It is necessary to obtain a vector image of figures (polygons) from noisy data to create various models of real objects. In this article we have considered the question of the parallelogram vectorization. A parallelogram is a common case of a polygon but it is quite simple to use and model. The article describes two different approaches to approximating the source data: the Douglas-Pecker algorithm and the least squares method for constructing paired linear regression, the parallelogram algorithm, and a comparative analysis of the results obtained on a specially generated dataset describing a noisy parallelogram.