An improved algorithm for computing local fractal dimension using the triangular prism method

Despite the many applications of fractals in geosciences, the problem of inconsistent results derived from different fractal calculation algorithms remains. Previous research found that the modified triangular prism method was the most accurate for calculating the fractal dimension of complex surfaces such as remote sensing images. However, when extending the application of the technique into local measurements, new problems arise. Hence, adjustment to the existing technique is needed. This paper introduces a new algorithm for calculating the fractal dimension within a local window based on the triangular prism method. Instead of using arbitrary geometric steps, the new algorithm computes the number of steps needed for fractal calculation according to the window size. The new algorithm, called the divisor-step method, was tested using 4000 simulated surfaces and found to be more robust and accurate than the conventional geometric-step method. The new divisor-step method is recommended especially for local measurements.