Topographical Tools for Filtering and Segmentation by Meyer Fernand;

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

Figure 6.6. An edge-weighted graph and its associated gravitational graph. A red node is highlighted and its upstream (in blue) is extracted

Figure 6.7. A node-weighted graph and its associated gravitational graph. A node with a red contour is highlighted and its downstream (in violet) is extracted. The downstream contains two distinct black holes, highlighted with a thick blue contour

6.4.2.6. Detection of the black holes

A black hole is a flat zone without outgoing arcs. Inversely a flat zone A which is not a black hole is characterized by the fact that it contains a node p and an arc (p → q) verifying p ϵ A and . The relation is false, which implies that the relation (p ⇄ q) also is false. Since (p → q) is true, the relation (q → p) is false: there exist no return arc from q to p, which is expressed by q ↛ p. This shows that p does not belong to a black hole, and consequently, the upstream of p is also not a black hole.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.