Bernard Laget

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.

A reductive approach to hypergraph clustering: An application to image segmentation

In the last few years, hypergraph-based methods have gained considerable attention in the resolution of real-world clustering problems, since such a mode of representation can handle higher-order relationships between elements compared to the standard graph theory. The most popular and promising approach to hypergraph clustering arises from concepts in spectral hypergraph theory [53], and clustering is configured as a hypergraph cut problem where an appropriate objective function has to be optimized. The spectral relaxation of this optimization problem allows to get a clustering that is close to the optimum, but this approach generally suffers from its high computational demands, especially in real-world problems where the size of the data involved in their resolution becomes too large. A natural way to overcome this limitation is to operate a reduction of the hypergraph, where spectral clustering should be applied over a hypergraph of smaller size. In this paper, we introduce two novel hypergraph reduction algorithms that are able to maintain the hypergraph structure as accurate as possible. These algorithms allowed us to design a new approach devoted to hypergraph clustering, based on the multilevel paradigm that operates in three steps: (i) hypergraph reduction; (ii) initial spectral clustering of the reduced hypergraph and (iii) clustering refinement. The accuracy of our hypergraph clustering framework has been demonstrated by extensive experiments with comparison to other hypergraph clustering algorithms, and have been successfully applied to image segmentation, for which an appropriate hypergraph-based model have been designed. The low running times displayed by our algorithm also demonstrates that the latter, unlike the standard spectral clustering approach, can handle datasets of considerable size.

A multilevel spectral hypergraph partitioning approach for color image segmentation

In many image processing applications, and in the human visual system, relationships among objects of interest are more complex than pairwise. Simply approximating complex relationships as pairwise ones can lead to loss of information. A natural way to describe complex relationships, without loss of information, is to use hypergraphs. In this paper, we use a Color Image Neighborhood Hypergraph representation (CINH), which extracts all features and their consistencies in the image data and whose mode of use is close to the perceptual grouping. We formulate a color image segmentation problem as a CINH partitioning problem. A new multilevel spectral hypergraph partitioning approach is presented. Our experiments on the Berkeley images database showed encouraging results compared with the graph partitioning strategy based on Normalized Cut (NCut) criteria.

Symmetric and semisymmetric graphs construction using G-graphs

Symmetric and semisymmetric graphs are used in many scientific domains, especially parallel computation and interconnection networks. The industry and the research world make a huge usage of such graphs. Constructing symmetric and semisymmetric graphs is a large and hard problem. In this paper a tool called G-graphs and based on group theory is used. We show the efficiency of this tool for constructing symmetric and semisymmetric graphs and we exhibit experimental results.

A New Property of Hamming Graphs and Mesh of d-ary Trees

In this article we characterize two well-known graphs used in many applications, particularly in network applications: Hamming graphs and meshes of d-ary trees MT(d,1). More precisely, we show that they are so-called

Hypergraph coarsening for image superpixelization

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Active appearance model-based segmentation of hip radiographs

-graphs.

Comparison of color median filters

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Pyramid of hypergraphs for image processing

-graphs are a new type of graphs constructed from a group. They have nice algebraic proprieties and can be regular or semi-regular.

Multitextured image segmentation with a pyramid

Image segmentation is a hard task and many methods have been developed to alleviate its difficulties. A common preprocessing step designed for this purpose is to compute an over-segmentation of the image, often referred to as superpixels. In this paper, we propose a new approach to superpixels computation. In a first step, a hypergraph-based representation of the image is built. Then, a coarsening approach is operated on the resulting hypergraph to group pixels which belong to the same homogeneous region. This leads to a smaller hypergraph where each component represents a superpixel of the image. Our approach is very fast and can deal with great sized images. Its reliability have been tested on several real images from nature scenes with comparison to other methods. We show in particular that hypergraphs offer a more accurate image representation than graphs.