| Русский Русский | English English |
   
Главная Архив номеров
23 | 10 | 2017
10, октябрь (October)

СОДЕРЖАНИЕ № 10 2013

ИНФОРМАЦИОННО-УПРАВЛЯЮЩИЕ КОМПЛЕКСЫ ПОДВИЖНЫХ ОБЪЕКТОВ
INFORMATING-CONTROLLING COMPLEXES OF MOBILE OBJECTS

Жеребин А.М., Топоров Б.П., Горлов В.М.
МЕТОД РЕГРЕССИОННОГО СИНТЕЗА СЛОЖНЫХ ТЕХНИЧЕСКИХ СИСТЕМ, ФУНКЦИОНИРУЮЩИХ В УСЛОВИЯХ КОНФЛИКТА И НЕОПРЕДЕЛЕННОСТЕЙ
с. 3–8
Контактная информация: vmgorlov @ mail.ru
Аннотация. Рассмотрены декомпозиционные подходы к решению задачи формирования оптимального облика сложных технических систем, функционирующих в изменяющихся во времени условиях конфликта и неопределенностей. В этом случае решаемая задача формализуется как неклассическая вариационная задача с высокой размерностью вектора управления. Предложена итеративная оптимизационная процедура, основанная на принципе регрессионного усечения моделей функционирования проектируемых систем с помощью метода регрессионного синтеза, позволяющего осуществить их подсистемную оптимизацию по строго адекватным глобальному частным критериям, значительно упростить при этом оптимизационные процессы, одновременно повысив степень обоснованности получаемых результатов проектирования.
Ключевые слова: внешнее проектирование; синтез; облик; декомпозиция; подсистемная оптимизация сложных технических систем; регрессия.

Zherebin A.M., Toporov B.P., Gorlov V.M.
THE METHOD OF REGRESSIONAL SYNTHESIS OF COMPLEX TECHNICAL SYSTEMS FUNCTIONING IN THE CONDITIONS OF CONFLICT AND UNCERTAINTIES
pp. 3–8
Annotation. The problem of synthesizing complex technical systems (CTSs), for example aviation moving objects and their information complexes, formulated as the problem of determining optimal according to the accepted criterion values of CTS conceptual parameters (that is the parameters influencing to the maximum extent their mission effectiveness and cost while solving the given set of targets), is one of the main problems solved at the initial stage of the CTS designing process – the stage of their external (conceptual) design. As it is practically impossible, in view of the high dimension and diversity of targets, to perform them using the CTSs of only one type, there arises the necessity of solving one more problem while designing CTSs – the problem of archetype, consisting in determining the rational quantitative and qualitative (according to the nomenclature of CTS types) composition of a certain interacting CTS set (park), on condition that this park is able to perform the whole given set of CTS targets of the given mission. These design problems are closely interconnected and must be solved together. In this connection there arises the problem of developing methodological approaches and methods allowing to provide the possibility of repeatedly solving the synthesis problem with acceptable resource spends and time expenditure. The materials of the present article offer one of the possible methods.
The problem, solved with the aid of the method proposed in the present article, of synthesizing CTSs functioning in conflict and uncertainty conditions changing over the time of the planned period is formalized as a non-classical variational problem. At that its characteristic feature is the control vector high dimension.
On the basis of the regressional synthesis method presented in the article an optimizational procedure has been developed implementing the principle of the designed system functioning model regressional truncation and allowing to perform the designed systems’ subsystem optimization on subtests strongly adequate to the global test and at that to simplify substantially the optimizational processes, at the same time raising the degree of justification of the obtained design outputs.
Keywords: External designing; Synthesis; Shape; Decomposition; Subsystem optimization of complex technical systems; Regression..




КОМПЬЮТЕРНОЕ ЗРЕНИЕ. ВИРТУАЛЬНАЯ РЕАЛЬНОСТЬ
COMPUTER VISION. VIRTUAL REALITY

Вичевская Ю.А.
ПОИСК ГЕОМЕТРИЧЕСКИХ ОСОБЕННОСТЕЙ ИЗОБРАЖЕНИЯ С ПОМОЩЬЮ ФУНКЦИИ ИНФОРМАТИВНОСТИ
с. 9–12
Контактная информация: ulka_him @ mail.ru
Аннотация. Рассмотрена возможность определения структуры изображений с помощью функции информативности. Разработана методика ее аналитического расчета, которая впоследствии экспериментально верифицируется с помощью программного обеспечения, осуществляющего расчет функции информативности, поиск ее экстремумов и визуализацию.
Ключевые слова: изображение; структура изображения; распознавание изображений; функция информативности.

