The genus of a digital image boundary is determined by its foreground, background, and Reeb graphs. (English) Zbl 1124.94001
The paper presents the proof of the theorem saying that the genus of the boundary of a digital image is precisely half of the sum of the cycle ranks of three particular graphs. These are: the “foreground graph” and “background graph”, which capture topological information about the digital image and its complement, respectively, and the Reeb graph, relative to the natural height function, associated with the digital image’s boundary. Several additional results are proved as well.
Reviewer: Agnieszka Lisowska (Sosnowiec)
MSC:
94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
05C10 | Planar graphs; geometric and topological aspects of graph theory |
57M15 | Relations of low-dimensional topology with graph theory |
68U10 | Computing methodologies for image processing |