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The object of this study is the process of filtering astronomical frames that contain images of potential objects in the Solar System. To contour the image of each such object and recognize it in contrast with the background of the frame, it is necessary to filter the image. Most often, a variety of high-pass filters are used to determine the high-frequency component of the image, which can be removed as a coarse-grained component. Any image filtering is aimed at increasing the signal-to-noise ratio and reducing the dynamic range of the background image. However, the filtering process is quite resource- and time-consuming. This is especially true for systems for parallel processing of series of astronomical frames in real time (online). Therefore, to solve the problem of lack of frame fragmentation, which leads to high consumption of RAM, a procedure for fragmenting astronomical frames has been proposed. Owing to the introduction of a formal connection between the values of frame pixels and fragments, as well as determining their number, it was possible to reduce RAM utilization. Testing was carried out using the following high-pass filters ‒ ideal filter, Butterworth filter, and Gaussian filter. Using the devised procedure for fragmenting astronomical frames has made it possible to reduce the utilization of RAM during filtering. As a result, with parallel processing, this has also made it possible to speed up the high-frequency filtering procedure itself. The procedure devised for fragmenting astronomical frames was tested in practice within the framework of the CoLiTec project. It was implemented in the On-Line Data Analysis System (OLDAS) of the Lemur software. The study showed that when using the devised procedure, RAM utilization was reduced by 7–10 times. And the speed of filtration itself increased by 2–3 times. Accordingly, the processing time for each astronomical frame was reduced by 2–3 times. [ABSTRACT FROM AUTHOR]

The variability of shooting conditions affects the quality of images of Solar System objects in a series of frames. Identification of a frame with the corresponding part of the sky becomes difficult if the quality is poor. Because of this fact, the detection quality indicators and estimation of the position of Solar System objects are significantly reduced when using already known methods and international astronomical catalogs. To solve this problem, the procedure of full identification of measurements of objects on digital frames was devised. This procedure is based on the formation of triplets (triangles) of primary identification from the side of the digital frame and the astronomical catalog. Positional coordinates on the frame and ideal tangential coordinates from the catalog were used. Owing to this, a comparison of the primary identification triplets was carried out by comparing the calculated angles of the triangle vertices. The identity of the hypothesis was determined by comparison with the acceptable deviation. The use of the developed full identification procedure makes it possible to reduce the number of false detections and improve identification with reference astronomical objects. The study showed that when identifying frames, astrometry has better accuracy of reference to the starry sky. In addition, the standard deviation of frame identification errors in this case is 6–9 times less than without using the devised procedure. The procedure developed for complete identification was practically tested within the framework of the CoLiTec project. It was implemented in the Lemur software for automated detection of new and tracking of known objects. Owing to the use of Lemur software and the proposed computational procedure implemented in it, more than 700,000 measurements of various astronomical objects under study were successfully identified. [ABSTRACT FROM AUTHOR]

The object of this study is images of various objects of the Solar System on a series of digital frames. The variety and quality of shooting conditions make it difficult to identify a frame with the corresponding part of the sky. This fact significantly reduces the quality indicators of detection and estimation of the position of objects of the Solar System using already known computational methods and international astronomical astrometric and photometric catalogs. To solve this problem, a procedure for preliminary identification of measurements of digital frames of one series was devised. This procedure is based on the determination of the shift parameters between the dimensions of a frame and the forms of a catalog or another frame. Also, taking into account the possibility of forming false measurements has made it possible to increase the accuracy of identification and resistance to various kinds of destabilizing factors. Based on this, the final estimation of the shift parameters between frames was performed. Due to these features, the use of the devised preliminary identification procedure makes it possible to improve identification with reference astronomical objects and reduce the number of false detections. The study showed that when identifying frames, the fitting gives the best accuracy of binding to the starry sky. Also, the standard deviation of frame identification errors in this case is 7–10 times less than without using the devised procedure. The procedure developed for preliminary identification of measurements of digital frames of one series was tested in practice within the framework of the CoLiTec project. It has been incorporated into the Lemur software for automated detection of new and tracking of known objects. Owing to the use of the Lemur software and the proposed procedure implemented in it, more than 700,000 measurements of various astronomical objects under study were successfully identified. [ABSTRACT FROM AUTHOR]

