Name
Abstract | ||
|---|---|---|
We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure, i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built by two operations that preserve homology of each region. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on the top level of the pyramid, since the number of cells is small. A top down process is then used to deduce homology generators in any level of the pyramid, including the base level, i.e. the initial image. The produced generators fit on the object boundaries. A unique set of generators called the minimal set, is defined and its computation is discussed. We show that the new method produces valid homology generators and present some experimental results. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.imavis.2008.06.009 | Image Vision Comput. |
Keywords | Field | DocType |
irregular graph pyramids,minimal set,valid homology generator,initial image,graph pyramid,unique set,base level,homology group,homology generators,new method,top level,image homology,homology generator,top down processing | Graph,Discrete mathematics,Singular homology,Homology (biology),Pyramid,Hierarchy,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
27 | 7 | Image and Vision Computing |
Citations | PageRank | References |
13 | 0.99 | 12 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Samuel Peltier | 1 | 77 | 10.05 |
| Adrian Ion | 2 | 222 | 21.11 |
| Walter G. Kropatsch | 3 | 896 | 152.91 |
| Guillaume Damiand | 4 | 367 | 35.56 |
| Yll Haxhimusa | 5 | 233 | 20.26 |