Design and formal proof of a new optimal image segmentation program with hypermaps

This article presents the design of a new functional 2D image segmentation algorithm by cell merging in a subdivision, its proof of total correctness, and the derivation of an optimal imperative program. The planar subdivisions are modeled by hypermaps. The formal specifications of hypermaps and segmentation are developed in the Calculus of Inductive Constructions. The proofs are assisted by the Coq system. The final program is written in C.