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4. Extracting local features

4.1. Tracking components in the filtration

To define connectedness on the complex, we specify neighboring relations as follows: the neighbors of each triangle ?T∈K′?T∈K′ (with T =3 T =3) are its three edges, while the neighbors of each edge ?T?T (with T =2 T =2) are the two adjacent triangles in the triangulation. We denote the neighborhood of simplex ?∈K′?∈K′ by N(?)N(?). According to the descending order, and since an edge in a regular triangulation is not larger than its two adjacent triangles, the intuition is that this edge can keep the two triangles disconnected until monocytes is processed itself. Eventually, this timing depends on image gradient and local shape.