Technical vision systems in intelligent mobile robots directly increase productivity and visibly reduce costs related to the quality error factor by providing flexible-automated control over the quality of the manufactured product. However, when the system recognizes the images of the object, difficulties arise due to the linear movement of the image (rotation of the image around the center of gravity and displacement in the coordinate plane). Such linear displacements cause methodological errors in the estimation of proximity measures between reference and recognizable objects. Since such destabilizing factors reduce the reliability of image recognition, it is important to overcome the issue of invariance to linear displacements of images. In the proposed algorithm, the contour points of the two-dimensional binary images of objects at the output of the vision system are displayed as coordinates on the Cartesian coordinate plane of the screen. The values of the indicated coordinates are not invariant to the linear displacement and rotation of the image. Therefore, in order to correctly recognize such images, it is necessary to ensure that the image points are invariant with displacement and rotation. In order for the image to be invariant to orthogonal displacement, the coordinate system must be moved to the center of gravity of the defined image. Then, the rotation angle of the reference object relative to the initial position is determined by the moments of inertia relative to the coordinate axes of the image. After the rotation angle of the image is estimated, the coordinates of the contour points are found by rotating the reference image in the computer memory by this angle. Then the coordinates of the contour points of the current image are compared with the coordinates of the contour points of the rotated reference image. This comparison provides accurate information on whether the current image is the same or different from the reference image. Thus, the proposed algorithm allows invariant recognition of twodimensional binary images. The higher the level of invariance, the lower the average risk ratio. The proposed algorithm was simulated on a computer and positive results were obtained.
risk
Pattern recognition, invariance, linear displacement, image rotation, vision system, average
Depending on the actual problems in technical vision systems of digital industry and intelligent robots, there are problems of perception and recognition of object regularities, as well as technological processes for processing and preparation of relevant data. The effectiveness and efficiency of the systems directly depends on the reliability of the accurate performance of the measurement process, the compatibility of the parameters of the recognition and reference images, and the adoption of the necessary decision with the obtained results related to pattern recognition. Such processes occur due to
2023 Copyright for this paper by its authors. the presence of destabilizing factors, because due to the influence of these factors, errors occur in the adjustment of measurement and imaging parameters [1,2]. It is precisely such errors that make it difficult for intelligent robots to make the right decisions. The decision-making of robot complexes has an influence of the degree of proximity between the recognized and reference images included in the database in image recognition. In modern industry, technical vision systems have become an alternative to the human factor in performing visual or manual quality control operations of products. Therefore, robotics companies are committed to increasing productivity and reducing costs associated with quality errors that can occur during human supervision. Basically, when recognizing images of objects in recognition systems, certain difficulties arise due to their linear displacement (rotation of the center of gravity of the image or change of its position in the coordinate plane). Thus, important problems arise when the manufactured product rotates on the conveyor line or changes its direction after production. Obviously, determining the spatial orientation of objects in an industrial setting is both a complex and economically expensive task. These factors cause changes in the number of products, absolute values of coordinate parameters, random measurement error in the values of object parameters. These and other unstable factors reduce the accuracy of object recognition, so the recognition system should be invariant to changes in the object's position [3,4].
Various methods and tools have been proposed in various literatures to ensure the invariance of the object's rotation around the center of gravity and the change of the object's position. However, these existing methods cannot provide the most accurate invariance in image recognition. In these works, in order to ensure the invariance of the linear displacement in the object images, the main attention is paid to the static moments, which are considered their main feature. The analysis of these methods showed that in this case the symbols are very complex and therefore the reliability is low. Therefore, research aimed at finding the best methods and tools to achieve image recognition variability in technical vision systems remains relevant [5,6,7].
During the recognition of images of objects in robotic complexes, certain difficulties arise due to the rotation, displacement and scaling of the image around the center of gravity. Such problems lead to the loss of information about the number of objects, their location and the absolute value of the proximity measure between objects, and random errors in the calculation of values. Since such destabilizing factors reduce the reliability of image recognition, it is important to overcome the issue of invariance to linear displacements of images [8,9].
