MEASUREMENT OF BOUNDARY FRACTAL DIMENSIONS - REVIEW OF CURRENT TECHNIQUES

Fractal dimensions are extremely useful in quantifying the degree of r uggedness of highly irregular objects. Since the introduction of the c oncept of fractal dimensions, by Mandelbrot [1], a large number of ana lysis strategies have been developed to allow the measurement of fract al 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 FA ENA algorithms. Matrix-based methods, ideally suited to image analysis systems, include Mosaic Amalgamation, Lattice Interception, the Dilat ion Method, the Blanket Algorithm, Displacement Method and the Distanc e Transform Method. The EXACT method is ultimately the most accurate v ector-based method capable of providing highly detailed Richardson plo ts, however accuracy is achieved at the cost of analysis speed. The ot her vector based methods are faster variants of the EXACT method. The Dilation Method based on erosion-dilation logic is probably the most c ommonly used matrix based method, however, the recently introduced Dis tance Transform Method is more accurate, produces more data and is sub stantially quicker.