Рассматривается механизм моделирования оптического потока как случайного векторного поля – замкнутых областей на плоскости изображений с определёнными уровнями яркости и динамикой изменения векторного поля. Оптический поток формируется однородным, одноуровневым точечным потоком восстановления. Характеристики векторного поля на плоскости изображения получаемого оптического потока связаны между собой формулами Пальма. Выбор типа составных элементов векторного поля – алфавита, определяющих морфологию поля на плоскости изображения, производится случайным образом. Предлагаемый подход позволит получать различные типы связанных между собой цифровых последовательностей изображений с горизонтальными, вертикальными и диагональными элементами, создаст предпосылки эффективно и гибко производить анализ движения на цифровых видеопоследовательностях, предоставит возможность использовать вероятностный фактор в процессе исследований алгоритмов обработки изображений и проведения детального факторного анализа для сравнения алгоритмов.

Актуальность работы. Получение количественных оценок эффективности алгоритмов анализа изображений является весьма актуальной задачей, в том числе и задача оценки эффективности контурных детекторов. Выбор надежных алгоритмов выделения контуров на изображениях волновых полей имеет особое значение при построении цифровых двойников нефтяных месторождений. Так, для изучения околоскважинного и межскважинного пространства необходимо использовать алгоритмы оконтуривания, обладающие высокой помехоустойчивостью в сложных сейсмогеологических условиях. Выбор таких алгоритмов должен быть основан на комплексном анализе качества выделяемых контуров, включающем такие элементы, как смещение, разрыв и смазывание границ. В этом плане большой интерес представляет метод получения оценок эффективности контурных детекторов на основе расчета обобщённого показателя качества выделения границ, предложенный в работе I. Boaventura и A. Gonzaga в 2009 г. Обобщённый показатель качества определён авторами статьи в виде нормы вектора в евклидовом пространстве. Одну из координат вектора составляет обратная величина метрики Прэтта, которая учитывает интегральную величину смещения элементов обнаруженного контура. Остальные координаты вектора формируются на основе бинарной классификации. В работах Д.В. Дубинина, А.И. Кочегурова и В. Герингера приведены исследования эффективности показателя качества I. Boaventura и A. Gonzaga путем вычислительного эксперимента. Эталонные изображения в процессе эксперимента аппроксимировались двумерным точечным потоком восстановления, что позволило реализовать принципы постановки эксперимента по Фишеру (принцип Рандомизации). Анализ полученных экспериментальных данных показал ряд недостатков обобщённого показателя качества A. Gonzaga и I. Boaventura. В частности, при малых отношениях сигнала к шуму (с/ш) были получены завышенные значения критерия Прэтта, что, в свою очередь, приводило к заниженным оценкам обобщённого показателя качества. Действительно, будучи чувствительным к локальным смещениям границы, критерий Прэтта плохо реагирует на пропуски элементов в разорванных контурах, что и приводит к неоправданно высоким значениям критерия при малых отношениях с/ш. Это утверждение было высказано А.В. Яскорским еще в 1987 г. и нашло свое доказательство в результатах вычислительного эксперимента. Таким образом, существует реальная необходимость повышения достоверности оценок качества детектирования, получаемых на основе обобщённого показателя I. Boaventura и A. Gonzaga. С этой целью предлагается в обобщенный показатель качества вместо критерия Прэтта ввести его модифицированный аналог (Modification Pratt's Figure of Merit), предложенный и детально рассмотренный нами в более ранних работах. Вопросам исследования обобщённого показателя I. Boaventura и A. Gonzaga с модифицированным критерием Прэтта посвящена настоящая работа. Методы и средства исследования: системный анализ, стохастическое имитационное моделирование, цифровая обработка изображений, методы визуализации данных. Также применялись методы анализа, основанные на постепенной формализации моделей путем активизации интуиции специалистов. Вычислительный эксперимент проводился в среде «Delphi», а валидация численной модели осуществлялась с использованием среды «Mathcad». Результаты исследования дадут возможность выбора объективного критерия оценки качества построения контурных границ при создании цифрового двойника нефтяного месторождения.

