Fractional Brownian Motion and Rao Geodesic Distance for Bone X-Ray Image Characterization

Osteoporosis diagnosis has attracted particular attention in recent decades. Textured images from the microarchitecture of osteoporotic and healthy subjects show a high degree of similarity, increasing the difficulty of classifying such textures. Thus, the evaluation of osteoporosis from the bone X-ray images presents a major challenge for pattern recognition and medical applications. The purpose of this paper is to use the fractional Brownian motion (fBm) model and the probability density function of its increments to compute a similarity measure with the Rao geodesic distance to classify trabecular bone X-ray images. When evaluated on synthetic fBm images (test vectors) with the well-known Hurst parameter H, the proposed method met our expectations in which a good classification of the synthetic images was achieved. A clinical study was conducted on textured bone X-ray images from two different female populations of osteoporotic patients (fracture cases) and control subjects. Using the proposed method, an area under curve rate of 97% was achieved.