A robust and accurate method for calculating the fractal signature of texture in macroradiographs of osteoarthritic knees

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Abstract
In osteoarthritis of the knee, horizontal trabeculae in the tibia thicken, leading to the appearance of horizontal striations on radiographs. Any attempt to understand and monitor the disease process must examine these changes. We have previously described a method of analysing the texture in these images that uses the mathematical morphology operations of dilation and erosion to calculate how image fractal dimension varies with resolution. This variation with resolution is the fractal signature. Calculation of fractal dimension should be independent of linear transformations in image values, and it is shown that careful choice of morphological structuring element is required for this. In this paper we describe the dependence of our method of calculating the fractal signature on image acquisition and digitization parameters. Errors due to variations in pixel size, X-ray exposure, and patient repositioning are small compared to the changes seen in the signature due to osteoarthritic change. Using pairs of orthogonal structuring elements, one tuned to calculate the signature due to horizontal image structure and the other for vertical image structure, texture directionality is examined. The difference between the two resulting signatures in individual knees is shown to be a measure of the change in texture seen in osteoarthritis.