Vichevskaya Yu.A.
SEARCHING GEOMETRIC FEATURES OF THE IMAGE BY FUNCTION OF INFORMATIVENESS
pp. 9–12
Annotation. Powerful visualization, spatial representation of objects and events, a wide range of special analyzing and modeling programs create for a user a comfortable environment for solving the intellectual problems. The process of transfer of graphic information in electronic form consists of two phases – scanning and recognition. Modern methods of manual and automatic recognition of images do not allow to process large volumes of data. To achieve a high quality of recognition we need a new method for analyzing the structure of graphic documents. Based on the function of informativeness, this method will allow to analyze the structure of images and ensure high performance in creating the electronic documents. The idea of a function of informativeness gives an opportunity to describe a formal ways (algorithms) of finding geometric features on images. The possibility to determining the structure of the image by using the function of informativeness was considered in the article. The technique of its analytical calculation was developed. It was experimentally verified by the software performing the calculation function of informativeness, search and visualization of its extremes. This technique can be used for writing programs that automatically generate a language for describing images.
Keywords: Image; Spatial structure; Recognition of images; Function of informativeness.



Выголов О.В., Визильтер Ю.В., Каратеев С.Л.
АЛГОРИТМЫ АВТОМАТИЧЕСКОГО ОБНАРУЖЕНИЯ И СЧИТЫВАНИЯ НОМЕРОВ ЖЕЛЕЗНОДОРОЖНЫХ ВАГОНОВ И ЦИСТЕРН
с. 13–19
Контактная информация: o.vygolov @ gosniias.ru
Аннотация. Предложены алгоритмы для решения задачи автоматического считывания номеров железнодорожных вагонов и цистерн на видеопоследовательностях. Отличительными особенностями рассматриваемых алгоритмов являются: использование на этапе разбиения на знакоместа двух различных алгоритмов сегментаций связных и трафаретных символов; формирование окончательной гипотезы о считанном номере с учетом оценок качества распознанных символов; специальная морфологическая обработка изображения, используемая на этапе выделения характерных черт трафаретных символов. Приведены результаты экспериментов на базе видеорегистраций вагонов и цистерн, которые демонстрируют возможность работы системы в реальном времени с достаточно высокими показателями качества считывания.
Ключевые слова: компьютерное зрение; обработка изображений; распознавание символов; автоматическая идентификация.

Vygolov O.V., Vizilter Yu.V., Karateev S.L.
ALGORITHMS FOR AUTOMATIC DETECTION AND READING OF RAILWAY WAGON AND TANK NUMBERS
pp. 13–19
Annotation. The task of automatic identification of railway wagons and tanks is one of the most important components of any project which aims to automate the control of the railway transport. The paper describes the original vision-based algorithms for a real-time detection and reading of railway wagon and tank numbers through the use of a single video camera. The input data is a video sequence of wagon or tank passing the camera, and the output is a number in a string format.
The general algorithm has the following structure:
 Acquire an image from the video camera;
 Process the image to detect and read a number. If successful then the following information is included in a list of hypotheses: the number in string format with estimates of the quality of recognition for the each digit, checksum of the number (true/false), the image fragment with the number, number position on the image;
 Check the end of current wagon. If successful then the list of hypotheses is processed and the wagon number is formed.
The algorithm for detection and reading of the number in a single image has a modular structure and includes the following steps:
 Detect number in the image;
 Segment the image number on a set of symbols;
 Recognize digits and estimate the quality of recognition;
 Form a hypothesis about the number in the single image.
The first original feature of the proposed algorithms is the use of two different procedures for symbol segmentation – based on connected and disconnected symbol models. The second is a special morphological image processing applied on the stage of disconnected symbols segmentation.
The estimation of recognition quality is based on a new method which uses three independently trained neural networks.
Processing the list of hypotheses obtained from the image sequence involves the following procedures:
 Remove false detections using estimations of position and motion of the number;
 Match the number strings using correlation based algorithm;
 Form the final number using the digits with maximal votes from the set of hypotheses.
Testing of the proposed algorithms was performed on a real data and demonstrated the possibility of real-time video sequence processing with the appropriate recognition rate.
Keywords: Computer vision; Image processing; Optical character recognition; Automated identification.



