Directly Computing the Generators of Image Homology using Graph Pyramids

Samuel Peltier (1, 2) , Adrian Ion (1) , Walter G. Kropatsch (1) , Guillaume Damiand (3) , Yll Haxhimusa (1)

1 PRIP - Pattern Recognition and Image Processing Group
2 SIC
3 M2DisCo - Geometry Processing and Constrained Optimization

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, and 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.

Domaines: Modélisation et simulation

Samuel Peltier, Adrian Ion, Walter G. Kropatsch, Guillaume Damiand, Yll Haxhimusa. Directly Computing the Generators of Image Homology using Graph Pyramids. Image and Vision Computing, 2009, 27 (7), pp.846--853. ⟨10.1016/j.imavis.2008.06.009⟩. ⟨hal-00366086⟩