Diabetic retinopathy is one of the most frequent complications of diabetes, which leads to severe consequences, including rapid and irreversible vision loss. The laser coagulation procedure to treat diabetic retinopathy consists in applying a series of microburns to the fundus to deal with macular edema. The existing hardware/software packages are primarily based on the use of a predetermined pattern for coagulate arrangement. However, due to the complex form of edema and vascular system, this approach leads to an uneven arrangement. To solve the problem, we propose a new approach based on the application of sphere packing algorithms (circle packing in two-dimensional images) in the specified area of interest. Since one of the main requirements for the laser coagulation procedure is that it should have the minimum duration, a problem of the computational complexity of the developed algorithms arises. This requirement is completely ignored by the existing approaches, therefore the development of new high-performance coagulate arrangement algorithms is highly relevant. In the paper, we propose seven new algorithms for coagulate arrangement and provide a detailed analysis of key characteristics of the algorithms. The characteristics considered have made it possible to extract information relating to the algorithm properties. Regularity is determined by the median, asymmetry and the kurtosis; determinism is determined by the variance and the mean.

A personalized medical approach can make diabetic retinopathy treatment more effective. To select effective methods of treatment, deep analysis and diagnostic data of a patient’s fundus are required. For this purpose, flat optical coherence tomography images are used to restore the three-dimensional structure of the fundus. Heat propagation through this structure is simulated via numerical methods. The article proposes algorithms for smooth segmentation of the retina for 3D model reconstruction and mathematical modeling of laser exposure while considering various parameters. The experiment was based on a two-fold improvement in the number of intervals and the calculation of the root mean square deviation between the modeled temperature values and the corresponding coordinates shown for the convergence of the integro-interpolation method (balance method). By doubling the number of intervals for a specific spatial or temporal coordinate, a decrease in the root mean square deviation takes place between the simulated temperature values by a factor of 1.7–5.9. This modeling allows us to estimate the basic parameters required for the actual practice of diabetic retinopathy treatment while optimizing for efficiency and safety. Mathematical modeling is used to estimate retina heating caused by the spread of heat from the vascular layer, where the temperature rose to 45 °C in 0.2 ms. It was identified that the formation of two coagulates is possible when they are located at least 180 μm from each other. Moreover, the distance can be reduced to 160 μm with a 15 ms delay between imaging.

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The paper proposes a technology for effective feature selection to localize individual characteristics of anatomical and pathological structures in the human eye fundus. Such an approach allows the intellectual analysis of features to be conducted using color subspaces and the regions of interest to be identified. This problem is relevant because in this way the efficiency of laser coagulation surgery can be improved. The technology is based on the texture analysis of certain image patterns. The initial textural attributes are derived from different statistical image descriptors calculated using the MaZda library (image histogram, image gradient, series length and adjacency matrices). The analysis of the feature space informativity and selection of the most effective features are carried out using the discriminant data analysis. The best-size image fragmentation windows for eye fundus clustering and sets of features that provide the necessary accuracy in identifying the regions of interest were derived via analyzing the following four image classes: exudates, thick vessels, thin vessels, and healthy areas. The feature selection technology was based on clustering using a K-means method, with the Euclidean and Mahalanobis distance used as a similarity measure. The required minimum size of the fragmentation window and the similarity measure were chosen from a criterion of the minimum clustering error among all the smallest window sizes. The article also presents a system for automatically forming a coagulate plan, expected to be used to support the decision-making during laser retinal coagulation surgery in the treatment of diabetic macular edema. This system is currently being developed based on the proposed technology.

For diabetic retinopathy treatment, laser coagulation is used in modern practice. During the laser surgery process, the parameters of laser exposure are selected manually by a doctor, which requires the doctor to have sufficient experience and knowledge to achieve a therapeutic effect. On the basis of mathematical modeling of the laser coagulation process, it is possible to estimate the crucial parameters without performing an operation. However, the retina has a rather complex structure, and when even low-cost numerical methods are used for modeling, it takes a long time to obtain a result. In this regard, the development of time-efficient algorithms for three-dimensional modeling is an urgent task, since the use of such algorithms will provide a compre-hensive study within a limited time. In this paper, we study the execution time of algorithms that implement various variations in the application of the splitting method and the finite difference method, adapted to the set problem of heat conduction. The study reveals the most efficient algorithm, which is then vectorized and implemented using the CUDA technology. The study was carried out using Intel Core i7-10875H and Nvidia RTX 2080 MAX Q and showed that an analog of the vector algorithm, focused on solving a multidimensional heat conduction problem, provides an acceleration of no more than 1.5 times compared to the sequential version. The developed vector-based algorithm, focused on the application of the sweep method in all directions of the three-dimensional problem, significantly reduces the time spent on copying into the memory of the video card and provides a 40-fold acceleration in comparison with the sequential three-dimensional modeling algorithm. On the basis of the same approach, a parallel algorithm of mathematical modeling was developed, which provided a 20-fold acceleration at full processor load.

