Fig. 2 | Scientific Reports

Fig. 2

From: A topological approach to positron emission particle tracking for finding multiple particles in high noise environments

Fig. 2

(a) A hollow sphere point cloud comprised of 500 points. (b) The corresponding persistence diagram showing homology groups H\(_{0}\) (connected components like points or edges), H\(_{1}\) (loops formed within data), and H\(_{2}\) (holes or voids in the data). As we expect, the hollow sphere has one persisting hole in the dataset, visualised by the outlying H\(_{2}\) point. The colouring in (a) simply represents the Z-position of the data points, allowing for easier visualisation of the three-dimensional plot.

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