Abstract: The article is devoted to the analysis of some geometric schemes and discussion of the issues arising in this connection of the theory of constructing second-order curves by methods of constructive synthesis. The article shows that the currently used definitions of the center of the second-order curve and the diameters of these curves conflict with the principle of indistinguishability of conics in projective geometry. The ways of eliminating these contradictions are proposed and a unified algorithm for constructing foci of second-order curves is developed on their basis. The author's reasoning, based on the apparatus of projective geometry, will reveal a number of contradictions in the currently existing definitions relating to second-order curves, and their elimination will provide an opportunity to develop a unified approach to the construction of some geometric images initiated by second-order curves and give them a general constructive justification. As a result of the analysis of geometric schemes, a number of concepts of projective geometry were clarified, which made it possible to unify the solution of problems related to the construction of focal points of second-order curves. A unified algorithm for constructing all four foci of the second-order curve is presented. Thus, the basis has been laid for expanding the fields of application of geometric models to imaginary geometric images covered by the concept of a "second-order curve", and conducting research on the resulting geometric images and schemes.

Keywords: geometric modeling, second-order curve, conic, focus, Simplex, imaginary image, collineation, improper point, asymptote, cyclic points

Abstract: This study examines the features of forming in data visualization. To do this, the authors hypothesize that there are special areas of interest on the charts. The user pays attention to them in order to decode data encrypted with graphics. The presence of such areas, and in some cases, points, are intuitively determined during the formation of the design rules of information graphics. To verify them, the study used the eye-tracking method and the cluster analysis method. The application of interdisciplinary principles and rules of infographics design has been studied on the example of horizontal and vertical bar charts, pie, pictorial and flow charts. The result of experiments with various types of charts showed the presence of additional areas of interest not previously indicated by data visualization specialists. This makes it possible to clarify the features of graphic forms and the formation of diagrams, allows you to verify the use of design rules formulated by the efforts of domestic and foreign specialists in the late XIX — early XX centuries. Such verification can be done using a methodology that includes statistical methods and the tracking method, which allows us to take into account the valuable experience of the past in modern information design. The presented procedure can be extended to other types of charts, diagrams and thematic maps, and have practical application in the analysis of big data visualization.

Keywords: pie chart, bar chart, pictorial chart, flow chart, area of interest, eye-tracking method, information graphics, data visualization, doughnut chart, formation

Abstract: The research is aimed at studying the elements that affect the visual perception of the film frame in order to develop methodological recommendations for the process harmonization of the film frame. The object of research is a film frame. The subject of the research is the technology of film frame processing. The purpose of this work is to obtain experimental data of the film frame viewing pattern and to identify statistical patterns to confirm or refute the formulated hypothesis. The goal of the study is to conduct an experimental study of the influence of composition on the parameters of the film frame viewing pattern. The influence of the factor of the mutual ratio of the areas of the centers of interest to the background on the parameters of the template for viewing the stimulus material is investigated. As a result, the methodology has been developed for conducting experimental studies of human perception of visual information using an eye-tracking software and hardware complex. When analyzing data on the influence of the objects size factor. The results obtained show that under the condition that objects occupy a small area of the frame, the observer needs more time to consider this frame. As well as in the case when objects occupy most of the frame (more than 40%). In the first case, due to the small size of the objects, it becomes more difficult for the observer to find objects in the frame space. In the second case, it takes time to identify objects, since they tend to be perceived as a background due to their large size.

Keywords: Cinematograph, Human visual system, Gestalt psychology, Statistical analysis of data, Experiment, Color scheme, Eye-tracker, Film frame, Visual appeal, Composition

Abstract: This article describes the methodology developed by the authors for conducting an experimental study of the perception of the graphical interface of remote control systems for dynamic objects using eye-tracking technology. The developed methodology is an integral part of research on the perception of visual information. The object of the study is a graphical interface of dynamic object control systems. The subject of the study is dashboards in a stimulus slide, their internal content (type, size, quantity). The methodology includes the development of a set of dashboards with different values of the displayed parameter, made in three types of diagrams (linear, columnar, curly quantitative) and in three sizes. The stimulus material of the experiment was developed using a special software module. This module performed the task of filling the stimulus with dashboards randomly. To conduct the experiment, an eye-tracking software and hardware complex was used, which captures the objective parameters of the eye pattern and allows you to shoot arrays of experimental data. Standard methods of mathematical statistics, such as analysis of variance, are used to process the results of the experiment. The developed technique was tested on a limited group. The scientific novelty of this work lies in the development of a methodology for conducting an experimental study on the influence of the factor of the number, type and size of diagrams in a graphic composition, its perception by the viewer.

Keywords: Computational experiment, Analysis of variance, Visual system, Software module, Statistical processing, AI Tracker, Infographics, Incentive material, Human-computer interaction, Intelligent interface

Abstract: This article discusses how to the goal pursuers can simultaneously achieve their goals in the group pursuit task. The proposed pursuit model suggests the pursuer to follow the set motion pattern, which is structured at each point of time. Such trajectory is a compound curve that takes into account the curvature constraints. The time of achieving the goal of each pursuer depends on the velocity and minimum radius of curvature of the trajectory. Multi-factor analysis of velocity modules and minimum radius of curvature of the trajectories of each pursuer for simultaneous achievement of their goals is the focus of this research

Keywords: Attainment, Multifactorial, Trajectory, Line, Curvature, Target, Pursuer, Persuit, Parallel, Plane

Abstract: This article reviews the example of using a geometric model of a hypersurface in multidimensional space on the Radishchev blueprint, which reflects interconnection between the four variables in solution of one of the tasks associated with structuring the technological process fulfilled by a welding robot. In structuring technological processes related to welding, it is necessary to solve the optimization task of determining the position of the foundation of welding robot relative to the welded brackets and the axis of the container of cylindrical shape. The welding process requires finding the most optimal welding robot, the geometric model of the kinematic chain of which would move the output link and welding head across all sections of welding seams. As an example, the author reviews the case when the robot is outside the cylindrical container, and welding objects inside and outside. For carrying out the optimization task, the author examines the correlation between the parameters that determine the position of the robot relative to the container, and the minimum possible vertical displacement of the center of the output link based on the graphic optimization model.  The multicomponent system comprised of the four parameters is studied based on the Radishchev blueprint. The author drew the combinations of curves that set the framework of curve lines of the dual level of the hypersurface in the four-dimensional space. For determination of the curves, the author found the combinations of projections of the dots on the Radishchev blueprint. The use of dual level lines on the Radishchev blueprint allowed determining most optimal position of the manipulator mechanism with regards to the cylindrical surface in welding the items for various industrial robots described in this article.

