There is ongoing research directed towards the development of cheap and reliable decision support systems for the detection and prediction of osteoarthritis (OA) in knee joints. Fractal analysis of trabecular bone texture X-ray images is one of the most promising approaches. It is cheap and non-invasive. However, difficulties arise when the fractal signature methods are used to quantify bone roughness and anisotropy on individual scales. This is because the fractal methods are able to quantify bone texture only in the vertical and horizontal directions, and previous studies showed that OA bone changes can occur in any direction. To address these difficulties, three directional fractal signature methods were developed in this study, i.e. a fractal signature Hurst orientation transform (FSHOT) method, a variance orientation transform (VOT) method, and a blanket with rotating-grid (BRG) method. These methods were tested and the best performing method was selected. Unlike other methods, the newly developed techniques are able to calculate fractal dimensions (FDs) on individual scales (i.e. fractal signature) in all possible directions. The accuracy of the methods developed in measuring texture roughness and anisotropy on individual scales was evaluated. The effects of imaging conditions such as image noise, blur, exposure, magnification, and projection angle and the effects of translation of the bone region of interest on texture parameters were also evaluated. Computer-generated fractal surface images with known FDs and X-ray images obtained for a human tibia head were used. Results obtained show that the VOT method performs better than the FSHOT and BRG methods.