MATHEMATICAL SUPPORT OF GEOMETRIC TRANSFORMATIONS OF IMAGES DURING DATA AUGMENTATION OF NEURON NETWORK TOOLS
Authors:   Kyiv National University of Construction and Architecture, Tereikovska Liudmyla , Tereikovskyi Ihor ,   National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
Published: February 2025

One of the key problems in the field of increasing the efficiency of neural network tools intended for the analysis of graphic materials is the formation of representative training databases. A promising way to overcome this problem is to increase the size of the training sample by applying the augmentation of training examples due to geometric transformations. However, the modern mathematical apparatus for modifying the geometric parameters of images has shortcomings that can reduce the quality of the obtained images or lead to their insufficient compliance with the tasks. The purpose of the work is the formation of mathematical support, which is used to implement geometric transformations of images during the augmentation of training data of neural network tools. The research methodology is based on the theory of digital processing of signals and images, system analysis and the theory of neural networks and involves the determination of key components of the mathematical support for affine transformations and the definition of the mathematical support for calculating the color of pixels when scaling an image using interpolation methods in various application conditions. As a result of the conducted research, mathematical support was formed, which is used to implement geometric transformations of images when augmenting the training data of neural network tools. The key components of the mathematical support of affine transformations related to the determination of the display dimensions of the modified image and the determination of the color of individual points of the modified image are defined. A mathematical apparatus has been defined that allows you to calculate the dimensions of the display area of the modified image, provided that a rectangular display area is provided. It is shown that in the task of augmentation of training data of neural network tools, it is advisable to perform image scaling using proven non-adaptive interpolation methods: nearest neighbor, bilinear interpolation, bicubic interpolation, Lanzosh interpolation, box filter, triangular filter. A mathematical apparatus for calculating the pixel color of a scaled image using each of the above interpolation methods is defined. The conditions that determine the expediency of using the specified methods in solving practical problems are outlined. It is shown that the method of the nearest neighbor is advisable to use in the case of the need to ensure the simplicity of implementation and high productivity of the augmentation procedure, when the noise of small details and the distortion of the shape of objects containing thin lines can be neglected. The bilinear interpolation method is recommended for use under the conditions of ensuring a balance between the quality of the scaled image and computational costs, and the bicubic interpolation method - under the condition that there are no strict limits on the computational resource intensity of the processing process, when it is necessary to achieve high image quality during scaling. The Lanzosh interpolation method is recommended for scaling images in cases where maximum preservation of quality and detail is required. The box method and the triangular filter method are appropriate to use when the speed of scaling is more important than the quality of the image obtained after scaling. Prospects for further research are related to the development of a methodology for adapting the means of integrated modification of geometry and visual characteristics of images to the conditions of augmentation of training data of neural network systems for video stream analysis.