Relevance. Obtaining quantitative estimates of the efficiency of image analysis algorithms is a very urgent problem, including the problem of evaluating the efficiency of contour detectors. The choice of reliable algorithms for extracting contours on images of wave fields is of particular importance when constructing digital twins of oil fields. So, to study borehole and interwell space, it is necessary to use contouring algorithms that have high noise immunity in difficult seismic and geological conditions. The choice of such algorithms should be based on a comprehensive analysis of the quality of the selected contours, including such elements as displacement, break and blurring of boundaries. In this regard, the method of obtaining estimates of the efficiency of contour detectors based on the calculation of the generalized indicator of the quality of boundary detection proposed in the work of I. Boaventura and A. Gonzaga in 2009 is of great interest. The generalized quality indicator is defined by the authors of the article in the form of a vector norm in Euclidean space. One of the coordinates of the vector is the reciprocal of the Pratt metric, which takes into account the integral value of the displacement of the elements of the detected contour. The rest of the coordinates of the vector are formed on the basis of binary classification. The works of D.V. Dubinin, A.I. Kochegurov and B. Goringer introduce the studies of the efficiency of the quality indicator of I. Boaventura and A. Gonzaga by a computational experiment. In the course of the experiment, the reference images were approximated by a twodimensional point recovery stream, which made it possible to implement the principles of setting up an experiment according to Fischer (the principle of randomization). The analysis of the obtained experimental data showed a number of shortcomings of the generalized quality indicator of A. Gonzaga and I. Boaventura. In particular, at low signal-to-noise (s/n) ratios, overestimated values of the Pratt's criterion were obtained, which in its turn led to underestimated estimates of the generalized quality indicator. Indeed, being sensitive to local displacements of the boundary, Pratt's criterion reacts poorly to omissions of elements in broken contours, which leads to unjustifiably high values of the criterion at low s/n ratios. This statement was made by A.V. Yaskorskiy in 1987 and found its proof in the results of a computational experiment. Thus, there is a real need to improve the reliability of the detection quality estimates obtained on the basis of the generalized index of I. Boaventura and A. Gonzaga. For this purpose, it is proposed to introduce into the generalized quality indicator instead of the Pratt's criterion its modified analogue (Modification Pratt's Figure of Merit), proposed and considered in detail by us in earlier works. This work is devoted to the study of the generalized indicator of I. Boaventura and A. Gonzaga with the modified Pratt criterion. Methods and means of research: system analysis, stochastic simulation modeling, digital image processing, data visualization methods, as well as the methods of analysis, based on the gradual formalization of models by activating the intuition of specialists. The computational experiment was carried out in the Delphi environment, and the numerical model was validated using the Mathcad environment. The research results will make it possible to choose an objective criterion for assessing the quality of building contour boundaries when creating a digital twin of an oil field.

Актуальность. В настоящее время при поиске нефтяных и газовых месторождений большое внимание уделяется более активному вовлечению в разведочный процесс слабо исследованных территорий, а также доисследованию природных резервуаров в районах промышленного освоения месторождений. Для этих целей широко применяются методы сейсморазведки, в результате чего формируются огромные массивы данных, подлежащие последующей обработке и интерпретации. Одной из задач, решаемой на этапе обработки, является надежное обнаружение сейсмических сигналов, особенно важное значение эта задача имеет при прослеживании волн, так как от достоверности обнаружения зависит качество построения отражающих границ. Поэтому построение эффективных методов и алгоритмов обнаружения сигналов на основе анализа ФЧХ, обладающих более высокой степенью устойчивости к помехам, является весьма актуальной задачей. Цель: на основе оптимальной и субоптимальной обработки ФЧХ сейсмических волн, получаемых при поиске нефтяных и газовых месторождений, построить методы обнаружения сигналов и исследовать их эффективность на моделях сейсмоимпульсов путем вычисления вероятностных характеристик ошибок обнаружения. Методы и средства исследования: методы статистического анализа и синтеза алгоритмов, теория случайных процессов, дискретное преобразование Фурье, методы обработки и интерпретации сейсмических данных, математическое моделирование и вычислительный эксперимент. Результаты. На основе метода максимального правдоподобия построена оптимальная процедура обнаружения сейсмических сигналов по их фазочастотным характеристикам. Получены аналитические выражения для вероятностей ошибок обнаружения. Показано, что оптимальное фазочастотное обнаружение обеспечивает результаты, близкие к результатам абсолютно оптимального метода обнаружения сигналов. Для практической реализации разработанного метода предложена субоптимальная обработка ФЧХ (равновесная обработка), не требующая информации о распределении энергии сигнала в частотной области. Проведены исследования помехоустойчивости метода обнаружения с равновесной обработкой, и получены оценки потерь в зависимости от числа использованных частотных компонент в спектре сигнала. Показано место применения разработанных методов обнаружения при решении задач прослеживания сейсмических волн.

