Measurement of boundary fractal dimensions: review of current techniques

Fractal dimensions are extremely useful in quantifying the degree of ruggedness of highly irregular objects. Since the introduction of the concept of fractal dimensions, by Mandelbrot [1], a large number of analysis strategies have been developed to allow the measurement of fractal dimensions. These analysis strategies can be divided into two broad groups, vector and matrix based methods. Vector-based methods include the structured walk algorithms such as the EXACT, FAST, HYBRID and FAENA algorithms. Matrix-based methods, ideally suited to image analysis systems, include Mosaic Amalgamation, Lattice Interception, the Dilation Method, the Blanket Algorithm, Displacement Method and the Distance Transform Method. The EXACT method is ultimately the most accurate vector-based method capable of providing highly detailed Richardson plots, however accuracy is achieved at the cost of analysis speed. The other vector based methods are faster variants of the EXACT method. The Dilation Method based on erosion-dilation logic is probably the most commonly used matrix based method, however, the recently introduced Distance Transform Method is more accurate, produces more data and is substantially quicker.