The Method for Generating a Set of Reference Images for Assessing the Condition of Critical Infrastructure Facilities Using Mobile Robots

. The purpose of this work is to improve the accuracy of critical infrastructure condition assessment using mobile robots by considering the geometric distortions of the current images during the formation of a set of reference images. The goal is achieved by determining the sampling step values by angles and sighting height without loss of accuracy. The most important result is the determination of acceptable discretization values in the range of angles and heights of a correlation-extreme navigation system. The significance of the obtained results is in solving the problem of forming a set of reference images, which will reduce the impact of changes in the geometry of sighting on the accuracy of the evaluation of objects. A special feature of the results obtained is the establishment of maximum permissible sampling steps in angles and heights of sight to ensure the required accuracy of object state estimation. When forming a set of reference images, the sampling step by height should be (0.06....0.11)% and (0.12....0.2)% relative to the initial flight altitude for the sighting surface with normal and high object saturation, respectively. The angular sampling step is 10...17 degrees and 6...10 degrees, respectively, for the same surface types. The difference from known works is that the perspective and scale distortions are considered at the stage of formation of a set of reference images, which ensures high accuracy of the system functioning in conditions of orientation and sighting geometry changes


INTRODUCTION
One priority area for assessing the condition of critical infrastructure objects, overhead power transmission lines above land and sea, and conducting search and rescue operations in water areas is the further development and use of flying mobile robots (MRs). They allow obtaining a necessary information on the observed objects regardless of the complexity of access to them, including daily, weather conditions, and seasonal variations. High-precision correlation-extremal navigation systems (CENS) are installed on board modern mobile robots, which simultaneously serve as the information extraction systems about the observed objects.
The efficiency of using such an MR is determined by numerous internal and external factors. Among these factors, with random characteristics, geometric conditions of sighting and orientation of the mobile robots hold a significant position. These conditions can lead to discrepancies between the images formed during monitoring, referred to as Current Images (CI), and the preprepared Reference Images (RI). This is due to the complexity of ensuring identical conditions to obtain the original information necessary both forming RI and CI. As a result, discrepancies arise due to perspective and scale distortions, which need to be considered during the secondary image processing stage for the image comparison. This circumstance inevitably necessitates the real-time elimination of such distortions, which complicates the procedure of forming the comparison result and, consequently, reduces the efficiency in the secondary processing of CENS. Moreover, the accuracy of CENS functioning is also decreased.
One possible way to solve this issue in assessing the condition of critical infrastructure objects, aerial power lines, and conducting search and rescue operations is to consider the potential perspective and scale distortions starting even from the stage of forming a set of reference images. This can be achieved by constructing a set of reference images for values of the discretization step in angles and elevation, at which the minimum permissible correlation link will be provided between the neighboring image fragments that form the initial set based on the selected informative indicator. Such an approach will ensure high accuracy indicators of CENS, and any discrepancies between the compared images will be limited to the discretization range in angles and elevation.
Thus, based on the requirements for ensuring accuracy, it is possible to determine the values of the discretization step within the ranges of elevation and viewing angles. Additionally, this approach will provide the necessary set of reference images with the minimum number of images without compromising accuracy and with the highest speed. As a result of implementing this approach, a reliable assessment of the condition of critical infrastructure objects and aerial power lines, as well as the search and rescue operations, etc., will be ensured.
To date, a significant number of publications have been dedicated to the development of methods and algorithms to enhance the efficiency of mobile robot operation. However, little attention has been paid to the formation of a set of reference images, the use of which leads to a significant reduction or complete elimination of the influence of perspective and scale distortions. Therefore, this article proposes a method for forming a set of reference images used in mobile robots for assessing the condition of critical infrastructure objects, aerial power lines over land and sea, and conducting search and rescue operations in water bodies, with consideration for reducing or eliminating the influence of scale and perspective distortions.
Let us examine the known methods and results for solving the problem of enhancing the efficiency of CENS and forming reference images for them.

PUBLISHED LITERATURE ANALYSIS
Chakraborty, P. et al. (2022) presented the results of detecting duplication forgery regions using the COMOFORD database, employing Discrete Cosine Transform (DCT), k-dimensional tree (kd-tree) for efficient sorting, and a reliable matching method. By using a 16 × 16 block size divided into four parts, forgery can be detected in PNG images with higher performance, identifying images with a quality factor of 0.5 and a threshold value of 10. Good results were also obtained for JPEG images.
Rohini The analysis of the literature indicates the prospects of using MR for monitoring ground objects and developing methods for generating reference images to reduce the volume of operations. However, reduction of computational costs remains unresolved issue when monitoring the states of critical infrastructure objects using flying mobile robots equipped with correlation-extreme navigation systems. This reduction is based on minimizing the number of fragments of reference images that can achieve the set goal while ensuring the required accuracy and reliability of monitoring critical infrastructure objects.

