Measuring the Fractal Dimensions of Surfaces

摘要: Abstract : The fractal dimension of a surface is measure its geometric complexity and can take on any non-integer value between 2 3. Normally, the topological surfaces 2; however, their dimensions increase with greater amounts or roughness. For example, 2.3 found to be common in describing relief earth. This paper discusses presents examples an algorithm designed fracticality surfaces. was developed at Ohio State University shown reliable robust. It placed interactive setting based premise that isarithm lines may used approximate surface. operates following scenario: Starting matrix Z-heights, interval selected are constructed A computed for each line by calculating lengths over number sampling intervals. surface's result averaging all adding 1. Potential applications this technique include new means data compression, quantitative roughness, generalization filtering.