Keywords: brackets, optimization problem, multidimensional space, Radishchev drawing, geometric modeling, movement synthesis of manipulator, welding, welding robot, hypersurface, cylindrical surface

Abstract: Linear surfaces are used in various spheres of human activity. One of the most common techniques of designing linear surfaces is based on the three directing curves. In some cases, one of these directing curves is not set, but rather replaced by some geometric condition imposed on the emerging surfaces, which can in form of a certain point correspondence established between the points of the rest two directing curves. The article reviews the example of designing such surfaces, which in an approximate form would restrict the zone that sets the permissible positions of links of the manipulator mechanism of certain given configuration in realization of permissible instantaneous states. The acquired linear surfaces underlie the algorithm for calculation of configurations, which do not intersect the restricted zone in case of a deadlock situation. The result of this research is the computer simulation of the motions of arm and torso mechanism of the Android robot using the obtained algorithm for calculation of configurations. The simulation of motion demonstrates that the use of linear surfaces in analysis of the relative position of the manipulator and restricted zones in the deadlock situations allows reducing the calculation time by 50-60 percent. Such reduction of calculation time is highly demanded in computer control of the arm and torso motions of the Android robot on a real time scale.

Keywords: spherical curve, manipulator mechanism, android robot, instant states, ruled surface, geometric modeling, movement synthesis of manipulator, forbidden area, kinematic pair, tapered surface

Abstract: This article reviews the experience of application of VR-AR technologies (virtual and augmented reality technologies) for visual demonstration of production facilities in the process of engineering and operation. The three-dimensional modeling in CAD systems is commonly used as a means for development of construction documentation, visualization of work at different stages of engineering, and preparation of objects for engineering analysis. The authors believe that the use of AR-solutions not in parallel, but along with modern CAD systems for solution of engineering and design problems would allow avoiding design flaws and simplify the process of demonstration of projects. Based on the blueprints and three-dimensional models of the parts and assembly of two-stage reduction gear used  for lifting a thermal furnace in metallurgical production, within the framework of development of the Unity multimedia application is developed the AR application for visual demonstration of the device. As the guide mark for visualization is selected the assembly drawing of the reduction gear in digital graphical format edited in the Vuforia portal. The guide mark database is imported into the Unity environment, the logic of implementation of the technique for demonstrating the assembly of the device and separate parts is written in script program. The application is installed on a smartphone and tested; pointing the camera at the printed assembly drawing allows seeing the 3D model of the reduction gear from different angles, hide any details and scrutinize the device. The AR-applications developed according to the proposed method can be used in the process of training operational personnel, which would improve the performance and quality of work during installation and maintenance of industrial facilities, as well as for displaying the projects during exhibitions and presentations of new products.

Keywords: 3D model, production, AR application, design, digital technology, AR – Augmented Reality, VR – Virtual Reality, demonstration, assembly drawing, training

Abstract: The scientific research related to the use of eye tracking technologies are currently of particular relevance. A substantial area of scientific knowledge, in which it is feasible to use eye tracking technologies, is associated with the study of perception of visual information. One of the trends of such research is the examination of the impact of compositional construction of visual image upon its perception by the viewer. The object of this research is elements of graphic composition (stylistic and color solutions). The subject is the methods and algorithms for digital processing of graphic material. The article employs the computational methods of color correction, eye tracking technology, expert assessment, statistical processing of the obtained experimental data. The scientific novelty of this work consists in the development of methodology of preparing and conducting computational experiments for the impact of the stylistic solution of graphic composition upon its perception by the viewer. The technique developed by the authors has proven itself in carrying out the experiments for studying the effect of color solution of the frame upon its perception by the viewer. The study revealed the statistical significance of the impact of stylistic solution of graphic composition upon viewer’s perception. The hypothesis that abstract graphic compositions are difficult for viewer’s perception was statistically proven. The acquired results can be used in constructing complex graphic images, which require the speed of information perception to view them.

Keywords: Visual appeal, Style decision, Experiment, Statistical treatment, Eye Tracker, Stimulus, Human Visual Perception, Abstract Composition, Digital post processing, Statistical significance

Abstract: One of the promising areas of software development is the modeling of shapes of various objects with graphical representation of the process itself. The relevance of creation of such systems is first and foremost substantiated by providing a potential user with opportunity to visualize the process of shaping the object under the influence of external factors. Such software modules are highly demanded in such fields as modeling of deformation of a steel ingot in manufacturing rolled steel, prediction of occurrence of defects caused by external influence upon objects of various shape, as well as visualization of work of technical equipment related to external impact upon the object, which changes its shape as a result of applied forces. Elaboration of such systems allows inventing emulators that are demanded in educational institutions, as they replace expensive equipment for training practical skills of the students. For example, in medical universities, such software and hardware systems can be used for acquiring practical skills of working with medical equipment, like installation of ultrasonography. The standard training process for carrying out ultrasound examination in a medical university consists of two stages: theoretical and practical. In the course of training, students are not allowed to use ultrasonography machine as many times to be able to acquire sufficient skills in working with medical equipment. Therefore, it is relevant to develop an assistant robotic system for training, which would serve as an emulator of an actual ultrasonography equipment. The first stage of implementation of such project is the development of a specialized software product that would allow visualizing the image of human organs in 3D format with an option of scaling, rotation and deformation, which occurs due to application of pressure on soft tissues using special joystick during ultrasonography examination.

Keywords: simulation model, IT technologies, software, 3D-object, modeling, digital cube, visualization, polygon grid, 3D-modeling, algorithm

Abstract: The author of the work has proposed an algorithm for determining catacaustics in a “source-reflector” optical system on a plane. Katakaustika is called the envelope of reflected rays from a given curve and the study of catacaustics in the design of optical systems is one of the main tasks. The paper gives examples of solving this problem and presents the corresponding visualization. Particular attention is paid to problems where the source and reflector are curved, because these tasks in the scientific literature have not been previously considered. The presented algorithm is based on the cyclographic projection of the spatial curve of the line and its optical property. It is versatile and suitable for all tasks where the source of optical radiation is given in the form of a central (point), parallel or scattered beam of direct (light rays). The main advantage of the algorithm is that in the end it turns out analytical, i.e. exact solution to the problem of determining catacaustics. The results of the study can be used in applied fields of geometric optics, as well as in various computer-aided design systems specializing in modeling lighting of geometric objects.

Keywords: source, wave front, optical conversion, catacaustic, cyclographic mapping, geometric optics, geometric modeling, receiver, reflector, algorithm

Abstract: The article describes a method for determining the linearity of crane rails of bridge cranes by processing photo images. The method does not require marking of the shooting points on the rails, the use of special devices and performing a large number of angular, linear or other measurements. The method uses a horizontal reference line drawn on the image or created using the image on the image of the thread hanging freely in front of the lens cord plummet. The line can also be created using the Plumb-bob program, which gives the image of a vertical line. The image processing algorithm is described using a raster image editor to determine the deviations of the axial points of the rail from the reference line. Various options are being considered for determining the size of one pixel depending on the shooting distance and the height of the camera above the rail. The results of measurements and their comparison with the results obtained by traditional methods, which showed a difference of 0-5 mm are presented. An algorithm for determining the number of pixels contained in a line corresponding to a given distance to any shooting point is described, which allows for the determination of deviations in the image anywhere in the crane path.