Кононов В.А., Конушин А.С.
ОПРЕДЕЛЕНИЕ ТИПОВ ОБЪЕКТОВ В ВИДЕОПОТОКЕ С КАМЕРЫ НАБЛЮДЕНИЯ НА ОСНОВЕ ПОКАДРОВОЙ КЛАССИФИКАЦИИ
с. 20–25
Контактная информация: vkononov @ graphics.cs.msu.ru
Аннотация. Представлен новый алгоритм определения типов объектов, найденных в видеопотоке. По сравнению с существующими методами предлагаемый алгоритм за счет независимой классификации каждого кадра способен корректно работать в случае возникновения таких типичных ошибок сопровождения, как «смена объекта сопровождения». Для тестирования алгоритма создана новая база видеофрагментов, снятых с камер видеонаблюдения. Проведенные эксперименты показали, что предложенный алгоритм улучшает общее качество работы системы видеонаблюдения.
Ключевые слова: сопровождение объектов; классификация объектов; видеонаблюдение.

Kononov V.A., Konushin A.S.
FRAME-WISE OBJECT TYPE CLASSIFICATION IN VIDEO SURVEILLANCE STREAMS
pp. 20–25
Annotation. In this paper a new algorithm for object classification in video surveillance stream is presented. In current algorithms a whole object tracklet is used for classification. This can lead to classification errors if object tracking has failed and tracking has switched from one object to another, which is called ID-switch. We propose a frame-wise classification, which can correctly handle such tracking errors. We consider a camera calibration to be known beforehand. In each frame a number of features are computed, including simple features like width, height, area, ratio of width and height, and more complex features like marginal integral histograms and number of peaks in the object mask. For classification of individual frames we use Random Forest, which can be naturally applied to multi-class classification problems. Then per-frame classification results for whole tracklet are passed to second classifier, which gives object type for the whole tracklet. Both classifiers have been trained on dataset with 3483 object tracklets without tracking errors. For evaluation of the algorithm a new ground-truth dataset was collected and manually annotated. It contains 1948 tracklets without tracking errors and 138 tracklets with tracking errors. The proposed algorithm showed promising results on this database. Compared to tracklet-wise classification the recall has improved from 42.6 to 95 % on tracklets with object switching error. The recall on whole dataset has improved from 86.3 to 93.4 %. Our algorithm can work in real time for 16 video streams simultaneously on workstation with Intel Core 2 Quad 2.83 GHz processor and 4 GB RAM.
Keywords: Object tracking; Object classification; Video surveillance.



Лебедев А.С., Гаганов В.А., Игнатенко А.В.
ОСОБЕННОСТИ РЕКОНСТРУКЦИИ ТРЕХМЕРНЫХ МОДЕЛЕЙ ВКЛЮЧЕНИЙ В АЛМАЗНОМ СЫРЬЕ НА ОСНОВЕ ФОТОИЗОБРАЖЕНИЙ
с. 26–32
Контактная информация: alebedev @ graphics.cs.msu.ru
Аннотация. Дано описание программной системы, которая позволяет автоматически реконструировать включения по набору фотоизображений алмаза. Предложены алгоритмы автоматической обработки фотографий для обнаружения и реконструкции трехмерных моделей включений, учитывающие специфику рассматриваемой задачи: высокий коэффициент преломления в алмазе и особенности распространения света в алмазном сырье. Предлагаемый алгоритм реконструкции протестирован на наборах реальных данных. В целом, система позволяет реконструировать класс контрастных, хорошо видимых на всех фотографиях включений.
Ключевые слова: реконструкция трехмерных моделей; обработка изображений; сегментация изображений; оценка фона.

Lebedev A.S., Gaganov V.A., Ignatenko A.V.
PECULIARITIES OF IMAGE-BASED RECONSTRUCTION OF THREE-DIMENSIONAL INCLUSION MODELS IN ROUGH DIAMONDS
pp. 26–32
Annotation. Nowadays the world diamond industry makes heavy demands on the software that automates the diamond cut process. To maximize the value of the diamond cut of rough we have to reconstruct three-dimensional models of foreign objects in rough. These objects are called inclusions. In this article we present the software system for automatic inclusion reconstruction by a set of images. We propose algorithms for detection and 3D-reconstruction of inclusion models based on specificity of the problem: high refraction index of rough and features of light distribution in rough. The system consists of three parts: estimation of inclusion probability map, approximate 3D-reconstruction of inclusions and inclusion model refinement. To build inclusion probability map we estimate the background image of rough without
inclusions using a simple physical model of light distribution and splines. Then we segment the difference between background and source image and classify segments using an SVM (Support Vector Machine) based classifier. Probability maps are then integrated into voxel grid. By segmenting voxel grid using slice-by-slice algorithm approximate inclusion models are reconstructed. Because of inconsistency in images inclusion models are not precise. Finally, each approximate inclusion model is refined from four most consistent directions. The shape of inclusion projections are obtained from probability maps. We average shapes from opposite images to improve the accuracy. The proposed algorithms were tested on real world data. On the whole, the system makes it possible to reconstruct a wide class of contrast, visible on all photos inclusions.
Keywords: 3D-reconstruction; Image processing; Segmentation; Background estimation.



