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 ava ilable: structured walk, box-counting, dilation and euclidean distance mapp ing (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, r esolution and topology were performed with three computer-derived methods ( box-counting, dilation and EDM), using mathematical objects and fragments c oming from impact and ore deposits breccias. Tests demonstrate that high pr ecision results can be yielded with the right technique and caution. EDM sh owed the highest precision (+/-0.01) and strongest reliability with less se nsitivity to size and resolution, with reproducible results for fragments a s small as 10,000 pixels of area. It was also the most accurate for mathema tical fractals. (C) 1999 Elsevier Science Ltd. All rights reserved.