Towards a unitary formulation for invariant image description: application to image coding

摘要

Here, we introduce a joint topology and harmonic analysis formulation for the extraction of global shape descriptors which are invariant under a given group of geometrical transformations. The topology approach allows the rigorous definition of the notions of shape, shape space, the invariant features space, and a metric between shapes. Therefore a new definition of complete- ness is given. A stability criterion is defined mathemati- cally. Using harmonic analysis, a unitary operator that is able to separate the shape information and the geo- metric transformation. Allows us to extract a relevant invariant shape descriptors under a given group of transformations.