Combining the measurement of bone mineral density (BMD) and the classification of the trabecular structure in cancellous bone improves the estimation of the degree of osteoporosis. A fractal method for the automatic quantitative classification of the trabecular structure in midvertebral slices of lumbar vertebrae is introduced. This method is based on the computation of the fractal dimension (box counting method) for varying binarization thresholds. Radiographic images from 30 lumbar vertebrae and CT images from an additional 16 lumbar vertebrae were analysed by calculating the dimension D in dependency of the threshold value T. The function D(T) was normalized by the average image grey value, eliminating the bone mineral density from the computations. The results show that the images of the lumbar vertebrae have fractal properties, and the function D(T) has a typical behaviour that allows the discrimination of the degree of osteoporosis. With two parameters extracted from the function D(T) the correlation coefficients with BMD were both -79% for the radiographic images, and -93% and -91% for the CT data, respectively.