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Hypergraphs for Generic Lossless Image Compression

Gillibert L., Bretto A.

Fundamenta Informaticae

2009

Vol. 91, nr 3-4

533-546

Hypergraphs are a large generalisation of graphs; they are now used for many low-level image processing, by example for noise reduction, edge detection and segmentation [3, 4, 7]. In this paper we define a generic 2D and 3D-image representation based on a hypergraph. We present the mathematical definition of the hypergraph representation of an image and we show how this representation conducts to an efficient lossless compression algorithm for 2D and 3D-images. Then we introduce both 2D and 3D version of the algorithm and we give some experimental results on some various sets of images: 2D photo, 2D synthetic pictures, 3D medical images and some short animated sequences.

A Data Mining Formalization to Improve Hypergraph Minimal Transversal Computation

Hébert C., Bretto A., Crémilleux B.

Fundamenta Informaticae

2007

Vol. 80, nr 4

415-433

Finding hypergraph transversals is a major algorithmic issue which was shown having many connections with the data mining area. In this paper, by defining a new Galois connection, we show that this problem is closely related to the mining of the so-called condensed representations of frequent patterns. This data mining formalization enables us to benefit from efficient algorithms dedicated to the extraction of condensed representations. More precisely, we demonstrate how it is possible to use the levelwise framework to improve the hypergraph minimal transversal computation by exploiting an anti-monotone constraint to safely prune the search space. We propose a new algorithm MTminer to extract minimal transversals and provide experiments showing that our method is efficient in practice.

A combinatorial based technique for impulsive noise removal in images

Rital S., Bretto A., Cherifi H., Aboutajdine D.

Image Processing & Communications

2001

Vol. 7, no 3-4

115-129

The aim of this work is the elimination of the impulsive noise from an image 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 hyperedges either as noisy or clean data. Similar to other techniques, the proposed algorithm uses an estimation procedure to remove the effects of noise. The efficiency of the proposed method was tested on gray scale images using objective image quality measures. The results show that the new method outperforms standard impulsive noise reduction algorithms.