Студитский А.С.
ЭФФЕКТИВНОСТЬ НАБЛЮДАТЕЛЬНЫХ ТЕПЛОВИЗИОННЫХ И ОПТИКО-ЭЛЕКТРОННЫХ СИСТЕМ
с. 33–36
Контактная информация: alexandr.studitskiy @ gmail.com
Аннотация. Рассмотрены особенности оценки эффективности наблюдательных систем в реальных условиях. Дана оценка влияния различных факторов среды, характеристик цели и особенностей восприятия наблюдателя на вероятность различения цели в реальных условиях. Показана возможность различения объектов на термограмме при равномерном и относительно неравномерном фоне.
Ключевые слова: критерий Джонсона; разрешение; обнаружение; тепловизор.

Studitskij A.S.
TARGET DISCRIMINATION CAPABILITY OF THERMAL IMAGING AND ELECTRO-OPTICAL SURVEILLANCE SYSTEMS
pp. 33–36
Annotation. The article describes the features of evaluation the effectiveness of observing systems in the environment. It shows the influence of various environmental factors, characteristics of the target and the observer perceptual on the probability of target discrimination in the field. The possibility of distinguishing objects in the thermal image with a uniform and cluttered background is showed in examples.
Keywords: Johnson criteria; Resolution; Detection; FLIR.




ГЕОИНФОРМАТИКА. ТЕХНОЛОГИИ ДИСТАНЦИОННОГО ЗОНДИРОВАНИЯ И МОНИТОРИНГА
GEOINFORMATICS. REMOTE PROBING AND MONITORING TECHNOLOGIES

Крушель Е.Г., Степанченко И.В.
ОБ АЛГОРИТМЕ ИДЕНТИФИКАЦИИ ПАРАМЕТРОВ ВЫБРОСОВ ВРЕДНЫХ ВЕЩЕСТВ В АТМОСФЕРУ
с. 37 – 42
Контактная информация: stilvi @ mail.ru
Аннотация. Представлено описание алгоритма идентификации расхода газовоздушной смеси и массы выброса вредного вещества в атмосферу от группы стационарных источников. Решение задачи идентификации дано для модели, положенной в основу Общесоюзного нормативного документа ОНД–86 «Методика расчета концентраций в атмосферном воздухе вредных веществ, содержащихся в выбросах предприятий». Приведены результаты вычислительных экспериментов, доказывающих сходимость алгоритма.
Ключевые слова: идентификация параметров; модель рассеивания вредных веществ; масса выброса; расход газовоздушной смеси; сходимость алгоритма.

Krushel E.G., Stepanchenko I.V.
ON THE INDUSTRIAL POLLUTANT FLOW PARAMETERS IDENTIFICATION ALGORITHM
pp. 37 – 42
Annotation. The paper deals with the algorithm for the estimation of gas mixture and mass emission pollutants flow into the atmosphere from the group of stationary pollutant sources. The identification problem solution is based on the allowed methodology of the atmosphere concentrations estimation of pollutions contained in the plants emissions (known in Russia as normative document ОНД-86). The problem statement is to show the ability of restoring the non-measured values of the mass emission and the gas flow consumption from the hot pollutant source by means of data mining of the near-earth pollutions concentrations direct measurements carried out in few separate points outside from the industrial plants sanitary protection zones. The distinctive feature of the identification problem is the essential non-linearity presence in the dependence between the concentrations values and the parameters to be identified. The gradient method is selected for problem solving. The criterion is chosen as RMS error between the actual measurements results and the supposed concentration amounts calculated correspondingly to the current parameters values by the methodology mentioned above. The computation experiments results are presented to illustrate the acceptable accuracy of the parameters convergence to the points corresponding to the criterion minimum.
The identification algorithm was investigated for various combinations of initial parameters. The best rate of convergence was achieved when the initial supposition of gas flow consumption was chosen at the level more than the actual value while the initial supposition of mass emission was chosen at the level less than the actual value.
The results are applicable for the algorithmic support of the ecology monitoring systems operating in the small cities with the advanced industrial sphere.
Keywords: Parameters identification; Model of pollutants dissipation; Mass emission; Gas flow consumption; Algorithm convergence.