Relevance. Currently, in the search for oil and gas fields, much attention is paid to more active involvement of poorly explored territories in exploration, as well as to the study of natural reservoirs in areas of industrial development of deposits. For these purposes, seismic methods are widely used, as a result of which huge data arrays are formed, which are subject to subsequent processing and interpretation. One of the tasks to be solved at the processing stage is reliable detection of seismic signals, this task is especially important when tracking waves, since the quality of construction of reflecting boundaries depends on the reliability of detection. Therefore, the construction of effective methods and algorithms for detecting signals based on the analysis of the phase response, with a higher degree of resistance to interference, is a very urgent task. The aim of the research is to construct methods for detecting signals based on the optimal and suboptimal processing of the phase-frequency characteristic of seismic waves obtained when searching for oil and gas fields and to study these methods effectiveness on models of seismic pulses by calculating the probability characteristics of detection errors. Methods and means of research: methods of statistical analysis and synthesis of algorithms, theory of random processes, discrete Fourier transform, methods of processing and interpretation of seismic data, mathematical modeling and computational experiment. Results. Based on the maximum likelihood method, an optimal procedure for detecting seismic signals by their phase-frequency characteristics is constructed. Analytical expressions are obtained for the probabilities of detection errors. It is shown that optimal phase-frequency detection provides results close to the results of the absolutely optimal signal detection method. For practical implementation of the developed method, suboptimal processing of the phase response (equilibrium processing) is proposed, which does not require information on distribution of signal energy in the frequency domain. The noise immunity of the detection method with equilibrium processing was studied and estimates of losses were obtained depending on the number of used frequency components in the signal spectrum. The place of application of the developed detection methods for solving problems of tracking seismic waves is shown.

The issues of improving the accuracy of determining the coordinates of a radio source by a single-position method due to the joint processing of multiple signals reflected from local objects are considered. The electronic terrain map was obtained on the basis of artificial images of a two-dimensional point-like reconstruction flow. The results of computer simulation are presented.

Relevance. Currently, much attention is paid to development of efficient systems designed for processing, storing and transmitting large streams of information obtained in the form of images of space-time fields in such areas of human activity as cosmonautics, geology and geophysics, cartography, navigation, defectoscopy and many others. in most of these systems, when implementing detection algorithms, real images are used as reference images. For example, this is typical for isolation and tracing of the boundaries of reflected waves in images of seismic fields obtained by searching for oil and gas fields. Representation of reference images in the form of real images allows you to adjust the algorithm to a specific subject area, but complicates the assessment of the quality of the algorithm used and the conduct of its objective comparison with other algorithms that implement similar procedures. The aim of the research is to investigate the effectiveness of selection of the contour pattern of images by different detection algorithms based on a generalized complex criterion proposed by the authors of this work. This will allow us to approach objectively to selection of the best detection algorithm and the optimal values of its parameters for any subject area. Methods and means of research. When conducting experiments, the methods of stochastic modeling of space-time signals and fields were used. The computational experiment itself was conducted in the environment of the "KIM SP" software complex. Results. The authors have carried out the analysis of methods for evaluating search operators and localization of boundaries and summarized the main types of errors. On the basis of the proposed classification of metrics for the efficiency of contour detectors, a generalized comprehensive criterion for assessing the quality of selection of contour patterns in images is considered, the possible components of a generalized quality indicator and formal approaches to the choice of weighting coefficients of metrics are shown. The paper introduces the example of implementation of a generalized quality indicator, including five metrics; its effectiveness is investigated for three quasi-optimal contouring algorithms ( Canny, Marr and ISEF) at various noise levels. The conducted research allowed drawing the conclusions on the objectivity of the obtained results and giving recommendations on the use of contouring algorithms.

