0000000000400989
AUTHOR
Alain Bretto
An Efficient Algorithm for Helly Property Recognition in a Linear Hypergraph
International audience; In this article we characterize bipartite graphs whose associated neighborhood hypergraphs have the Helly property. We examine incidence graphs both hypergraphs and linear hypergraphs and we give a polynomial algorithm to recognize if a linear hypergraph has the Helly property.
Application of Adaptive Hypergraph Model to Impulsive Noise Detection
In this paper, using hypergraph theory, we introduce an image model called Adaptive Image Neighborhood Hypergraph (AINH). From this model we propose a combinatorial definition of noisy data. A detection procedure is used to classify the hyperedges either as noisy or clean data. Similar to other techniques, the proposed algorithm uses an estimation procedure to remove the effects of the noise. Extensive simulations show that the proposed scheme consistently works well in suppressing of impulsive noise.
Hypergraph imaging: an overview
Hypergraph theory as originally developed by Berge (Hypergraphe, Dunod, Paris, 1987) is a theory of finite combinatorial sets, modeling lot of problems of operational research and combinatorial optimization. This framework turns out to be very interesting for many other applications, in particular for computer vision. In this paper, we are going to survey the relationship between combinatorial sets and image processing. More precisely, we propose an overview of different applications from image hypergraph models to image analysis. It mainly focuses on the combinatorial representation of an image and shows the effectiveness of this approach to low level image processing; in particular to seg…