АВТОМАТИЗАЦИЯ ПРОЕКТИРОВАНИЯ, КОНСТРУИРОВАНИЯ И ТЕХНОЛОГИЧЕСКОЙ ПОДГОТОВКИ ПРОИЗВОДСТВА
AUTOMATION OF ENGINEERING, DESIGN AND PRODUCTION TECHNOLOGICAL PREPARATION

Битюков Ю.И., Денискин Ю.И., Калинин В.А.
РАЗРАБОТКА CAD/CAM/CAE-СИСТЕМЫ ДЛЯ ИЗГОТОВЛЕНИЯ КОНСТРУКЦИЙ ИЗ ВОЛОКНИСТЫХ КОМПОЗИЦИОННЫХ МАТЕРИАЛОВ МЕТОДОМ НАМОТКИ
с. 43 – 50
Контактная информация: yib72 @ mail.ru
Аннотация. Рассмотрена задача разработки и реализации CAD/CAM/CAE-системы для изготовления конструкций из волокнистых композиционных материалов методом намотки. Приведены общая организация системы, назначение ее функциональных блоков и преимущества системы.
Ключевые слова: CAD/CAM/CAE-системы; композиционные материалы; математическое моделирование; управляющая программа.

Bityukov Yu.I., Deniskin Yu.I., Kalinin V.A.
DEVELOPMENT OF CAD/CAM/CAE-SYSTEM FOR MANUFACTURING STRUCTURES MADE OF FIBROUS COMPOSITES BY WINDING
pp. 43 – 50
Annotation. In the design of complex equipment we observe a replacement of the traditional processing means of geometric-graphical information by the paperless technologies. Thanks to that new opportunities appear to use of automated design systems. New technologies arise which associate with the use of electronic models of design object. The main advantage of using the electronic model of the product is possibility of its use in the different modules of the systems of continuous design of the class CAD/CAM/CAE. The core of such systems is a unified database in which the geometric model of the product keeps. In the modern CAD/CAM/CAE-systems geometric modeling of objects, computer solution of geometrical and engineering-graphics tasks occupy the central place. When the object is created primarily, the geometry of the object and its components are formed. Then other tasks of design, technology and manufacturing are solved.
Currently, the enterprises designing and manufacturing of sophisticated machinery actively used CAD/CAM/CAE-systems. It is due to several reasons. The most important reason is a management of a quality of products. It is especially important when products enter the world market. Such systems ensure the complex fulfillment of design works reducing their terms and improving quality. A depreciation and reliability improvement are the main purposes of such systems.
Considering the development and implementation of CAD/CAM/CAE-system for manufacturing of constructions of fibrous composite materials by the winding method. Giving the general organization of the system, the appointment of its functional units and the benefits of the system.
Keywords: CAD/CAM/CAE-systems; Composite materials; Mathematical modeling; Control program.



Назаров А.П., Окунькова А.А., Павлов М.Д., Тарасова Т.В., Смуров И.Ю.
РАЗРАБОТКА ВАРИАНТОВ КОМПОНОВОК ПРИ ПРОЕКТИРОВАНИИ ОБОРУДОВАНИЯ ДЛЯ СЕЛЕКТИВНОГО ЛАЗЕРНОГО ПЛАВЛЕНИЯ
с. 51 – 57
Контактная информация: a.okunkova @ stankin.ru
Аннотация. Рассмотрены особенности разработки методики проектирования оборудования для селективного лазерного плавления. Представлены типовое устройство оборудования и основные принципы его работы, при помощи известного метода закодированы базовые движения составляющих узлов и механизмов (подвижных блоков). Для синтеза вариантов решений компоновок оборудования наложены некоторые ограничения, основанные на известных законах физики и накопленном практическом опыте. Построены графы синтеза вариантов компоновок, на основании которых предложена методика проектирования компоновок и синтеза вариантов решений. При помощи разработанной методики показаны шесть принципиально разных и новых решений компоновок оборудования для селективного лазерного плавления.
Ключевые слова: проектирование оборудования; разработка вариантов конструкции; оборудование для селективного лазерного плавления.