Various methodologies and tools have been proposed to ensure the invariance of the rotation of object images around the center of gravity and large-scale changes in the image. However, these methods and techniques cannot provide the most accurate invariance in object recognition. Therefore, research aimed at finding the best methodologies and tools to achieve invariance in image recognition remains relevant [10,11].
In order to clarify the solution to the problem of image detection and measurement of its parameters, the methods of recognition in the applied system were analyzed. Unlike all the methods in the table, more attention was paid to its geometric features. There are several ways to achieve sensitivity in transformations in the field of recognition systems, in particular, two groups of approaches can be distinguished among the most commonly applied transformation transitions. The methods of the first group include spatially insensitive properties (for example, the method of moments, the Fourier method of images). On the other hand, those who adopt an alternative approach work with object models and try to combine the objects observed and used in training by choosing parameters [12,13,14].
The method based on the analysis of the amplitudes of the individual harmonics of the Fourier spectrum of images has a number of advantages, such as a small number of important features, an unambiguous relationship between the rotation of the image or the corresponding rotation, the scale of the spectrum. The harmonic shift of the spectrum can be used to measure the corresponding shift in the image [15,16,17].
Mellin and Fourier-Mellin transforms also reduce the number of features like Fourier transforms, which simplifies the recognition scheme. The double-scale invariance of the latest method allows to stabilize the verticality of the statistical characteristics of the measurement images based on them, thereby increasing the accuracy of the measurement. These methods are performed only in coherent optical systems and require fairly sophisticated image analyzers to achieve some degree of invariance [18,19,20].
The secant method is used to recognize images that are large enough to be contoured using segments or straight sequences. For this method, it is not enough to draw the contours of the images, but also to divide the angular area of the image into segments that can contain several or more objects. The most important condition when using this method is the stability of the visible shape of the object [21,22,23].
After comparing different algorithms and schemes for solving the problems of recognition and identification of known objects, it can be concluded that among the most promising schemes are the characteristics of the object determined (controlled) by synchronous detection of the center of the image and the geometric moments of its image. its Fourier transform is used, or one of the methods of determining the position of the main maximum of the correlation function of an object description, which correlates schemes using a priori synthesized discriminant functions. However, when there are sufficiently arbitrary and a priori unknown changes in geometric parameters (properties), for example, the scale and shape of its description, for example, the use of the recognized methods of consideration is not effective enough [24,25].
Space has a Х0У0 coordinate system and a certain description. When the coordinate axes are rotated, the coordinates of the image also change. Therefore, the task is to determine the angle of rotation of the coordinate axes and, accordingly, at what angle the image is rotated. According to the task, the following sequence of steps was performed.
The initial coordinates of the image are set х0,у0 2. The new image coordinates are calculated by the following formulas when the axes are rotated 3. The initial axial and centrifugal moments of inertia of the figure relative to the axes are determined according to the following formulas
The aim of the study is to find the angle of rotation of the coordinate axes. In other words, it is necessary to find the angle by which the figure is rotated relative to the original Х0У0 coordinate axes.
Where
ОХ0 və ОУ0 4. The axial and centrifugal moments of inertia of the figure relative to the rotating axes ОХ1 and ОУ1 were found
To solve this equation, the double angle formula for sine and cosine is applied through the tangens function.
1 1 = 0− 0 ∙ 2
Then, when formula (11) is used, formulas (12) and (13) will be written as follows:
According to obtained 1 = 2 ∙ ( + )
2 + 1 2 = 2 ∙ ( + )
2 − 1 1 = Returning to the original equation and the beginning, without substitution, is finally
Here, is the angle that takes into account in which quadrant the figure will be located in the Cartesian coordinate plane as a result of the rotation of the coordinate axes (table 1).
Here, as well as in the solution of option 1 (arctg), one should take into account in which quarter the figure is located as a result of the rotation.
