-dim: cycles)