Keywords: non-contact measurements, straightdness, reference line, plumb, basis, pixel, photo images, camera, crane rail, deviation

Abstract: With automated planning of the movement of the arm mechanism of an anthropomorphic robot in organized space, there is a need to reduce the time it takes to calculate the trajectory in the space of generalized coordinates. The indicated time significantly depends on the calculation time of the vector of increments of the generalized coordinates at each calculation step in the synthesis of motions along the velocity vector. In the article the geometric studies based on the study of the size and shape of a region in a multidimensional space of generalized speeds specifying the permissible instantaneous states of the arm mechanism of an anthropomorphic robot are carried out. Based on this study a method is proposed that allows one to reduce the time of iterative search of the vector of increments of generalized coordinates. To establish analytical dependences reflecting the relationship between the geometric parameters of the specified area and the generalized coordinates of the arm mechanism, which determine the positions of the configurations, hypersurfaces in four-dimensional space are used. For this, the equations of interpolating polynomials located in four mutually perpendicular planes are used. Based on these four interpolating polynomials, a fourth-order hypersurface equation is obtained that reflects the relationship of geometric and kinematic parameters. The article also presents the results of virtual modeling of the movement of the arm mechanism of an anthropomorphic robot, taking into account the position of the forbidden zone in the system ACAD. The results of calculations using the obtained analytical dependences showed a reduction in the calculation time of test tasks. The conducted studies can be used in the development of intelligent motion control systems of autonomously functioning anthropomorphic robots in an organized environment without the participation of a human operator.

Keywords: kinematic model, geometric modeling, space of generalized coordinates, movement synthesis of manipulator, objects of multidimensional space, humanoid robot, instant states of mechanism, velocity vector, nodal points of mechanism, linear shifts

Abstract: The purpose of this article is to demonstrate the possibility of identifying minerals characteristic of desert regions under expeditionary conditions and in small laboratories that do not have the means to provide energy dispersive microanalysis (EDXMA) or mapping methods of wave dispersive spectroscopy (WDXRS), due to the use of hotel points as an identification technique and areas of interest (ROI) on a sample of correlation spectral image analysis (QAVIS) software. It is proved that this technique allows the identification of individual, resource-valuable minerals using the integral frequency and integral spatial characteristics, as well as the Fourier spectrum itself and the correlogram between the samples. Registration was made on the JEOL JSM system digitized by P.L. Alexandrov (IBCh RAS). The measurements were carried out using QAVIS software, developed at the Far Eastern Branch of the Russian Academy of Sciences by the team of the Laboratory for the Analysis of Oceanological Information (developers - Goncharova A.A., Fischenko V.K.), Department of Information Technology, Pacific Oceanological Institute named after V.I.Ilicheva FEB RAS. Efficiency of video processing is provided by using one of the “fastest” discrete Fourier transform libraries - FFTW and careful optimization of the QAVIS program code by the authors of this program (the program works with computer video memory, which allows you to process all frames of the video stream at the same time as it is viewed on a computer screen). Thus, it has been shown that program correlation-spectral analysis can serve in working with desert and relevant minerals not only for additive analysis of minerals using scanning microscopy methods, but also for distinguishing submicrostructures of these formations and obtaining histograms of statistical distributions of their descriptors.

Keywords: FFTW library, mineral shape computation, real time mode, Fortran, C general-purpose programming language, Discrete Fourier Transform, correlation spectral analysis, two-dimensional Fourier transform, image analysis, surface roughness

Abstract: The article presents the results of determining the moisture-binding ability and plasticity of food products. Many indicators depend on the ability of meat and fish to bind moisture, including juiciness, tenderness, yield, loss during heat treatment, and appearance. The objects for research were Baikal omul, fresh and salted, beef meat in thawed condition. The moisture-binding ability and plasticity of the objects of study were evaluated by the pressing method. The paper presents the calculations performed using the traditional method and the method of digital processing of color images. Digital image processing was performed using a program developed by the authors, the article provides drawings and tables obtained during image processing. The undoubted advantage of the processing program compared to the traditional method is a significant reduction in time for processing images and the ability to process a large amount of data in a short time. When creating the necessary shooting conditions, the digital image processing method for determining the moisture-binding ability and plasticity of food products can be successfully used for laboratory research in determining the quality of meat and fish products.

Keywords: Grau-Hamm method, pressing method, RGB color model, digital image processing, plasticity, water binding ability, non-destructive testing methods, pixel, ashless filter, data processing

Abstract: The article presents an algorithm for modeling a composite curve of the first order smoothness. The necessary formulas for determining the bypass consisting of arcs of third degree polynomials are given. The first option describes the approximation of the entire array of points with the requirement of incidence of the first and last points of the contour. The second option considers the modeling of a curve, with the requirement of incidence of the first point and the free end at the last point, using the principle of drawing curves. In the third variant, the curve must pass through the last point of the array, and at the first point it must meet the requirement of the first order of smoothness tangentially obtained in the previous step. Special points are preliminarily defined on the object - the breakpoint of the contour and points with vertical and horizontal tangents that impose smoothness conditions on the modeled bypass. To model a curve, the least-squares approximation is performed by third-degree polynomials on the set of ordered points bounded by the break points that make up the edge. The advantage of the developed contour modeling method is, firstly, the possibility of processing a large array of points with the observance of a given accuracy. Secondly, it is much easier to ensure the smoothness of the first degree of bypass compared to other methods that use various functions of connecting arcs of the bypass, and it is also important to significantly reduce the amount of data being processed, while maintaining the required specified accuracy. Further works will present the remaining options and formulas for the calculation and their application in the field of reverse engineering, in solving problems of geometric modeling in image processing.

Keywords: reverse engineering, smoothness of the curve, least squares method, approximation, curve fitting, geometric modeling, point clouds, image processing, 3D scanning, data compression

Abstract: The subject of research is the optical transformations of pairs of basic geometric objects on a plane that simulate various sources of radiation. In the general case, when solving problems of geometric optics on a plane, the task of transforming one beam of rays into another, for example, converting rays of a point source into a system of parallel rays, is distinguished. Such tasks require the creation of a relatively simple method based on the laws of geometrical optics and allowing one to obtain reflective lines of a certain geometry corresponding to the given initial data. Obtaining a reflective line for different combinations of central, parallel and scattered direct beam transformations in this work is based on the cyclographic display method. The method is based on the optical properties of a cyclographic model of a spatial curve of a line and makes it possible to obtain reflective curves of various shapes during optical transformations of straight beams. The use of this method in building a source-receiver system makes it possible to select a receiver (or source) from a variety of receivers (sources) with the same reflector line. The study showed that the cyclographic mapping method makes it relatively easy to obtain reflective lines during optical transformations of various beam beams, while the analytical algorithm makes it possible to obtain parametric equations of this line. The results of the work can be used in the design of various optical systems in the antenna, laser and lighting engineering industries.