Relevance. At present, deconvolution methods are widely used to process data for a variety of applied purposes, such as radio and sonar detection, navigation, hydroacoustics, geophysics, etc. These methods are of great importance in seismic prospecting when searching for oil and gas fields in thin-layered geological environments, where waves reflect from interfaces and interfere with each other thus making it extremely complicated to identify the boundaries of different geological media. The problem becomes even more complicated due to irregular noise in all seismic records. Therefore, to trace the boundaries in thin-layered media, many algorithms for signal compression are used, which are commonly based on deconvolution methods. However, in traditional deconvolution methods phase spectra are neglected and considered to be either minimum-phase or zero-phase spectra. Meanwhile, it is the phase of seismic signals, or rather the complex law of the change in phase spectra, that carries important information on location of reflecting boundaries. Hence, the resolving power of a signal is primarily determined by the complexity of its phase characteristic. Therefore, the development and investigation of the efficiency of a phase-frequency deconvolution algorithm is of great importance for processing and interpreting seismic materials. The aim of the research is to develop an algorithm for phase-frequency deconvolution on the basis of the method of phase- frequency tracking of seismic waves that was proposed earlier; to analyse the efficiency of this algorithm in models of geological environments; to test the algorithm for processing and interpreting general deep point materials obtained at a number of oil fields in the Tomsk region, Russia. Methods: digital processing of space-time signals and fields, discrete Fourier transform, mathematical modeling and a computational experiment. Results. The authors have developed the deconvolution algorithm based on the method of phase-frequency tracking of seismic signals. The algorithm differs from the previous solutions in its capability to analyse instantaneous phase spectra. The paper introduces the characteristic features of the phase spectra that form the basis of the algorithm. Investigations of the algorithm in models of a wave seismic field, as well as experimental processing and interpretation of actual data were carried out. The results obtained confirm the potential of phase- frequency deconvolution to analyse thin-layered geological media.

The paper proposes phase-frequency algorithms with equilibrium and non-equilibrium processing based on the pre-developed phase-frequency tracking methods for resolving complex signals in wave seismic field images. It further shows that transition to equilibrium processing enables significant reduction of requirements to apriori information on the properties of useful signals, while non-equilibrium processing increases the resolution of the signals to a great extent. The conducted analytical argument and simulations testified that the algorithms can assure a sufficiently high extraction of signals in their interference zones and harder incoherent noise at propagation of complex signals in dispersive media. The simulation results are justified by real data obtained in processing of seismic wave fields.

Relevance. At present, deconvolution methods are widely used to process data for a variety of applied purposes, such as radio and sonar detection, navigation, hydroacoustics, geophysics, etc. These methods are of great importance in seismic prospecting when searching for oil and gas fields in thin-layered geological environments, where waves reflect from interfaces and interfere with each other thus making it extremely complicated to identify the boundaries of different geological media. The problem becomes even more complicated due to irregular noise in all seismic records. Therefore, to trace the boundaries in thin-layered media, many algorithms for signal compression are used, which are commonly based on deconvolution methods. However, in traditional deconvolution methods phase spectra are neglected and considered to be either minimum-phase or zero-phase spectra. Meanwhile, it is the phase of seismic signals, or rather the complex law of the change in phase spectra, that carries important information on location of reflecting boundaries. Hence, the resolving power of a signal is primarily determined by the complexity of its phase characteristic. Therefore, the development and investigation of the efficiency of a phase-frequency deconvolution algorithm is of great importance for processing and interpreting seismic materials. The aim of the research is to develop an algorithm for phase-frequency deconvolution on the basis of the method of phase-frequency tracking of seismic waves that was proposed earlier; to analyse the efficiency of this algorithm in models of geological environments; to test the algorithm for processing and interpreting general deep point materials obtained at a number of oil fields in the Tomsk region, Russia. Methods: digital processing of space-time signals and fields, discrete Fourier transform, mathematical modeling and a computational experiment. Results. The authors have developed the deconvolution algorithm based on the method of phase-frequency tracking of seismic signals. The algorithm differs from the previous solutions in its capability to analyse instantaneous phase spectra. The paper introduces the characteristic features of the phase spectra that form the basis of the algorithm. Investigations of the algorithm in models of a wave seismic field, as well as experimental processing and interpretation of actual data were carried out. The results obtained confirm the potential of phase-frequency deconvolution to analyse thin-layered geological media.

