High precision boundary fractal analysis for shape characterization

Numerous kinds of particles in geological and environmental sciences may be characterized by their boundary fractal dimension. Several methods are available: structured walk, box-counting, dilation and euclidean distance mapping (EDM). The precision and stability of these techniques is variable and usually low precision fractal dimensions are obtained (+/-0.1). Validation on mathematical fractals and tl sts of the effects of pixelization, size, resolution and topology were performed with three computer-derived methods (box-counting, dilation and EDM), using mathematical objects and fragments coming from impact and ore deposits breccias. Tests demonstrate that high precision results can be yielded with the right technique and caution. EDM showed the highest precision (+/-0.01) and strongest reliability with less sensitivity to size and resolution, with reproducible results for fragments as small as 10,000 pixels of area. It was also the most accurate for mathematical fractals. (C) 1999 Elsevier Science Ltd. All rights reserved.