Image Analysis Procedures for Characterizing the Fractal Dimension of Fineparticles

Abstract

Fractal geometry developed by Mandelbrot is finding many applications in the description of rugged fineparticles and fineparticle systems such as packed powder beds. In the earlier publications dealing with the fractal structure of fineparticle boundaries a great deal of the experimental work was carried out manually. This was time consuming and limited the amount of investigative work which could be undertaken in a given context. In this communication several algorithms for automating the evaluation of the fractal dimensions of rugged fineparticle boundaries by automated image analysis are explored. Comparative data generated by the various procedures are presented.

Patch formation and developmental polarity in mycelial cord systems of Phanerochaete velutina on a nutrient‐depleted soil

“…(s)} against log s, yielding a gradient of -Dj^^,. The subtraction term is necessary to avoid an overestimate of the area of the structure at large box sizes since border boxes are not entirely filled by the set (Kaye, 1989). Donnelly et al (1995) photographed mycelial systems and performed image analysis on a projection from the negatives.…”

Fractal Characterization of the Structure of Aerosol Agglomerates Grown at Reduced Pressure

“…A variety of measurement techniques have been described by Kaye and co-workers (Kaye, 1978(Kaye, , 1981(Kaye, , 1983(Kaye, , 1984Kaye et al, 1984Kaye et al, , 1985Kaye et al, , 1987. Two methods that we have used for fractal analysis are the perimeter method (equal-sided circumscribing polygon method) and the dilation method.…”

“…If there is a constant power-law relation between P and S over the range of S, the object is said to have a fractal perimeter. A plot of ln(P) versus ln(S) for a number of estimates using different values of S would yield a straight line with a slope of m. The fractal dimension, D, is then calculated by D = 1 -m. The perimeter method is conceptually simple but is labor-intensive and difficult to implement in an image analysis system, although steps are being made in this direction (Kaye et al, 1987). Other methods are more suitable for automation.…”

Combustion fume structure and dynamics. Final report

“…In addition to the particle area, several shape parameters were measured, including the fractal dimension. Fractal dimensions are frequently measured by the "successive squares" or "boundary dilation" algorithms [8,49,16,50,51,521; however, interpretation of the results from any single algorithm is sometimes difficult. For this reason, three techniques were used to measure the fractal dimension.…”

“…This relation was fit to the data for the range of L,, discussed above. Dcont This fractal dimension is measured by the contour-dilation method [49]. The boundary of the object (including the boundaries of holes) is dilated by 2 pixels (one pixel on each side) in each dilation step Nd (Figure 17).…”