METHODS, RESULTS, AND DISCUSSION
The decision function (DF), as a result of comparing the current and reference images, is generally described by the following expression: where SP F is the image comparison operator; ( , , ) Sr CI t  is the current image; According to the approaches adopted by where orientation ν , it is hypothetically necessary to create a set of reference images {•}, whose use during the determination of ( , ) Rrt will minimize the influence of geometric distortions and achieve the best accuracy in assessing the state of critical infrastructure objects: . In other words, it is necessary to find discretization parameters in height h , viewing angles ,   , and orientation ν , that, when used during the formation of the set of reference images {•}, will subsequently ensure that when selecting one of the reference image fragments, ( , ) min  Rrt . Solution of the problem. Let's examine the influence of geometric distortions on the formed CENS CI. For this purpose, we will use geometric constructions. The influence of scale distortions is shown in Fig. 1, and the influence of perspective distortions is shown in Fig. 2. Changes in the altitude of the MR (as seen in Fig. 1a)) result in linear changes in the image dimensions, while changes in the viewing angles of the CENS (Fig. 1b)) lead to trapezoidal (non-linear) changes in the CI dimensions ( 11 mn  , 12 mn  ). Scale distortions of the CI relative to the original size (m1  n1) of the image can be described by the following expressions: where 01 h h h    is the change in the altitude of the MR.
Changes in the viewing angles also cause distortions in the CI dimensions, which can be determined according to the following expressions: where 21 θ θ θ    is the change in the orientation angle of the MR.
Unlike the scale distortions, perspective distortions do not only lead to changes in slant height but also affect the relative dimensions of the CI. This is an important aspect that must be considered when selecting RI from the set, as ambiguity may arise due to high correlation between images for other geometric viewing conditions.
Thus, taking into account the geometric distortions, the decision function (DF) can be represented in the general form by the expression: Expression (9) implies that the smaller the discretization step, the higher the degree of mutual correlation between RI and CI. Let's assess the impact of geometric distortions on the correlation degree of the compared images. For this purpose, we use the results of statistical modeling performed using the classical correlation algorithm for typical viewing surfaces with normal F1 ( min max V V V 10...15    ) and high object density F2 ( max VV  ). During modeling, it was assumed that the size of the RI is 100 100  pixels. The sizes of the CI correspond to the selected shooting mode with normal and high object density, which are 1280 720  pixels. The flight height of the MR was chosen from 500 to 600 meters. Both the brightness of the objects themselves and the contrast between them were used as informative parameters to describe the objects in the image.
The results of modeling the influence of scale distortions on the coefficient of mutual correlation (CMC) of the compared images are presented in Fig. 2, while the results for perspective distortions are shown in Fig. 3.
When determining the dependence of the CMC on changes in the viewing angle, it was assumed that α 40  . The analysis of the results presented in Fig. 2 and Fig. 3 of the modeling shows that the formation of the unimodal DF that ensures high accuracy in estimating the states of critical infrastructure (SCI) ( is possible with a discretization step in height within the range of 0.06….0.11 relative to the original flight height for viewing surfaces (VS) with normal object density. For VS with high object density, this parameter can be in the range of 1.12….1.2. The discretization step in angles for VS with normal object density should be selected within the range from 10 to 17 degrees, and for VS with high object densitywithin 6 to 10 degrees. The feasibility and possibility of using a larger discretization step in height and viewing angles for highly object-dense viewing surfaces are justified due to the inevitable appearance of false objects in the images when the viewing conditions change.  As mentioned above, let's consider that perspective distortions, unlike scale distortions, lead not only to changes in the slant height but also to changes in the relative sizes of CI.
In other words, it is possible to reduce the number of RI fragments in the sought set since the correlation degree for certain changes in angles and heights can be the same. This condition can be expressed as follows: Satisfying condition (10) allows reducing the number of RI fragments in the set and decreases the computational burden during the formation of the DF. However, it leads to ambiguity in selecting the RI fragment from the set. Elimination of this ambiguity occurs during the secondary processing stage.

CONCLUSIONS
As a result of the conducted research, a method for forming a set of reference images (RI) has been developed. The method is based on determining the values of the discretization step in angles and height of the CENS (correlation-extremal navigation system), which allows considering the influence of geometric distortions on the system's performance during the formation of the RI set. Such an approach significantly simplifies the algorithm of the secondary processing of the system and ensures high accuracy of its functioning under changes in the viewing geometry. Moreover, the computational costs are substantially reduced by forming the minimum permissible number of reference images in the set based on the discretization parameters in angles and height.
During further research, a series of experiments are planned to collect statistical data and expand the database to achieve the best accuracy in evaluating the state of critical infrastructure objects.