A GAMMA-CONVERGENCE APPLIED TO MULTISPECTRAL IMAGE

Lddir Zait, M; Smara, Y

Bulletin des sciences géographiques de l'INCT
Volume 9, Numéro 1, Pages 22-27
2005-04-30

A Gamma-convergence Applied To Multispectral Image

Abstract

The main objective ofthis paper is to develop a mode\ which combines in the same process image classification and restoration. Image classification consists of assigning a label to eacb site of an image to produce a partition into homogeneous labeled areas. The classification problem concerns many applications, like in the field of remote sensing: land use management, monitoring. urban areas. Observed images are often affected by degradations. The purpose ofrestoration is to find .an original image describing a real scene from the observed one. This problem can be identified by inverse problem. ln general, it is ill-posed in the sense of Hadamard. The existence and uniqueness of the solution are not guaranteed. It is therefore 11ecessary to introduce an a priori coustraint 011 the solution. This operation is the regularization. We can distinguish two types of regularization: lhe linear one and the non-linear. In lhis paper, we develop a model proposed by C.Samson, combining classification and restoration with non linear regularization. lt's based on works developed for phase transitions in fluid mechanics by Yan der Walls-Cahn-Hilliard, and uses a Gamma-convergence theory. This model is named variational mode!, due to the fact that calcul us of variations is ils main lOùl. The classification-restoralion is obtained by mlnimizing a sequence of functionals. The result is a classified and restored image. ru1d corresponds to an image composed of homogeneous classes, separated by minimum length boundaries. The minirnization problem is transformed by Euler-Lagrange equations into PDEs (Partial Differential Equations) resolution problem. We have experimented lhis mode! on synthetic and satellite images. For real images, we have considered images from SPOT-1 sa te Ili te representing the regions of Blida in south-west of Algiers (capital of Algeria). We will discuss at the end of the paper the results we bave obtained.