Based on the received formulas (16), a program was written to confirm the correctness of the received formulas. For example, the rotation of the quadrilateral, whose coordinates are listed in the table below, was considered (Table 3)
In the proposed algorithm, the contour points of the two-dimensional binary images of objects at the output of the vision system are displayed as coordinates in the Cartesian coordinate plane of the display. The values of the indicated coordinates are not invariant to the linear displacement and rotation of the image. Therefore, in order to correctly recognize such images, it is necessary to ensure that the image points are invariant with displacement and rotation. In order for the image to be invariant to orthogonal displacement, the coordinate system must be moved to the center of gravity of the defined image. Then, the rotation angle of the reference object relative to the initial position is determined by the moments of inertia relative to the coordinate axes of the image. After the rotation angle of the image is estimated, the coordinates of the contour points are found by rotating the reference image in the computer memory by this angle. Then the coordinates of the contour points of the current image are compared with the coordinates of the contour points of the rotated reference image. This comparison provides accurate information on whether the current image is the same or different from the reference image. Thus, the proposed algorithm allows invariant recognition of two-dimensional binary images.
A block diagram of the algorithm for computer simulation is given in the figure. The main program consists of subroutine input, figure coordinates input after rotation, rotation angle calculation subroutine, and result print blocks. The process of entering the initial data received in the subprogram entry into the computer takes place. Cartesian coordinates of a plane figure are taken as initial data. Then we rotate the arbitrarily drawn plane figure at a certain angle. The new coordinates of the plane the angle formed during rotation. Also, the subroutine used interacts directly with the coordinate input block after rotation. Calculation of new coordinates during rotation is determined according to the following formulas: The implementation of the rotation angle calculation subroutine consists of the following formulas: 1 = 0 1 = 0 + 0 + 0 2 2 − 1 1 + 1 1 2 2
As can be seen in Figure 3, as a result of the applied algorithm, the rotation angles received the same values. Therefore, the proposed algorithm performs the necessary operations by returning the angle α that has fallen to other quadrants to the first quadrant each time. Thanks to this, 2D binary images can be recognized as rotation invariant, regardless of the rotation angle. The first column of the table specifies the rotation angles of the figure. Columns 2 and 3 show the rotation angles calculated by formula (16) based on the arctg function.
A comparative analysis of algorithms for invariant recognition of two-dimensional binary images showed that there is no method that can fully solve this problem. Instead, there are algorithms that can partially solve the problem within certain constraints. One of the reasons for not solving the problem is that the trigonometric functions of the rotation angle take different signs in different quarters during image rotation. Therefore, the obtained result is not adequate to each other in different quarters. Therefore, the proposed method completely overcomes this drawback. Theoretical and computer modeling results show that the proposed formula gives accurate results only in the first quarter. Since trigonometric functions have different signs in different quadrants, the same formula does not give correct results in other quadrants. Therefore, the proposed algorithm performs the necessary operations by returning the angle α that has fallen to the other quarters to the first quarter each time. Because of this, 2D binary images are known to be rotation invariant regardless of the rotation angle. Computer modeling proves that the proposed method is correct.
[1] F.A. David, Computer Vision First Indian Edition, Pearson Education, 2003. [2] M. R. Miller, R. Miller. Robots and Robotics: Principles, Systems, and Industrial Applications.
