In recent years the progress in algorithms optimization has resulted in many solutions in the area of fully automatic reconstructing of 3D model of any object from a sequence of non-metric images. An important step in the formation of a 3D model is so-called matching process of homologous points in the sequence of images. This stage is still a bottleneck for the reconstruction of objects consisting of uniform surfaces, such as sculptures, reliefs, or even the human body. The solution may be to apply an artificial variety to surfaces by covering them with a random texture pattern. A wide range of multimedia projectors, with increasingly higher resolutions and luminosities, enables us to perform the projection of any texture on the object, and then to register it. In this article, we present the idea of creating an artificial pattern, a structure that will provide significant improvement of automatic point identification stage, and the proper mapping of homologous points in the sequence of images. While creating a pattern allowing easy feature extraction does not present much of a problem, assurance of its uniqueness for the whole object for matching purposes, requires a deliberate idea. Statistical formulation of the problem demonstrates the high efficiency of the method.