Accurate sky identification is one of the most important functions of an automated telescope mount. The more accurately the robotic telescope is navigated to the investigated part of the sky, the better the observations and discoveries made. In this paper, we present mathematical methods for accurate sky identification (celestial coordinates determination). They include the automatic selection of the reference stars, preliminary and full sky identification, as well as an interaction with international databases, which are a part of the astrometric calibration. All described methods help to receive accurately calculated astrometric data and use it for the positional calibration and better navigation of the automated telescope mount. The developed methods were successfully implemented in the Collection Light Technology (CoLiTec) software. Through its use, more than 1600 small solar system objects were discovered. It has been used in more than 700,000 observations and successful sky identifications, during which, five comets were discovered. Additionally, the accuracy indicators of the processing results of the CoLiTec software are provided in the paper, which shows benefits of the CoLiTec software and lower standard deviation of the sky identification in the case of low signal-to-noise ratios. [ABSTRACT FROM AUTHOR]

The object of this study is the aperture brightness of the image of the object, which has a variety of typical shapes in the frames of the series. It directly depends on the stability of the shooting conditions of the objects under study. Thus, determining the exact aperture brightness of an object in the frame becomes more difficult. For this purpose, a method was devised for determining the aperture brightness of an object using the typical shape of its image on a series of frames. This method is based on the formation of a typical shape of a digital image of an object based on data from all frames of the series. The typical shape makes it possible to take into account the peculiarities of the formation of the image of the object on each frame of the series. Based on this, a more accurate estimate of the initial approximation of the parameters of all Gaussian images of the object is performed. In addition, the adaptation of the method to the standard shape makes it possible to perform a more accurate assessment of the aperture brightness of the object in comparison with the analytically defined profile. An estimate of the aperture brightness of the object was derived using the least squares method. Due to minimization using the Levenberg-Marquardt algorithm, the use of the method improved identification with reference objects and reduced the number of false positives. The study showed a decrease in the standard deviation of frame identification errors by 5–7 times when using a typical shape of a digital image. The devised method for determining an object's aperture brightness using its image's typical shape was tested in practice within the framework of the CoLiTec project. It was implemented in the intra-frame processing unit of the CoLiTecVS software for the automated construction of brilliance curves of the studied variable stars. Owing to the use of the CoLiTecVS software and the proposed computational method implemented in it, more than 700,000 measurements of various objects under study were successfully processed and identified. [ABSTRACT FROM AUTHOR]

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The appearance of "blurred" digital images is a consequence of the violation of the immobility of the camera during the shooting of the objects under study. To this end, a procedure was devised for matched filtering of the blurred digital image of the object using its typical image form in a series of frames. This procedure is based on the automated formation of a typical form of a digital image, as well as on the choice of special parameters for the transfer function of the matched filter. Adapting the procedure specifically to the typical form makes it possible to perform a more accurate assessment of the required parameters of the blurred digital image compared to the analytically set profile. The formation of a typical form makes it possible to take into account the features of the very formation of the blurred image on each frame of the original series. Based on this, a more accurate assessment of the initial approximation of the parameters of all Gaussians of the object image is performed. In practice, matched filtering makes it possible to highlight blurred images of objects against the background of substrate noise. Also, using the matched filtering procedure makes it possible to improve the segmentation of images of reference objects and reduce the number of false detections. The devised procedure for the matched filtering of a blurred digital image using its typical form has been tested in practice as part of the research in the framework of the CoLiTec project. It was implemented in the intraframe processing unit of the Lemur software for the automated detection of new and tracking of known objects. Owing to the use of Lemur software and the proposed computational procedure introduced into it, more than 700,000 measurements of various objects under study were successfully processed and identified. [ABSTRACT FROM AUTHOR]