Suspended graphene is difficult to image by scanning probe microscopy due to the inherent van der Waals and dielectric forces exerted by the tip, which are not counteracted by a substrate. Here, we report scanning tunneling microscopy data of suspended monolayer graphene in constant-current mode, revealing a surprising honeycomb structure with amplitude of 50-200 pm and lattice constant of 10-40 nm. The apparent lattice constant is reduced by increasing the tunneling current I, but does not depend systematically on tunneling voltage V or scan speed v(scan). The honeycomb lattice of the rippling is aligned with the atomic structure observed on supported areas, while no atomic corrugation is found on suspended areas down to the resolution of about 3-4 pm. We rule out that the honeycomb structure is induced by the feedback loop using a changing vscan, that it is a simple enlargement effect of the atomic lattice, as well as models predicting frozen phonons or standing phonon waves induced by the tunneling current. Although we currently do not have a convincing explanation for the observed effect, we expect that our intriguing results will inspire further research related to suspended graphene.

Received 22 November 2016DOI:https://doi.org/10.1103/PhysRevB.94.219902©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLattice dynamicsMechanical & acoustical propertiesMechanical deformationThermal conductivityCondensed Matter, Materials & Applied Physics

The relevance of the study. The procedures for determining temporary shift, which are widely spread in practice, do not always guarantee the accuracy in defining static corrections. The arising errors lead to a distortion of kinematic parameters of the reflected waves. This affects adversely all subsequent constructions. Therefore, development of the effective method for determining the temporary shift is the relevant issue. The prospects of increasing the reliability of designing the structures, prepared for oil and gas exploration, are related to the successful solution of the problem. The aim of the study is to develop and explore the reliability of the algorithm for determining the temporary shifts between seismic traces based on the optimal and suboptimal processing of phase-frequency characteristics of the reflected waves recorded when searching for oil and gas fields. The methods used in the study: statistical synthesis and analysis of optimal decision rules, digital signal processing, methods of discrete Fourier transform, mathematical modeling and computer experiment. The results. The authors showed the possibility of extracting useful in from the phase-frequency characteristics of seismic signals for obtaining the effective estimates of temporary shifts between traces. Based on the theory of statistical solutions the optimal algorithm for determining the temporary shifts by the instantaneous mutual phase spectra was built. For practical implementation of the algorithm, the authors proposed a transition from optimal to suboptimal processing of the components of the instantaneous mutual phase spectra by summing the equilibrium. it is shown that the equilibrium processing leads to almost twice reduction of the total signal/noise ratio for practically used strip of frequency. Even such losses allowed obtaining rather reliable estimates of temporary shifts at the intense irregular interference and symmetric distributions of temporary shifts with large dispersion.

The paper presents the results of a quantitative estimation of the edge detection quality using modified Pratt-Yaskorskiy criterion, as well as generalization and adaptation of both approaches based on the generalized quality criterion as part of «CS sF» stochastic simulation software package. The reference images are approximated by the two-dimensional high rise renewal stream offering the stationarity properties with no aftereffects and ordinariness. The efficiency of the proposed metrics is considered for three edging algorithms (Marr-Hildreth, ISEF and Canny) at different levels of the additive normal noise. The estimated errors of the first and second kind are given, which allow referring to the efficiency of the proposed generalized quality criterion.

The paper presents the results of the investigation of the I. Boaventura und A. Gonzaga integrated performance evaluation method of edge detection [1-2], obtained using the bundled software of stochastic simulation ≪CS sF≫ [3]. The methods and approaches of stochastic simulation were used in the experiments and the reference images were approximated with the two-dimensional renewal stream [4-7]. The performance of the outline drawing detection was evaluated by Boaventura und Gonzaga method for three algorithms of the edge detection (≪ Canny≫, ≪Marr-Hildreth≫ and ≪ISEF≫) under different levels of peak signal-to-noise ratio. The results of the investigation are presented as dependences of the estimate probability of the correct edge detection, the type 1 and 2 errors, on S/N ratio. The performance analysis of the above three algorithms for the images, produced on the basis of morphology type ≪A≫ and ≪F≫, is done based on the performed evaluation.

Zusammenfassung In diesem Beitrag wird ein stochastischer Algorithmus zur Bildgenerierung durch einen zweidimensionalen Markov Renewal Process (MRP) betrachtet. Die Zustandsraumauswahl und Gittereigenschaften, die die Gitterform (eine Form der Konturstruktur) voraussetzt, werden manuell in Voraus vom Operator bestimmt. Der Algorithmus lässt verschiedene Typen der Gitterformstrukturen zu. Horizontale, senkrechte und diagonale Elemente bei einer 8-fach-Nachbarschaft sind erlaubt. Er bietet eine hervorragende Grundlage für Entwurf, Analyse, Validierung und Qualitätssicherung von Bildverarbeitungsalgorithmen.