Combinatorics and Image Processing

In this paper, we introduce an image combinatorial model based on hypergraph theory. Hypergraph theory is an efficient formal frame for developing image processing applications such as segmentation. Under the assumption that a hypergraph satisfies the Helly property, we develop a segmentation algorithm that partitions the image by inspecting packets of pixels. This process is controlled by a homogeneity criterion. We also present a preprocessing algorithm that ensures that the hypergraph associated with any image satisfies the Helly property. We show that the algorithm is convergent. A performance analysis of the model and of the segmentation algorithm is included.