Fig. 1 | Scientific Reports

Fig. 1

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

Fig. 1

(a) From left to right: a vertex (0-simplex), a line (1-simplex), a triangle (2-simplex), a tetrahedron (3-simplex), and so on into higher dimensions. The graph on the right is an example of a simplicial complex with three disjoint connected sets. (b) Čech complex (left) versus Vietoris-Rips complex (right). The Čech complex forms loops by requiring all vertices to share a common intersection, while the V-R complex connects vertices pairwise, leading to the formation of higher-dimensional shapes.

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