Topographical Tools for Filtering and Segmentation 2 by Meyer Fernand;

Author:Meyer, Fernand;
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2019-03-19T00:00:00+00:00

We consider an edge-weighted graph G(nil, η) and its associated dendrogram X. The ultrametric flooding distance associated with G is χ.

The nodes of the graph G belong to the set N and are denoted by the letters: p, q, r, s, …

The nodes of the dendrogram are the closed ball centered at nodes of G and are denoted by

The diameter of a closed ball is obtained through the operator (s, t) neighbors; ). Thus, . If is a leaf, its diameter is

The weight of the smallest edge in the cocycle of is . If is the root, then .

If is not the root of the dendrogram, it has a father

The ceiling value of a ball is equal to the lowest ceiling value of its leaves: successor of )

We may compare the flooding level of closed balls with scalars thanks to the following equivalence:

. Similar relations hold with replacing the relation “ = ” with relations “ < ”, “ ≤ ”, “ > ”, “ ≥ ”.

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