Keywords: evolvent, reflective lines, cyclographic mapping, pencil of rays, geometrical optics, Optical transformations, evolute, ruled surface, intersection line, spatial visualization

Abstract: The article presents new methods of experimental study of the influence of color on the perception of a movie frame by the viewer and software algorithms for processing the obtained statistical data. The object of scientific research is filmed and edited film material, including individual graphic images of video frames. The subject of the research is graphic models of color solutions, digital color correction methods, digital cinema and video processing algorithms. The specificity of the computational experiment put into practice is that it is conducted online using the Internet resources.The described method is the development of existing methods for the experimental study of human oculomotor activity using I-tracking technology. The proposed methods and algorithms for experimental studies of the influence of color solutions on their perception allow us to objectively measure statistical data and analyze the work of human visual activity according to various criteria. The development of an Internet application has allowed many more subjects to be involved in a computational experiment and to increase the reliability of statistical results.

Keywords: Computing Experiment, Human Visual Perception, Visualization, Digital Color Correction, Graphic Model, Color Scheme, Film Frame, Cinema, Internet Resources, Statistical Data Processing

Abstract: The paper proposes the solution of a number of problems related to the optimization of recognition of information signs by the correlation-extremal contour method based on the evaluation of similarity invariant with respect to affine transformations.A description is given of a speed-efficient algorithm for obtaining regions of a certain color and its parallelization. It is shown that solving this problem allows reducing both the number of objects presented for recognition and the number of standards used, as well as obtaining a better contour description of objects and, therefore, significantly increasing the speed of the recognition algorithm itself. The solution of the problem of optimization of calculations in the recognition algorithm itself is given. It is shown that one of the ways to solve this problem for a particular chosen recognition algorithm is to parallelize the computation of the similarity estimate by the affine transformation parameters. Another presented way of solving the problem of optimization of computations was focused on obtaining estimates of the similarity of the current standard with objects from the local area of the image, which is determined on the basis of the parameters of affine transformation and dimensions of the standard. It is noted that the created algorithmic software allows to solve problems of recognition of information objects in real time.

Keywords: affine transformation, optimization, color segmentation, parallel algorithm, pattern recognition, image processing, computer graphics, standart image, adaptive description, correlation-extreme contour method

Abstract: The object of the study is a numerical simulation of the process of incremental forming of sheet metal in the manufacture of thin-walled parts on equipment with numerical program control. Particular attention is paid to the problem of constructing the surface of deformation of a sheet blank, under the influence of a working tool.The subject of the study is the solution of the problem of constructing a smooth three-parameter body with a layered structure using Bézier boundary surfaces from given interpolation nodes. The body is built on a frame, consisting of a set of curvilinear octagonal portions, in which the opposite boundaries have different parametric lengths.The method of investigation is a method for constructing a three-parameter body with a layered structure using Bezier boundary surfaces using the technology of parametric solid modeling. The novelty of the study is to develop a method for constructing a smooth three-parameter body of a layered structure on an arbitrary frame in the form of Bézier.Main conclusions. The use of the cubic Bézier function with parameterization along the length of the arc for describing the body of a multilayer structure provides additional advantages in controlling the shape and internal space of the body than the construction constructed using the generalized Hermite interpolation.Parametric three-dimensional bodies of this type can be effectively used in finite elements with irregular boundaries to avoid difficulties in constructing a model for such structures.

Keywords: lamellar deformation, Bézier surface, Bézier curve, interpolation, lamellar body, body portion, three-parameter body, solid modeling, incremental forming, multilayer structure

Abstract: The object of the study are open digital terrain models located on the Internet. The subject of the study is the procedure for eliminating the errors of digital terrain models aimed at increasing the reliability of calculations of the morphometric characteristics of basins of water bodies. This article is devoted to the improvement of methods for processing and modifying geoinformation features by processing digital high-altitude relief models. The approaches outlined in this paper are aimed at increasing the reliability of calculating the main morphometric characteristics of the relief by eliminating errors in the original data. Usually for morphometric analysis, cartographic works are used, according to which the defined relief forms contain subjective errors. The values of these errors can then affect the results of the analysis, since the quantitative characteristics depend on where and how the boundary of the form passes. Given the presence in the initial open data of a number of high-altitude distortions that indicate their inapplicability to use for qualitative morphometric analysis at the level of private watersheds, the paper considers ways to adjust their geometric characteristics by eliminating the influence of tree vegetation and preserving the relief's relief using the Lagrange coefficients. A comparison of the results of a particular morphometric analysis obtained using corrected relief models with results obtained from other data is given. To increase the reliability and automate the processing of the digital model of the river basin relief, which is a regular network, it is necessary to carry out analysis in private watersheds with an area from 0.6 to 0.8% of the total area of the basin.

Keywords: geoinformation system, normalized difference vegetation index, forest vegetation, digital elevation model, Lagrange interpolation polynomial, normal Gaussian distribution, geometric modeling, remote sensing data, morphometric analysis, open source

Abstract: The presented article deals with the application of affine transformations in solving problems with second-order curves, namely, stretching and contraction with respect to a straight line, that is, transforming a circle into an ellipse and vice versa.Ellipse finds the widest application in various fields due to the grace of form and its properties: in art, design, architecture, physics and technology, astronomy, its properties are described in fiction. The construction of an ellipse can be done very accurately with the help of improvised tools (pegs, threads, kinks of the circle, using a strip of paper), special adaptations and modern computer systems of mathematical modeling and CAD. The methods of constructing an ellipse are based on its properties, which also determines its shape.Using the laws of affine transformation will help to strengthen the skills of applying the properties of an ellipse and solving problems in determining its basic parameters. Method of work. The article presents methods of transformations aimed at determining the large and small axes of an ellipse, constructing tangents to an ellipse, and determining the points of intersection of a straight line with an ellipse.As a result of the work, algorithms for solving problems have been obtained that allow the authors to determine the intersection point of a straight line with surfaces of the second order (paraboloid, hyperboloid of one sheet) and a truncated cone using the method of a related transformation. The authors also determine the axes of the ellipse, the points of tangency and the intersection of the line with the ellipse. Scientific novelty. A method is proposed that makes it possible to simplify the solution of design problems on the intersection of a second-order surface with a straight line and a second-order surface, which will contribute to an increase in the accuracy and adequacy of their construction.The properties and essence of the affine transformation of an ellipse into a circle are shown and vice versa. The algorithms for solving various geometric problems based on the application of related transformations are demonstrated. The materials of the work are of practical importance, since they significantly broaden the concept of how to solve various problems with second-order curves.

