. Le-but-Étant-d-'évaluer-d, on trace log N (k) en fonction de log k puis on détermine un intervalle sur lequel ce tracé semble affine. d est la pente de la droite obtenue. Précisons que le même type de calcul peut aussi caractériser l'image en niveau de gris (i. e. en 3D), mais que les résultats n'ont pas été concluants dans l'aplication présentée ici

. Soit, image, où I(x, y) est le niveau de gris du pixel (x, y). I est lissée par convolution avec, par exemple, un noyau gaussien K ? de variance ?. Notons I ? l'image régularisée I ? = K ? * I. Supposons que I est si irrégulière que la surface (x, y, I(x, y)) de R 3 a une aire infinie

S. Ont-une-aire-finie, Quand ? tend vers 0, I ? tend vers I et S ? tend vers l'infini. La dimension de régularisation dim R mesure la vitesse de convergence de S ? vers l'infini. Formellement : dim R = 2 + lim ??0 log(S?) ? log ?

L. Lacunarité, Lév90] est un paramètre fractal du second ordre qui décrit la texture d'une image. De même que la dimension de régularisation, nous l'avons appliquée sur l'image en niveaux de gris

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