Non-scalable functions as biological object boundary models
Authors: Gridin V.N. , Gazov A.I. , Novikov I.A. , Solodovnikov V.I. , Trufanov M.I. 
Published: January 2022

This article considers the possibility of creating an algorithm for universal image preprocessing that would simplify its segmentation and is suitable for any type of medical or biological study methods. The authors propose a number of equally applicable functions that describe the changes in the parameters of a raster image along the normal to the border of an arbitrary biological object and at the same time doesn’t depend on the instrumental method of image acquisition. The work also determines the absence of any parametric adaptation as the boundary condition for reducing the subjective contribution to the final scientific and practical result. Methods. Based on the biological foundations, the following three simple mathematical expressions were chosen for changing brightness on the border of a biological object: All the functions participating in calculations were not scaled, their size corresponded to the coordinates expressed as raster image dots. The Pearson’s correlation without reliability assessment was used to describe the probabilities of the object’s border being present in the coordinate x=0, and to assess its affinity with properties of the proposed synthetic functions. The basis of functions was tested using digital images of three fundamentally-different objects obtained with different physical detectors: sagittal section of the MRI scan of human head capturing the hippocampus area (Siemens Magnetom Skyra, Germany); optical section of eye cornea (Pentacam, Oculus, Japan); image of transverse histological section of human skin stained with hematoxylin and eosin obtained with microscope (Olympus BX65, Olympus, Japan). In addition, practical evaluation of the applicability of the developed approach was done by processing 100 two-dimensional images of different arbitrarily selected brain MRI sections. A field of probability of the presence of “biological border” in each dot of the image was built for each image. Results. The best affinity — with significant outperformance — to all kinds of digital images of biological objects’ borders was found in the compound function described by the formula. Its affinity to object’s borders on the MRI images was 0.87–0.99; for the borders of biological objects on the images obtained with optical methods it was lower than 0.99 only in two out of seven tests (0.95 and 0.97). Discussion. The high affinity of the proposed compound function may be associated with the fact that the three members of this synthetic expression correspond to three individual additive physical phenomena manifesting its biological basis. The first member is responsible for general biological contrast differentiation — the delineation of tissues appears sharpest at the borders of the organs. The second member describes the conventional membrane present in all healthy organized biological structures, including epithelial lining of the esophagus, muscle fascia, developed mucous membrane etc. The third member of the proposed function characterizes the blurred junction of arbitrarily-uniform structures. The proposed mathematical apparatus describes the formation of scalar field of probabilities for selected borders of biological structures and can easily be transformed into vector representation. Additional advantage of the developed and tested mathematical apparatus is the fact that the formulated approach can be used for determining the orientation of brightness increment gradient. This, in turn, allows distinguishing additional properties of biological objects based on calculation of the direction of development and growth of the tissue and structural anisotropy.