Numerous physiological processes holding place in vital organisms: fullness of nutritive products and gases, excretion of rubbish products etc. are formed on a materialisation of freeing of several forms of element particles by porous membranes. Similar processes play a estimable purpose in countless areas of medical therapy based, in particular, on synthetic organs: synthetic lungs-heart, synthetic kidney, encapsulated drugs or vital cells, cultivation of synthetic tissues etc. [1–۵]. Porous membranes focus to H2O or atmosphere catharsis indirectly influences also tellurian health [6–۸]. In all a above-mentioned cases porous membranes play a purpose of filters separating some biochemical media or of scaffolds for seeding and cultivation of tissues. The mechanisms of subdivision or of settling particles (cells) count on biophysical, automatic and micro-structural properties of a porous materials. Examples of biophysical properties are electric- and heat-conductivity, dielectric constant, pH level, etc. Mechanical properties imply specific gravity, Young module, break- or fracture-resistance, etc. The idea of micro-structural properties concerns spatial distribution, density, distance and figure of a components a investigated element consists of, in particular—of pores and/or of a walls that apart them.
It was shown in several former papers [9–۱۳] that mechanism record total with sufficient selected little imaging methods might be an effective apparatus for material’s porosity research and evaluation. The 2D cross-sections of a samples of porous materials yield engaging though rarely perplexing images of magnified pores as cavities and channels perspicacious a material, as shown in Fig. ۱.
Fig. ۱
Examples of nucleus microscope images of several porous materials’ cross-sections
In many cases a pores are of opposite distance and rarely strange shape. However, a idea of irregularity needs some explanation. We call regular curves (contours) or 3D shapes that can be precisely described by elementary methodical functions or geometrical objects. Weakly irregular are contours or 3D shapes that can be described as parameterized compositions of calculable series of unchanging curves (contours) or 3D shapes. Curves (contours) or 3D shapes are strongly irregular if they are conjunction unchanging nor wrongly irregular. The category of strongly strange curves (contours) and 3D shapes can be divided into a sub-classes of random and chaotic objects. Random curves (contours) or 3D shapes are insincere to be means to be described by probabilistic models [14, 15]. Chaotic objects can be described by fractals [16] or any other, some-more sophisticated, fanciful tools. Below, it is insincere that pores with sufficient correctness can be described as random-shape objects. Therefore, no geometrical indication is suitable for their accurate description. The statistical geometry or morphology formed methods [17, 18] seem to be some-more suitable for numerical research of this form of structures. However, deliberation images of pores as instances of specific 2D pointless fields seems to be some-more rational. On a other hand, porosity is a 3D rather than a 2D skill of a firm body. Therefore, it arises a non-trivial problem of receiving information about a 3D structure of a porous element by research of images presenting a 2D cross-sections. The problem is comparatively elementary if a samples of a investigated element can be cut into frequently distanced together slices, as due in [12, 19] Unfortunately, this can't be done, e.g. in a box of high infirmity of a samples. In such case, we are faced with a some-more worldly statistical preference creation problem to be solved by regulating modernized computer-based methods. In this paper some concepts concerning overcoming a problem of 3D morphological structures outline not formed on research of stacks, though of singular 2D images, are presented. The blank information about a 3rd dimension of a examined porous materials’ samples can (at slightest partially) be extracted from a liughtness turn placement in a cross-section images or should be deduced underneath a arrogance of 3-dimensional morphological isotropy of a samples. Below, both methods will be shortly described. However, statistical porosity characteristics report usually some aspects of a investigated materials’ focus in their biomedical applications. The relations between quantifiable morphological parameters and large-scale properties of porous materials are still an open problem requiring additional observations and experiments and it is not deliberate here.
The research of strange structures (in particular, of pores) is not a new problem. Its origins date a Buffon’s needle problem that instituted a growth of stochastic geometry [20]. Roughly speaking, this area of investigations concerns a properties of pointless compositions of unchanging geometrical objects. This is not utterly a problem of rarely strange shapes review outset in biomedical engineering, element engineering, geophysics, geomorphology, etc. [11, 14, 17, 21]. However, any of a disciplines mentioned here uses a specific initial information merger methods and this causes that a analogous information estimate methods are not directly germane in other focus areas. For example, echo-sounding methods of geophysical information merger and SEM imaging of pores yield rigourously opposite forms of initial data, notwithstanding a fact that in both cases they regard reduction or some-more strange morphological structures.
The paper is orderly as follows. The “Materials” territory shortly presents a materials used as a source of picture information subjected to mechanism analysis. The “Theory and methods” territory consists of 4 subsections. The “Preliminary picture processing” subsection presents initial operations directed during encouragement a peculiarity of SEM images before their analysis. The “Basic assumptions” subsection describes some dissimilar geometry objects used in mechanism research of pores. The “Characteristics of strange object” subsection contains definitions of simple parameters used to report strange shapes of pores. The “Rough research of 3D objects’ porosity” subsection is clinging to display of due dual approaches to research of a volumes of pores on a basement of research of their 2D sections: 1st formed on statistical prolongation of geometrical information and 2nd formed on research of liughtness profiles. “Conclusions” enclose remarks summarizing a work.