A computational method for the automated formation of a typical form of a digital image of the investigated objects on a series of digital frames has been developed. Due to the imperfection of the mounting of digital cameras, as well as their automated mounts, their immobility at shooting during exposure time can be disturbed, which leads to the formation of "blurred" images of objects of various forms. Due to such inaccuracies in the tracking of objects on digital frames, even in one series, the typical form of the image of objects can vary from frame to frame. This fact of the difference in the standard form significantly complicates the execution of various image processing tasks. In order to simplify the evaluation of the image parameters of objects in a series of digital frames, it has been proposed to use a typical image on a digital frame corresponding to the average image of objects as a model of object images. In this case, the appearance of the image of the object, its form, the distribution of brightness in the image will be determined only by the typical image. This paper proposes a computational method for the automated formation and evaluation of the typical form of the image of an object in a digital frame based on the initial data- the actual given digital frame. This computational method is based on the selection of single images of objects and the formation of their rectangular area. Next, the offset is evaluated, and the selected single images of objects are normalized to calculate the typical form of the object image. Using the method makes it possible to highlight objects against the background of noise and reduce the number of false detections. It is recommended to apply the method only in the case when the frames have defects and "blurs" during the shooting, otherwise there will be unreasonable additional computational costs. The developed computational method was successfully tested in practice within the framework of the CoLiTec project and implemented in the intraframe processing unit of the Lemur software. [ABSTRACT FROM AUTHOR]

A computational method for matched filtration with analytical profile of the blurred digital image of the investigated objects on digital frames has been developed. Such «blurred» objects can be the result of an involuntary shift of a fixed camera, an incorrect choice of the mode of guiding the telescope (diurnal or object tracking) or a failure of the diurnal tracking. This computational method is based on the analytical selection of the typical form of the object’s image, as well as on the choice of special parameters for the transfer function of the matched filter for the blurred digital image, which makes it possible to evaluate the required parameters of the blurred digital image. In addition, determining the number of Gaussians of the object’s image makes it possible to perform the most accurate assessment of the initial approximation of the parameters of their shape. Thus, matched filtration makes it possible to highlight the investigated objects with a blurred image of a typical shape against the background of substrate noise. Using the computational method of matched filtration makes it possible to improve the segmentation of images of reference objects on the frame and reduce the number of false detections. The developed computational method for matched filtration with analytical profile of the blurred digital image of the investigated objects on the frames was tested in practice as part of the research of the CoLiTec project. It was implemented in the intraframe processing unit of the Lemur software for the operational automated detection of new and observation of known objects with a weak brightness. Owing to the Lemur software using and the proposed computational method introduced into it, more than 500,000 measurements of the various investigated objects were successfully processed and identified [ABSTRACT FROM AUTHOR]

Modern conditions of enterprise operation are characterized by a large number of negative factors. First of all, such factors include decrease in business activities of stock markets, low level of exchange fluctuations predictability etc. These factors generate additional financial risks and lead to significant losses and damages, and as a result they can cause the financial crisis situations. The novelty of scientific challenges contains the following tasks: to develop the complex of economic mathematical models which allows assessing the impact of uncontrollable external factors on financial activity; to create preventive financial strategies ensuring stable functioning and development of the enterprise under threats. The development of models is based on methods of multivariate analysis (principal component analysis, the method of the development level, the method of gravity center, hierarchical agglomerative methods and iterative cluster analysis, discriminant analysis, classification trees), econometric methods (pool data models, logit- and probitmodels, vector autoregression technology, error correction models), simulation methods and system dynamics approach. The models implication in companies’ activity has allowed developing financial strategy balanced on various directions while considering the potential financial risks. [ABSTRACT FROM AUTHOR]