Many image processing problems are ill-posed and must be regularized. Usually, a roughness penalty is imposed on the solution. The difficulty is to avoid the smoothing of edges, which are very important attributes of the image. In this paper, we first give conditions for the design of such an edge-preserving regularization. Under these conditions, we show that it is possible to introduce an auxiliary variable whose role is twofold. First, it marks the discontinuities and ensures their preservation from smoothing. Second, it makes the criterion half-quadratic. The optimization is then easier. We propose a deterministic strategy, based on alternate minimizations on the image and the auxiliary variable. This leads to the definition of an original reconstruction algorithm, called ARTUR. Some theoretical properties of ARTUR are discussed. Experimental results illustrate the behavior of the algorithm. These results are shown in the field of 2D single photon emission tomography, but this method can be applied in a large number of applications in image processing.

Deterministic edge-preserving regularization in computed imaging

Developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined. Particular attention is paid to common estimation structures and to practical problems not properly solved yet. The problem of image reconstruction and restoration is first formulated. Some of the current regularization approaches used to solve the problem are then described. The concepts of a priori information and compound criterion are introduced. A Bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated. The practical aspects of computing the solution, first when the hyperparameters are known and second when they must be estimated, are then considered. Conclusions are drawn, and points that still need to be investigated are outlined. >

Image reconstruction and restoration: overview of common estimation structures and problems

The problem of segmenting images of objects with smooth surfaces is considered. The algorithm that is presented is a generalization of the K-means clustering algorithm to include spatial constraints and to account for local intensity variations in the image. Spatial constraints are included by the use of a Gibbs random field model. Local intensity variations are accounted for in an iterative procedure involving averaging over a sliding window whose size decreases as the algorithm progresses. Results with an 8-neighbor Gibbs random field model applied to pictures of industrial objects, buildings, aerial photographs, optical characters, and faces show that the algorithm performs better than the K-means algorithm and its nonadaptive extensions that incorporate spatial constraints by the use of Gibbs random fields. A hierarchical implementation is also presented that results in better performance and faster speed of execution. The segmented images are caricatures of the originals which preserve the most significant features, while removing unimportant details. They can be used in image recognition and as crude representations of the image. >

An adaptive clustering algorithm for image segmentation

A statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions. The model is a joint probability distribution for the array of pixel gray levels and an array of labels. In boundary finding, the labels are binary, zero, or one, representing the absence or presence of boundary elements. In partitioning, the label values are generic: two labels are the same when the corresponding scene locations are considered to belong to the same region. The distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels, using the Kolmogorov-Smirnov nonparametric measures of difference between the distributions of these features. The number of model parameters is minimized by forbidding label configurations, which are assigned probability zero. The maximum a posteriori estimator of boundary placements and partitionings is examined. The forbidden states introduce constraints into the calculation of these configurations. Stochastic relaxation methods are extended to accommodate constrained optimization. >

Boundary detection by constrained optimization

L'analyse d'image touche a l'heure actuelle de nombreux domaines, avec des objectifs aussi varies que l'aide au diagnostic pour les images medicales, la vision artificielle en robotique ou l'analyse des ressources terrestres a partir des images prises par satellite. Le but du traitement de ces images est a la fois simple dans son concept et difficile dans sa realisation. Simple en effet, puisqu'il s'agit de reconnaitre des objets que notre systeme visuel percoit rapidement, du moins pour la majorite d'entre eux. Difficile cependant, car dans la grande quantite d'informations contenues dans l'image, il faut extraire des elements pertinents pour l'application visee et ceci independamment de la qualite de l'image. L'analyse d'image s'est donc dotee d'outils et de methodes puissants issus de domaines aussi varies que les mathematiques, le traitement du signal, ou l'informatique. Cet ouvrage presente un des aspects les plus importants du traitement des images : la " segmentation ". Il recapitule d'abord les grandeurs observables et calculables sur une image et les algorithmes de manipulation des structures de donnees associees. Il detaille ensuite les traitements preliminaires, tels le filtrage du bruit et les deux types d'approche de la segmentation, l'extraction des contours et celle des regions. Chacune fait l'objet d'une etude theorique et de nombreux resultats illustrent les performances. Une des originalites de l'ouvrage est l'etude comparative des differentes techniques appliquees sur un meme corpus d'images reelles.

https://hal.archives-ouvertes.fr/hal-00706168/document

B. Chalmond

Papers

Image restoration using an estimated Markov model