About lacunarity, some links between fractal and integral geometry, and an application to texture segmentation
Résumé
In this work, we apply two techniques for segmentation of different states of one texture (e.g. deformations of an homogeneous texture) : - fractal geometry, that deals with the analysis of complex irregular shapes which cannot well be described by the classical Euclidean geometry - integral geometry, that treats sets globally and allows to introduce robust measures. We focus on the study of two parameters, lacunarity and Favard length, and proove a theoretical link between them. As an application, we are able to achieve automatic classification of lung diseases on the basis on SPECT images.