A hierarchical invariant representation of spatial topology of 3D objects and its application to object recognition

This paper presents a novel invariant representation of spatial topology of 3D objects which may have arbitrary genera and the number of connected components or separating edges. An object is represented by topological invariants in different hierarchies. We apply this representation to object recognition for 2D image inputs and 3D volume images respectively. For fast implementation of this algorithm, we use the cubic pyramid for spatial resolution transformation and fast skeletonisation.