About lacunarity, some links between fractal and integral geometry, and an application to texture segmentation

Two techniques are applied for segmentation of different states of one texture (e.g. deformations of a homogeneous texture): fractal geometry, which deals with the analysis of complex irregular shapes which cannot be described by the classical Euclidean geometry, and integral geometry, which treats sets globally and makes it possible to introduce robust measures. The author focuses on the study of two parameters, lacunarity and Favard length, and proves a theoretical link between them. As an application, the author achieves with an excellent accuracy automatic classification of lung diseases on SPECT images. Classical techniques tried on those images given poor results