Keywords: perpendicular straight lines, related points, conjugated diameters, axis of kinship, ellipse, affine transformation, circle, tangent, curves, intersection

Abstract: The goal of the presented study is to increase the effectiveness of recreating realistic shadows of dynamic 3D movie characters at the stage of digital post-processing of film and video material due to mathematically justified temporary replacement of high-poly three-dimensional surface modeling by low-polygonal without compromising the quality of the final product in the cinematographic industry. The object of this scientific research is the filmed and mounted film and video material and individual graphic images of film frames. The subject of the article are models, methods and algorithms for digital processing of video material. The methods of three-dimensional surface modeling by various polygons, program algorithms for geometric calculations of invisible lines and projections of 3D objects onto a three-dimensional surface are studied. New effective methods and software algorithms for reducing the dimensionality of the polygonal 3D model have been developed, which are justified mathematically and have made it possible to significantly reduce the amount of computer calculations of dynamic shadows without degrading the quality of the video material. An example of the practical implementation of new models and methods for recreating shadows in cinematography is given.

Keywords: Low-polygonal Modeling, 3D Model, Dynamic 3D Object, Shadows Recreation, Digital Video Post-processing, Cinematography, Video Frame, Geometric Computation, Efficiency Improvement, Mathematical Justification

Abstract: The study is devoted tp algorithms of segmentation of satellite images for various systems of technical vision. For the segmentation of images authors use sections on graphs. Preliminary segmentation is performed based on the minimal spanning tree to improve performance. When describing the properties of super pixels, information about the height and color of the regions is taken into account. The height of the areas is calculated based on the stereo images. The color of segments is calculated on the basis of color invariants. All super pixels in accordance with their characteristics belong to the areas of buildings, grass cover, trees and shrubs, shaded areas, etc. The image is an undirected weighted graph, the nodes of which are segments of the image. The weights of the vertices of a graph are numbers that determine the membership of a certain class. To divide regions into clusters, the method of cuts on graphs is used. The novelty of the study is the algorithm for segmenting satellite imagery based on super pixels and graphs. The segmentation time on the basis of the developed algorithm decreases several times in comparison with the method of cuts on graphs. The developed algorithm is used to allocate buildings to images. Comparison of the developed algorithm with existing approaches of building allocation is shown, its advantages are shown. Examples of the operation of the algorithm are given by the authors of the article and the results of the research are described.

Keywords: pattern recognition, computer vision, image processing, satellite imagery, graph cuts, spectral graph theory, superpixels, image segmentation, scene analysis, color invariants

Abstract: The subject of the present research is the theoretical research of Hilbert curve properties that allow to arrange an efficient access to image pixels during slider filter image processing by using Hilbert curve as a image point traversal order. The effect is achieved by means of reducing the number of repeated memory operations during adjacent image pixels and equally distributing restored pixels at horizontal and vertical steps between image pixels. The research method is the theoretical analysis. The validity of theoretical results is proved by previous experimental researches the authors of the present article refer to. The novelty of the research is caused by the fact that the authors give a theoretical substantiation of previous experimental researches. The authors give their evaluation of a number of memory operations that can be avoided during image point traverse along Hilbert curve depending on the size of a sliding filter. The authors also carry out a comparison with other continuous traversal orders (such as horizontal steps between pixels from the point of view of counting distribution of readings during filtration. 

Keywords: graphical computing, continuous traversal order, memory access pattern, memory bandwidth, high performance, theoretical analysis, sliding image filter, image processing, Hilbet curve, image memory layout

Abstract: The subject of the research is the morphometric properties of Al2O3 (aluminum oxide) micro-disperse system. The authors pay special attention to the fractional composition and particle sphericity factor for defined particle groups constituting the disperse system. The authors state that image analysis allows to use the sphericity factor for evaluating elements of the particle surface combined with the interpretation of a real geometrical shape of individual particles. This allows to better define the dispersion factor as an important property of a disperse system because this parameter may be a measure of substance activity in a disperse system. Digital images for analysis ere obtained using a scanning electronic microscope with a high resolution S3400N HITACHI (made in Japan). Images were analyzed using a universal software ImageJ-FiJi. The object of the research was the powder Al2O3 of Sigms-Aldrich brand (article 265497, α-phase, particle average size is 10 micron). The powder was made at mills with spherical grinding bodies. The main conclusion of the research is that image analysis is a powerful tool that can be used to define physical properties of disperse systems. For the first time in the academic literature the authors focus on analyzing angles created by particle brim peaks. By calculating the dispersion factor, the authors have demonstrated that data obtained during particle image analysis allows to increase efficiency in defining the real factor of particle dispersity with the average validity of 5%. 

Keywords: Aluminium oxide, disperse systems, surface texture, granulometry, sphericity factor, morphology, image analysis, dispersion factor, microscopy, metrology

Abstract: Improvement of the quality of mechanical parts and products is one of the high-priority tasks. This task is achieved by increasing accuracy, automation of control and implementation of a single concept of part accuracy assurance at all stages of life cycle. The tool to solve this task is a universal algorithm created by the authors to construct and visualise a geometrical model of a real part. The scientific novelty of the resaerch is caused by the fact that the authors take into account information capacity of elements, coordinate planes and axes and materialized sets of parts bases. The practical important of the algorithm is proved by the results of using it as a method of regulating dimensional and geometrical accuracy of a mechanical part. In the process of building a geometrical model, the authors have used the modular principle where a possible number of freedom degrees deprived by each element of the module is known beforehand. Geometrical model's properties, notes and recommendations are input in the form of a matrix into the data base. The geometrical model starts with the image of a generalized coordinate frame OXYZ on a one-three view contour drawing of a mechanical part. The number and image of coordinates and initial calibration accuracy of each main base are determined by the number and image of movements that haven't been spent by the base for creating a generalized coordinate system. Angular coordinate sizes and graduation errors are calculated starting from coordinate axes with the 4 and 2 information capacity and marked on projections perpendicular to turning point axes. Linear coodinate sizes and their graduation errors are calculated along relevant coordinate axes together with the reference coordinate values including zero values. The surface of elements which bases materialize coordinate systems and executive surfaces have an inclined form that is visualized on the model as the main wavy lines tangent to the elements. The main feature of this approach which also reflects the novelty thereof is that it allows to objectively evaluate all necessay geometrical characteristics of a mechanical part based on the principle of unity of bases. The algorithm offered by the authors may form the basis for developing the automated quality management system in the processes of mechanical part design and production. 

