Measuring fractal dimensions. Sensitivity to edge-processing functions

Abstract

The fractal dimension is a useful tool in quantitative histology and cytology, and its measurement is easily implemented on computerized image analysis systems. However, the optimal conditions for capture of images and the effect of image-processing functions on the measurement of the fractal dimension have not been reported. Edge-processing functions were applied to images of Euclidean (square) and fractal (Koch island, renal angiogram) objects. The fractal dimension of processed images was measured using implementation of the box-counting method, and the area of thresholded image was also recorded. The method was shown to be accurate, with errors of < 1.5% for objects with known fractal dimensions, and highly reproducible, with a reliability coefficient of 0.972 (95% confidence limits of 0.868-0.987). The fractal dimension of the fractal images showed a marked (> 15%) reduction when a binary noise reduction function was applied with the minimum neighbors limit set above 3. In contrast, the fractal dimension of the Euclidean square was unchanged by this function. The reduction in fractal dimension was due to the erosion of complex convolutions at the edge of the fractal objects. Edge-processing functions should be avoided when manipulating images of fractal objects.