Uniqueness theorem of reconstruction of preimage by its image under degenerate mapping

One of the urgent problems in the construction of computer vision systems is the problem of determining the spatial orientation and spatial position of an object from a photograph. For example, this task is especially important for autonomous driving systems, where the positioning of nearby vehicles is a key issue for autonomous vehicles in an urban environment. In this regard, for example, in 2019, the Baidu Robotics and Autonomous Driving Laboratory together with Peking University, set an appropriate task for the Kaggle community (https://www.kaggle.com/c/pku-autonomous-driving) and provided more than 60,000 copies of three-dimensional cars marked from 5,277 real images. In this article, we formulate some results that are the mathematical basis for substantiating methods for solving the abovementioned reconstruction problems in computer vision systems.