Keywords: accuracy, geometrical properties, coordinate plane, coordinate axes, automation, control, visualisation, set of bases, algorithm, geometrical model

Abstract: The immediate object of studies is the module for automatic detection for the manipulator mechanism collisions with the prohibited zones, which is used in intellectual robot guidance. The object of studies involves geometrical analysis characterizing the position of the manipulator mechanism and the known prohibited zones.  The authors provide detailed analysis of analytical value of the allowed configurations sphere within the space of generalized coordinates with two prohibited zones present in the working space of a manipulator. The generalized coordinates space is provided for by the axes of the rectangular coordinates system based upon the directions of angles  providing for the movements in the turning pairs.  It is offered to use the sufficient condition for the collisions based upon the usage within the space of allowed configurations. All of the allowed configurations within the generalized coordinates space are reflected by a geometrical object.  The said geometrical object is provided for via analytical means with the use of several kinematic surfaces limiting it. The main result of the study is shorter calculation period for test assignments regarding virtual modeling for the manipulator movement of a "Komodo dragon" mobile robot with the use of the detection algorithm for collisions between the mechanism and the environment. The special input of the authors into the issue involves the development of the knowledge database assignment, which is used for intellectual guidance for manipulator motion in the familiar environment.  The novelty of the study is due to the development of the more productive method of information analysis on the position of manipulator mechanism and prohibited zones based upon the analytical dependencies, which are used to establish the allowed configuration space. The use of this space  for the trajectory synthesis within the generalized coordinates space allows one to correct the manipulator motion in order to predict and to exclude the dead-end situations when synthesizing the velocity vector movement.

Keywords: kinematic couples, intelligent robots, restricted areas, knowledge base, the virtual model operation of movements, kinematic surfaces, geometrical analysis, robot traffic control, area of allowed configurations, space of generalized coordinates

Abstract: The objects of the study are articulated lever mechanisms based on the use of third-order third-class structural groups by the Assur-Artobolevsky classification. These mechanisms are studied and designed as actuators of high-performance machines. Of the many lever mechanisms of the third class, the so-called limit-forming mechanisms are singled out to become the object of studies,  making it possible to obtain approximate outgrade of the output link, and, consequently, of the working tool by using the limit positions of the lever diads. The third class articulated lever mechanisms of the third class are being analyze, due to their kinematic features these mechanisms allow to provide approximate out-riggers of the output link in both its extreme positions in accordance with the preassigned operating schedule of the machine.The method of the study of hinged mechanisms with approximate stops of the out-put link in the two extreme positions according to the given cyclogram is the method of constructive geometric modeling as the basis for the development of an analytical geomet-ric model of the mechanisms under consideration. Based upon the constructive geometric modeling  the authors propose the method for designing six-link mechanisms of the third class with two approximate stops of the output link in the extreme positions according to the preassigned cyclogram. Possible branching of the kinematic scheme of this mechanism is revealed. An analytical geometric model for the synthesis of six-link hinged mechanisms of the third class as executive devices for high-performance machines for printing, food, textile and a number of other industries has been created by the authors.

Keywords: dwells, free parameters, Chebyshev approximation, working body, geometric construction, branching, cyclogram, kinematic scheme, hinged mechanism, Geometric modeling

Abstract: The article reviews algorithmic support of multispectral video systems in the part of automatic selection of the most informative channels, which are video sensors of different spectral ranges, forming images of different informativeness depending on weather conditions. Such systems can be used to increase the awareness of aircraft pilots or operators of unmanned aerial vehicles in difficult weather conditions. The usage of these algorithms is considered using the example of airborne systems of improved (enhanced) vision where it is necessary to give the pilot a single combined image of the external situation, due to the limited space of the information-control field of the cockpit and the increased requirements for decision-making. The development and research was carried out using the base of video sequences obtained in the course of real flight experiments of the prototype of a three-channel video system as well as expert judgment on the consistency of the results of the work of algorithms with visual perception. The study is the further development of image analysis algorithms in terms of their informativeness. The article proposes a new adaptive algorithm for automatic selection of individual video channels for their subsequent integration based on the information-free metric of informativity. The proposed automatic calculation of the priority of video channels for informativeness showed its consistency with the subjective perception of useful information by the human operator.

Keywords: multispectral system, computer vision system, human-machine interface, image fusion, combined images, visual perception, image information value, evaluation of the information value, image analysis, enhanced vision system

Abstract: The issues arising in the implementation of the technical approach to the recognition of the group point object (GPO) images on the basis of the binding elements of the continuous associated images (CAI) are considered. The basic CAI formation models of the point scene defocusing are analyzed. For bell-shaped and rectangular impulse response obtained defocusing filter selection rules limiting circuit CAI level with maximum fault tolerance quantization of the image brightness. Concretize methodology harmonization CAI model parameters with the density of the GPO members. For clarity and simplify the operator interface work with models CAI highlight - radius of the filter impulse response the ratio of the radius with a threshold localize spatially compact objects is obtained. Synthesized numerical method for the formation of base procedure ASO, characterized by one - two orders of magnitude higher performance than with an approach based on the fast Fourier transform for compact GPO. The method is based on the filtering properties of the deltoid brightness distribution GPO elements and limitations of the low pass filter window size based on the number of quantization levels of its impulse response. The results are aimed at ensuring the quality of the detection procedures, permits and GPO recognition in noisy images, set in a one-dimensional, two-dimensional and three-dimensional spaces in their technical implementation.

Keywords: spatial compactness, model optimization, spatial localization, point scene analysis, image recognition, point field, continuous associated images, group point object, fast filtering, numerical methods

Abstract: The article describes the technical, algorithmic and software components machine art system designed to automate the creation, reproduction and restoration of artistic images by simulating the method of mixing colors on the palette and brush application. The system consists of a robotic arm, which provides applying paint on the basis, and automatic palette - a special device for mixing paint and supplying the desired color mixture to the working tool of the robot, controlled by special software. The algorithms, used in the system of image processing, belong to the field of artificial intelligence. Mathematical and software components of the described system have been tested on a set of test images. An experimental stand was built work out the basic elements of the mechanical part of the system. During the study a new image processing algorithms along with specialized software and hardware have been created. For the first time software and hardware system for mixing paint for a single brush stroke has been developed. This automated palled allows implementing a full-color painting in fully automatic mode. The presented machine art system can be widely used in various branches of the fine arts, design, restoration, while creating paintings, murals, decorative design with technical objects, household items, light- resistant for durable printing and so on. In the future authors plan to create a system for large-format images and introduce a feedback system.

