Image = Structure + Few Colors

Topology plays an important role in computer vision by capturing the structure of objects. Nevertheless, its potential applications have not been sufficiently developed yet. In this paper, we combine topological properties image with hierarchical approaches to build a topology preserving irregular pyramid (TIIP). The TIIP algorithm uses combinatorial maps as data which implicitly capture terms critical points. Thus, can achieve compact representation image, and points (maxima, minima saddles). parallel algorithmic complexity building is \(O(\log d)\) where d diameter largest object. We promising results for reconstruction using only few color values although fine details including texture image.