McGraw-Hill Education , 2017. [3] R.O. Duda, P.E.Hart., D.G.Stork. Pattern classification, 2nd Edition, Wiley, 2001. [4] L. Jianzhuang , 2D Shape Matching by Contour Flexibility, IEEE Transaction on Pattern Analysis and Machine Intelligence, 19.1 (2008), pp. 1 – 7. [5] R. G. Mammadov, Correction of estimation errors of the measure of affinity between objects at recognition patterns for intellectual systems, in: Proceedings of the International Scientific Conference “Problems of Cybernetics and Informatics”, Baku, 2006, pp. 21-24. [6] K. Senthil Kumar, Object Recognition Using Shape Context with Canberra
Distance, Asian Journal of Applied Science and Technology (AJAST), 1.2(2017), pp. 268-273. [7] B.Siciliano, O. Khatib, Springer Handbook of Robotics. 2nd edition, Verlag Berlin Heidelberg, 2016. [8] D. G. Lowe, Distinctive image features from scale-invariant keypoints, Int. J. Comp. Vision, 60.2 (2004), pp. 91–110. [9] S. Nantogma, Y. Xu, W. A . Ran, Coordinated Air Defense Learning System Based on Immunized
Classifier Systems, 13(2021), pp. 271. [10] R. G. Mammadov, E.R. Rahimova, G.M. Mammadov. Increasing the Reliability of Pattern Recognition by Analyzing the Distribution of Errors in Estimating the Measure of Proximity between Objects, in: Proceedings of the 15th International Conference “Pattern Recognition and Information Processing (PRIP'2021)” , Minsk, Belarus, 2021, p.111-114. [11] R. F. Abdel-Kader, R. M. Ramadan, F. W. Zaki, E. El-Sayed, Rotation-Invariant Pattern Recognition Approach Using Extracted Descriptive Symmetrical Patterns (IJACSA), International Journal of Advanced Computer Science and Applications, 3.5(2012),pp.151-158. [12] H. Jiang, S. X. Yu, Linear solution to scale and rotation invariant object matching, in: Proceedings of IEEE Conference of Computer Vision and Pattern Recognition, 2009, pp. 2474–2481. [13] L. Baozhen , W. Hang, S. Weihua, Z. Wenchang, S. Jinggong, Rotation invariant object detection using sectorring hog and boosted random ferns, The Visual Computer, 34.5 (2018),pp.707–719. [14] R.G. Mammadov, T.Ch. Aliyev, G.M. Mammadov, 3D Object Recognition by Unmanned Aircraft to Ensure the Safety of Transport Corridors, in: Proceedings of İnternational conference on problems of logistics, management and operation in the East-West transport corridor (PLMO), Baku Azerbaijan, 2021, pp. 209-216. [15] R. G. Mammadov, E.R. Rahimova, G.M. Mammadov. Reducing the estimation error of the measure of proximity between objects in pattern recognition, in: Proceedings of the International Conference on Automatics and Informatics (İCAİ’2021), Varna Bulgaria, 2021, pp. 76- 81. [16] R.G. Mammadov, T.Ch. Aliyev, Definition of orientation of objects by the system of technical vision, in: Proceeding of the third international conference “Problems of cybernetics and informatics, Baku, 2010, pp. 259-262. [17] V. Artale, M. Collotta, C. Milazzo, G. Pau, A. Ricciardello, Real-Time System based on a Neural Network and PID Flight Control, Applied Mathematics and Information Sciences 10 (2016),pp.395- 402. [18] E. Toshiaki, E. Shuichi , K. Toshiyuki, 3D Object Recognition based on the Reference Point Ensemble, in: Proceedings of the International Conference on Computer Vision Theory and Applications, Portugal, 2014, pp.261-269. [19] V.H.S. Ha, J.M.F. Moura, Affine-permutation invariance of 2-D shape, IEEE Trans. Image
Process. 14.11 (2005),pp. 1687–1700. [20] J. Cortadellas, J. Amat, F. Robust normalization of silhouettes for recognition application, Pattern
Recognition Lett. 25 (2004),pp. 591–601. [21] R.G. Mammadov, T.Ch. Aliyev, G.M. Mammadov, 3D, Minimization of the Average Risk in Pattern Recognition for Smart Grid Systems, in: Proceedings of conference 6th “Computational Linguistics and Intelligent Systems” COLİNS 2022, Gliwice Poland, 2022, pp.365-375. [22] K. R Muller., S. Mika, G. Ratsch, K. Tsuda, B. Scholkopf, An introduction to kernelbased learning algorithms, IEEE Transactions on Neural networks 12 (2001),pp.181 – 202. [23] Z. Naser, B. Faris, Thermal Face Recognition Using Moments Invariants, International Journal of
Signal Processing Systems, 3.2(2015), pp. 94-99. [24] S. Subbotin, The neuro-fuzzy network synthesis and simplification on precedents in problems of diagnosis and pattern recognition, Optical Memory and Neural Networks (Information Optics), 2013, pp. 97 – 103. [25] A. Dovbysh, I. Naumenko, M. Myronenko, T. Savchenko, Information-extreme machine learning on-board recognition system of ground objects with the adaptation of the input mathematical description, in: Proceedings of 3rd International Workshop on Computer Modeling and Intelligent Systems, National University - CEUR Workshop Proceedings 2608, 2020, pp. 913-925.