Keywords: non-photorealistic rendering, tinting, cybernetic art, color mixing, robotics, polygraphy, robotic painter, machine painting, brush stroke placement, artificial intelligence

Abstract: The subject of the present research is the development of the algorithm for the fast inverse discrete transform of the 8x8 ITU-T H265 (HEVC) video coding standard. The authors of the article analyze differences between the structures of the inverse transform matrix and inverse discrete cosine transform matrix as well as approaches that may be applied to factorization of the aforesaid matrix. They also provide an evaluation of a number of operations necessary to perform the transfer. The authors conduct a numerical experiment to prove the efficiency of the developed algorithm from the point of view of the speed of performance on the central processing unit (CPU). The research method used by the authors is the theoretical analysis and numerical experiment including collection of relevant information and analysis of results. To conduct the numerical experiment the authors have written a C-language program that executes a standard algorithm of the inverse transfer (direct multiplication of the transform matrix and coefficient vectors) and the fast algorithm of the inverse transfer as it is described in the theoretical part of the research. Then the authors have compared the productivity results. The novelty of the research is caused by the fact that the authors offer a new algorithm for the fast transfer of the 8x8 HEVC standard and the scheme of inverse matrix factorization. Compared to previous researches and algorithm, the given algorithm requires fewer arithmetic operations, thus takes less time. At the end of their research article the authors make conclusions regarding the possibility of the fast inverse transfer of the HEVC standard, offer their own scheme for the aforesaid 8x8 matrix factorization and develop the fast algorithm for the inverse transfer based on the discovered factorization schemes. 

Keywords: algorithm analysis, lossy compression, codec, video compression, inverse discrete transform, matrix factorization, fast algorithm, HEVC, software codec, hardware codec

Abstract: The subject of the research is the algorithms for evaluating the information value of composite images. Composite images are formed by multispectral vision systems including multispectral enhanced vision systems used in aviation. These systems show the external space for pilots even in bad weather conditions or late at night, thus increasing operational capacities of aerial vehicles. These systems combine information incoming from physically different sensors into one composite image that is supposed to have essential information features coming from all combined video channels. The research is b ased on the computer modeling of image combination in the two-zone TV-thermal enhanced vision system using the actual images made by the visual sensors. The authors offer a new structural-semantic qualitative evaluation of the information value of composite images based on the preservation (distortion) of various information depending on their spectral energy and space characteristics. Based on the aforesaid method of evaluating the information value, the authors compare different methods of combination of images for the two-zone enhanced vision systems.

Keywords: image analysis, evaluation of the information value, information value of images, visual perception, composite images, combination of images, human-machine interfaces, computer vision systems, multispectral system, enhanced vision systems

Abstract: The article presents a technique of automated image processing in aircraft systems of visual monitoring of the outside the cabin environment for use in the design and subsequent testing of such means. The method was developed taking into account specifics of ensuring the safety of aircraft in the night time and characteristics of modern optoelectronic systems used in manned and unmanned aircraft. The authors describe a technique of calculating the maximum range of the evaluation of low-level television imaging systems used in the composition of assets and systems of aircraft equipment. The research methodology combines the methods of system analysis, design, electro-optical systems, design and testing of aircraft equipment, methods of quality control of complex systems. Scientific novelty of the results is in the fact that they were obtained specifically for ensuring the safety of aircraft and can be used in the interests of rational justification characteristics, design of quality control and testing of similar systems intended for use in equipment ergonomics systems for various purposes.

Keywords: electronic optical transducer, automated image processing, distance of visual detection, system of image visualization, monitoring the situation outside the cabin, night vision goggles, safety of night flights, charge-coupled device, qualimetry technical systems, aircraft equipment

Abstract: The object of research is a new way of defining and visualizing a photorealistic terrain. The method to render a terrain as easily as a texture is proposed. A terrain model is coded as differential height map, i.e. the carrier surface is defined by algebraic means and only deviation from this basic surface is stored in the each node. Such a modeling method simplifies creation of smooth detail levels and shading. The data of height grid is not a subject to geometry transformations as the triangle vertices are. The geometry transformations are only required for the carrier surface. During the recursive voxel subdivision on each level, we project the centers of the voxels onto basic plane. The computed coordinates, as well as in the case of ordinary RGB texture map, will define address in the so called "altitude map" or "shape texture". The altitude corresponding to this address and a level of details is calculated, and are used to modify coefficients of the base plane equation. As a result will be obtained a surface modulated with the values from the altitude map. Visualization in real time on graphical accelerators is implemented. The method is based on the analytic geometry in space, differential geometry and vector algebra, interpolation theory and matrix theory, based on mathematical modeling and computer science. The main conclusions of the study are: the ability to generate the terrain using the same mechanism as for the texture color to display the terrain and changing levels of detail. The image interpolation is used for filtering heights dynamically similar to color texture. In comparison with the known methods the proposed method computation time substantially does not dependent on the resolution of the height map when generating a terrain.

Keywords: regular elevation grid, graphics processing units, scalar perturbation functions, levels of detailisation, shape texture, voxel-based terrain, height-based terrain, irregular elevation grid, ray-tracing method, non-polygonal representation of terrain

Abstract: The author studies geometrical transformation of functionally defined three-dimensional shapes. The paper suggests description of geometrical objects using functions and implementing the methods of transformation of the describing function for geometric operations such as projection, offsetting, set-theoretic and functions of metamorphosis including morphing nonhomeomorphic objects as well as more complex geometric operations: sweeping by moving solid object and twisting of objects. Of all existing methods the functional representation is the most accurate way of describing object geometry, needs less space for storing data required. Functional representation provides compactness and flexibility in setting surfaces and objects obtained as a result of logical operations on volumes. Using functional representation of objects makes it possible to implement new effects on objects due to the introduction of operations on functions. It can be useful in modelling some complex movements of object and particles in scientific applications and games. The method of the research is based on the use of systematic and targeted approach in the evaluation of algorithmic solutions, theory of sets and analytic geometry, interpolation theory and matrix theory, mathematic modeling and theory of computing systems. The main conclusions of the study are: the possibility of implementing complex geometric operations (metamorphosis, projections, offsetting, twisting, sweeping) on objects; proposed method of describing threedimensional scene objects using reference surfaces and functions of the perturbation has a more compact description in comparison with known methods of specifying functionally defined objects; in comparison with known algorithms the rendering algorithm determines the point on the surface of functionally defined objects in less time due to the smaller number of calculations; the proposed functional description of objects simplifies the implementation of the mentioned above operations on geometric functions of the perturbation.

