Analysis of texture in macroradiographs of osteoarthritic knees using the fractal signature

Texture of regions of macroradiographs (x5) of six normal and five osteoarthritic knee joints, taken on a high resolution microfocal x-ray unit, are examined using mathematical morphology. Radiographs of bones are two-dimensional projections of attenuation coefficient through the three-dimensional (3D) joint structure. Visible texture represents the summation of the attenuation from numerous thin plates of bone. Where there is no organization in the trabeculae, resultant radiographs approximate a fractal surface. Varying structuring element size in mathematical morphology allows estimation of fractal dimension over a range of resolution. Variation of fractal dimension with resolution, the fractal signature, indicates how images deviate from fractal surfaces. By correct choice of structuring element, a texture analysis method using the fractal signature has been developed, tolerant to changes in image acquisition and digitization. Texture in regions of radiographs of normal tibia approximates a fractal surface with dimension 2.8 as does vertical structure in arthritic patients. In osteoarthritic knee joints, horizontal tibial trabeculae thicken. Horizontal structure in the tibia on radiographs of arthritic patients deviates from the fractal model. This is indicated by peaks in the fractal signature whose height and position match a visual assessment of the degree of arthritic change.