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Technologies for pattern recognition are used in various fields. One of the most relevant and important directions is the use of pattern recognition technology, such as gesture recognition, in socially significant tasks, to develop automatic sign language interpretation systems in real time. More than 5% of the world’s population—about 430 million people, including 34 million children—are deaf-mute and not always able to use the services of a living sign language interpreter. Almost 80% of people with a disabling hearing loss live in low- and middle-income countries. The development of low-cost systems of automatic sign language interpretation, without the use of expensive sensors and unique cameras, would improve the lives of people with disabilities, contributing to their unhindered integration into society. To this end, in order to find an optimal solution to the problem, this article analyzes suitable methods of gesture recognition in the context of their use in automatic gesture recognition systems, to further determine the most optimal methods. From the analysis, an algorithm based on the palm definition model and linear models for recognizing the shapes of numbers and letters of the Kazakh sign language are proposed. The advantage of the proposed algorithm is that it fully recognizes 41 letters of the 42 in the Kazakh sign alphabet. Until this time, only Russian letters in the Kazakh alphabet have been recognized. In addition, a unified function has been integrated into our system to configure the frame depth map mode, which has improved recognition performance and can be used to create a multimodal database of video data of gesture words for the gesture recognition system.