Keywords: geometric objects, geometric operations, perturbation function, quadrics, collision detection, three-dimensional morphing, set-theoretic operations, local deformation, global deformation, visualization

Abstract: the article describes a parameterization of models of radar images of groups of “string” and “cluster” point objects. The authors study probabilistic characteristics of sufficient statistics for their distinction, necessary for the selection of decision rules optimal according to specified criteria under different conditions of observation. The article reviews a method of modeling the distortion of observed reference chains that reduced all the diversity of observations down to two parameters: curvature of the trajectory of the chain and degree of deviations of observed coordinates of point objects from their reference position. This technique allows formalizing and reducing the complexity of comparing competing methods of identification chains. The paper lists features of software for testing competing algorithms of distinguish group of objects. The authors suggest using ratio of the diameter of the graph of hierarchical grouping of objects detected to the total length of the edges of this graph as the statistics of distinguishing. Based on these mathematical models by statistical experiments the authors obtained sample estimates of the laws of probability for distribution of the sufficient statistic for distinguishing different values of model parameters. Taking into account the complexity and the properties of the mentioned method of distinguishing chains and groups the authors recommend it to be used in the construction of systems of recognition of group of point objects in high priori uncertainty regarding the parameters of the conditions of observation for groups with power not less than 10. The proposed architecture of the software package allows testing detection algorithms with signature having various number and type of parameters.

Keywords: distinguishing, chains recognition, group points object, distinguishing group of objects, nonstationary form, outline analysis, recognition by form, analysis of the graph form, hierarchical grouping graph, structural analysis of the graph

Abstract: The article reviews a problem of a video stream frames segmentation in a “bottom-upwards” approach, which can’t be solved in a single processing step due to errors in binarization. For achieving the desired accuracy some additional processing units are needed, the working of each one end with a shift of working receiver operating characteristic (ROC). Intermediate positions of the displaced characteristic is saved in the operating points set up after each shift. The set of operating point makes a path to the area of required accuracy. This it’s only needed to match the sequence of processing units to get the required accuracy. The author developed a classification of approaches to segmentation in the “bottom-upwards” analysis that allows to determine the most effective processing units. A system of video analysis meeting the most recommendations was developed. Each block of segmentation is represented by a family of algorithm allowing to determine object coordinates with required accuracy, including subpixel accuracy. Fot the described system of video analysis the article presents it’s path and criteria for selecting operating points during the setup. The discussed classification approaches to segmentation along with criteria for selecting operating points and visualization method can be used in developing other systems of video analysis.

Keywords: wavelet transform, segmentation, image pyramid, ROC- characteristics, criterion, visualization, bottom-upwards, sub-pixel accuracy, classification, video data

Abstract: the article present a solution for the problem of choosing an eff ective algorithm for determining the set of nearest points for 3D image recognition. The eff ectiveness of the algorithm for determining the set of nearest points aff ects eff ectiveness of the entire image recognition algorithm that uses the set of nearest points as a required step in the image recognition process. The authors present an algorithm for determining the set of nearest points by dividing the space into cubes, analyze the algorithm and shows mathematical relations of the algorithm time complexity. The article illustrates a solution for the task of the algorithm for dividing the space into cubes evaluating which consists of the splitting into elementary operations and expressing the time of execution via microoperations through constants for obtaining the degree of complexity and asymptotic relations showing the ratio of the algorithm execution time increase depending on the size of the input data. The article provides the estimations of the degree of the time complexity for the two implementations of the algorithm for dividing the space into cubes: sequential implementation and parallelized implementation. The authors present the parallelized implementation of the algorithm, obtain estimates its complexity and compare it by the time complexity with the known algorithms.

Keywords: image recognition, algorithm complexity, set of nearest points, algorithm efficiency, 3D image, image processing units, parallel algorithms, dynamic data structures, point distribution, vector space

Abstract: creation of the automated systems in the field of biotechnologies is an important area of scientific and technological research and development. Solving the problem of objective measurements, accuracy and time limits during the analysis of the images of wood samples is the main purpose of this work. The article presents the algorithm of detecting the texture transition border in the early and late wood on digital images optimal by the criteria of likelihood maximum. The author describes a hardware and software system that runs the synthesized algorithm on the base of methods of recognition and analysis of the images of the wood cellular structure, which minimizes time-consuming operations and improves the result quality. The article shows and analyzes the characteristics of the work of the developed software for real digital images. The results of this work can be used for engineering and scientific researches in the field of forestry to improve their reliability and performance.

Keywords: Software, image analysis, texture boarders, coordinated filtration, borders detection, software, biotechnologies, image recognition, algorithm synthesis, digital processing

Abstract: the article proposes generalized mathematical and software models for static and dynamic texture generation on the stream processors. The mathematical model allows to evaluate the efficiency of different approaches to the texture generation. The given methodology provides high performance due to the ability of choosing the optimal method of texture generation and can generate not only textures predefined by the developer, but also arbitrary dynamic textures, displayed according to the incoming external data.

Keywords: Software, stream processors, image processing, post-effects, graphics processors, wavelet transforms, texture generation, static textures, dynamic textures, procedural materials

Abstract: The article reviews the methods of automatic pattern recognition of the speech signals recorded at the moments when announ cers proved positive emotions from speech samples on the same subjects recorded in a testees’ neutral state. This article investigates the abilities of nonlinear dynamics methods for evaluation of informative indicators of emotional state. Studies were performed on the basis of analyzing the reconstruction of attractors of the speech signal. The authors analyzed different ways of selecting optimal parameter values for the reconstruction of the attractor (the time delay between the elements of the time series and embedding dimension). Authors proposed the new quan titative criteria for classifying samples of the speech signal of a person experiencing emo tions based on the estimates of the maximum vector reconstruction of the attractor in four quadrants. The research was based on frag ments of the Russian-language database (Tver). A model of emotional body language, which consists of a database of two levels (phrases and phonemes) was formed and served as a basis for evaluation of the efÞ cie n cy of the developed software module of the automatic recognition of human emotions.

Keywords: Software, speech, speech signal, emotional state, time series, emotion, emotion recognition, nonlinear dynamics, attractor reconstruction, classification

Abstract: The article describes an algorithm for detection of respiratory noise, based on the idea of growing pyramidal network adapted to operate with fuzzy descriptions of objects in the learning samples set and enriched with the linguistic interpreter for the processing results. The article contains a general functional diagram and detailed description of the individual stages of work. To describe the symptom space and the interpretation of results authors used the theory of fuzzy sets. The functioning of the algorithm is carried out in two modes: training and recognition. Neural classes models, contained in the constructed network, are interpreted in fuzzy statements, which are then used in the learning mode and provide a set of production rules for the algorithm of fuzzy logical inference. The given algorithm has a software realization, the article presents the results of testing its software implementation.

Keywords: Software, classiÞ cation, recog nition, graphs, fuzzy logic, breath sounds, auscultation, respiratory sounds, model, algorithm

Abstract: In this article authors consider the problem of spam determination and filtering based on the support vector machine. A modi fication of construction of a separating hyper plane using Fejer mappings is given. Authors suggest replacing the projection operation with the sequence of mapping operations to allow the work with the time-varying data, specific to the problems of classification of documents.

Keywords: Software, classification of informa tion, spam, strong separability problem, Hil bert space, support vector method, the hyperplane, Fejér mapping algorithm conver gence, filtering