A Fractal-based morphological image processing approach to analyze complex structures characterized by closed domains

Fractal geometry concerns the study of non-Euclidean geometrical figures generated by a recursive sequence of mathematical operations. These figures show self-similar features in the sense that their shape, at a certain scale, i equal to, or at least "similar" to, the same shape of the figure at a different scale or resolution. This property of scale invariance often occurs also in some natural events. The basis of the method is the very comparison of the space covering of one of those geometrical constructions, the "Sierpinski Carpet", and the particles location and size distribution in the portion of surface acquired in the images. Fractal analysis method, consists in the study of the size distribution structure and disposition modalities. Such an approach was presented in this paper with reference to the characterization of airborne dust produced in working environment through the evaluation of particle size disposition and distribution over a surface. Such a behavior, in fact, was assumed to be strictly correlated with i) material surface physical characteristics and ii) on the modalities by which the material is "shot" on the dust sample holder (glass support). To get this goal, a 2D-Fractal extractor has been used, calibrated to different area thresholding values, as a result binary sample image changes, originating different fractal resolutions plotted for the residual background area (Richardson plot). Changing the lower size thresholding value of the 2D-Fractal extractor algorithm, means to change the starting point of fractal measurements; in such way, it has been looked for possible differences of powders in th lower dimensional classes. The rate by which the lowest part of the plot goes down to residual area equal to zero, together with fractal dimensions (low and high, depending on average material curve) and their precision (R-2) of 'zero curve' (Richardson Plot with area thresholding value equal to zero, i.e. whole fractal distribution), can be used as criterions to classify the materials and working actions producing dust. For the intrinsic structure of the procedure and algorithms the proposed 2D Fractal Analysis, originally developed for particles, can be successfully applied to man others sectors as biology (cell and tissues), medical imaging, food industry, advanced materials characterization, nanoparticles, composite materials, alloys, etc..