Hierarchies Relating Topology and Geometry

Cognitive Vision has to represent, reason and learn about objects in its environment it has to manipulate and react to. There are deformable objects like humans which cannot be described easily in simple geometric terms. In many cases they are composed of several pieces forming a "structured subset" of Rn or Zn . We introduce the potential topological representations for structured objects: plane graphs, combiand generalized maps. They capture abstract spatial relations derived from geometry and enable reconstructions through attributing the relations by e.g. coordinates. In addition they offer the possibility to combine both topology and geometry in a hierarchical framework: irregular pyramids. The basic operations to construct these hierarchies are edge contraction and edge removal. We show preliminary results in using them to hold a whole set of segmentations of an image that enable reasoning and planning actions at various levels of detail down to a single pixel in a homo...

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: Walter G. Kropatsch, Yll Haxhimusa, Pascal Lienhardt
• Keywords: DAGSTUHL 2006, DAGSTUHL 2007, Deformable Objects, Potential Topological Representations, Simple Geometric Terms