In this paper, we propose a new method based on texture analysis for the early diagnosis of bone disease such as osteoporosis. Our proposed method is based on a combination of four methods. First, bone X-ray images are enhanced using the algorithm of Retinex. Then, the enhanced images are analyzed using the fully anisotropic Morlet wavelet. This step is followed by the quantification of the anisotropy of the images using the Rényi entropy. Finally, the Rényi entropies are used as entries for a neural network. Applied on two different populations composed of osteoporotic (OP) patients and control (CT) subjects, a classification rate of 95% is achieved which provides a good discrimination between OP patients and CT subjects.