Following B.B. Mandelbrot's fractal theory (1982), it was found that the fractal dimension could be obtained in medical images by the concept of fractional Brownian motion. An estimation concept for determination of the fractal dimension based upon the concept of fractional Brownian motion is discussed. Two applications are found: (1) classification; (2) edge enhancement and detection. For the purpose of classification, a normalized fractional Brownian motion feature vector is defined from this estimation concept. It represented the normalized average absolute intensity difference of pixel pairs on a surface of different scales. The feature vector uses relatively few data items to represent the statistical characteristics of the medial image surface and is invariant to linear intensity transformation. For edge enhancement and detection application, a transformed image is obtained by calculating the fractal dimension of each pixel over the whole medical image. The fractal dimension value of each pixel is obtained by calculating the fractal dimension of 7x7 pixel block centered on this pixel.

Reference is made to the Sobel and Roberts gradient operators used to enhance image edges. Overall, the Sobel operator was found to be superior to the Roberts operator in edge enhancement. A theoretical explanation for the superior performance of the Sobel operator was developed based on the concept of analyzing the x and y Sobel masks as linear filters. By applying pill-box, Gaussian, or median filtering prior to applying a gradient operator, noise was reduced. The pill-box and Gaussian filters were more computationally efficient than the median filter with approximately equal effectiveness in noise reduction.

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