Nazarov A.P., Okunkova A.A., Pavlov M.D., Tarasova T.V., Smurov I.Yu.
DEVELOPMENT OF SELECTIVE LASER MELTING MACHINE DESIGN VARIANTS
pp. 51 – 57
Annotation. The group of the machining processes in the frames of conception “Additive manufacturing” has been created in consequence of rapid prototyping methods development. Nowadays by these methods can be produced not only the models, but as well final functional product in accordance to its engineering specification. The product produced by these methods “grows” from particles layer by layer, in the opposite traditional mechanical methods based on the cutting process. This conception gives the possibility of creation the unique parts with complex geometry inside and outside. For example the parts as heat exchanger, filter with the complex system of spiral cooling channels for the aviation industry. The tendency says soon on the market will be available the selective laser melting machine to produce multi material parts. To produce the multi material parts the designers are looking for the possibility of the alternative ways of selective laser melting machine construction and conception. As a solution for this task could be the method of selective laser melting machine construction modeling represented in the frames of this article. The method can be realized be computer aided design modeling and based on the algebraic laws and practical experience.
The development of the machine design normally decided on the first steps of projects. It is the one of the most important step their when designers make a decision on the main movements of the future machine. On the step it is important to research all potential solutions for the machine. For this purpose the authors took an advantage of mathematical approach as algebraic and logic commutative law. The research on this field says for the production of 3D parts by selective laser melting could be used the machine completed by separated moving blocks.
The practice said there are at least five main movements for selective laser melting process. To proof it the authors considered in the article one the most known conception of the machine for selective laser melting. The each main movement was described and coded. To reduce the machine construction variants they have been limited by application of the physical laws and particle experience. The graph of machine design variants have been drawn in accordance of the limitation. Inverse coding shows the plenty possible variants, some of them were represented by designers on the image. As a second step of the machine design modeling some of the change in the order of moving blocks were done. Some results of this research were represented on the image.
Keywords: Machine design modeling; Machine design variants development; Selective laser melting machine.




ПРОГРАММНОЕ И АППАРАТНОЕ ОБЕСПЕЧЕНИЕ ПРОЦЕССОВ И СИСТЕМ
HARD- AND SOFTWARE OF PROCESSES AND SYSTEMS

Балонин Ю.Н.
ПРОГРАММНЫЙ КОМПЛЕКС MMATRIX-2 И НАЙДЕННЫЕ ИМ МИНИМАКСНЫЕ МАТРИЦЫ
с. 58–63
Контактная информация: tomaball @ mail.ru
Аннотация. Рассмотрен программный комплекс MMatrix-2 поиска и исследования матриц ортогональных базисов – минимаксных матриц. Описаны основные функции комплекса, представленные кнопками и окнами интерфейса. Приведены портреты полученных матриц Ферма, Адамара, Мерсенна и Эйлера. Показаны способы трансформации одних типов матриц в другие.
Ключевые слова: ортогональные матрицы; минимаксные матрицы; матрицы Адамара; матрицы Мерсенна; матрицы Ферма; матрицы Эйлера; портрет матрицы.

Balonin Yu.N.
THE SOFTWARE COMPLEX MMATRIX-2 AND SEARCHED MINIMAX MATRICES
pp. 58–63
Annotation. The software complex MMatrix-2 to search and research matrices of orthogonal bases – minimax-matrices – is observed. The main features of the complex and the button's and window's interface are described. System optimizes orthogonal matrix in terms of the minimum of the maximum absolute values of their elements. Portraits of searched Fermat, Hadamard, Mersenne and Euler matrices are obtained. It is shown how to transform one type of matrix to the other one. Portraits make visual characteristic of the structural matrix invariants. For ease of analysis, the portrait of the matrix can be colored. The difference in the orders of the typical matrices allows to show the way to increase or decrease the order of an orthogonal matrix. The multiplicity of orders of Hadamard matrices to 4 (except for the matrices of 1 and 2 orders) creates the preconditions for the proof of the conjecture of Hadamard. The results of the system are interested for the traditional application area: error-correcting coding and security. It provides background information for the procedures of protective mask and image compression.
Keywords: Orthogonal matrix; Minimax matrices; Hadamard matrices; Mersenne matrices; Fermat matrices; Euler matrices; Matrix portrait.

 

 
Поиск
Баннер
Журнал КОНТРОЛЬ. ДИАГНОСТИКА
Rambler's Top100 Яндекс цитирования