When laser coagulation of eye retina is carried out, the laser beam is directed to target retinal areas selected by an ophthalmologist. The exposure to laser light produces a photocoagulate. When using laser coagulation, the main problem is selecting both the laser exposure areas that would cover all pathological zones and the laser exposure parameters to prevent retina damage. Any patient has an individual fundus structure. The individual structure of pathological and anatomical elements must be taken into account to achieve the desired therapeutic effect. The formation of coagulates in all hemorrhage-affected areas results in the desired therapeutic effect. The vascular layer must be heated to a sufficient temperature to form a coagulate. Such an effect can be predicted using mathematical modeling of laser exposure. In this paper, we consider methods of mathematical modeling of laser exposure based on the solution of a heat equation. The methods are compared in terms of their computational complexity and solution stability. An analysis of the possibility of predicting the therapeutic effect using methods of mathematical modeling of laser exposure is carried out.

1 Самарский национальный исследовательский университет имени С.П. Королёва, Самара, Россия, 2 Институт систем обработки изображений РАН -филиал ФНИЦ «Кристаллография и фотоника» РАН, Самара, Россия Аннотация При анализе вещества с кристаллической наноструктурой наибольший интерес пред-ставляет задача параметрической идентификации кристаллических решёток. Однако суще-ствующие методы решения данной задачи, такие как метод оценивания параметров ячейки Браве и метод оценивания объёма ячейки Вигнера-Зейтца, не обеспечивают требуемую точность. В настоящей статье предлагается алгоритм параметрической идентификации кри-сталлических решёток на основе градиентного метода наискорейшего спуска для решения проблемы низкой точности идентификации. Исследование возможности структурной иден-тификации проводилось с использованием большого набора искажённых решёток. Полу-ченные результаты показали существенный рост точности по сравнению с существующими методами параметрической идентификации.Ключевые слова: параметрическая идентификация, элементарная ячейка, кристаллическая решётка, ячейка Браве, ячейка Вигнера-Зейтца, градиентный метод наискорейшего спуска.Цитирование: Широканев, А.С. Исследование алгоритма параметрической идентифи-кации кристаллических решёток с применением градиентного метода наискорейшего спус-ка / А.С. Широканев, Д.В. Кирш, А.В. Куприянов // Компьютерная оптика. ВведениеЗадачам реконструкции трёхмерных объектов на сегодняшний день уделяется большое внимание [1 -4]. К таким задачам относится реконструкция трёх-мерной модели кристаллической решётки. Одним из методов определения параметров трёхмерной модели решётки является рентгеноструктурный анализ [5, 6].С появлением электронной микроскопии стало возможно наблюдать атомарную структуру вещества. Линейное разрешение электронного микроскопа дос-тигает порядка 0,1Ǻ [7]. Данное достижение приво-дит к необходимости решения задачи вычисления па-раметров элементарной ячейки кристаллической ре-шётки по изображениям, полученным с электронного микроскопа.Определение параметров элементарной ячейки по наномасштабным изображениям, полученным с элек-тронного микроскопа -сложный, многоэтапный про-цесс: двумерные изображения предварительно обра-батываются; реконструируется трёхмерная структура узлов кристаллической решётки; решается задача па-раметрической идентификации, то есть оцениваются параметры элементарной ячейки по трёхмерному на-бору узлов. Несмотря на существование методов оп-ределения параметров ячейки без предварительной реконструкции узлов решётки [8], описанный подход является наиболее универсальным.Элементарная ячейка в кристаллографии является фундаментальным понятием, которое определяется как минимальный воображаемый объём кристалла, параллельные переносы (трансляции) которого в трёх измерениях позволяют построить трёхмерную кри-сталлическую решётку в целом [9]. Элементарная ячейка должна описываться конечным набором пара-метров и образовывать любую кристаллическую структуру.Примером элементарной ячейки является ячейка Вигнера-Зейтца [9]. Данная ячейка пред...