Existence and uniqueness theorems for solutions of inverse problems of projective geometry for 3D reconstruction from photographs

Abstract

The paper considers the problem of calculating the parameters of the plane of a spatial
triangle from its central projection. Under certain conditions, the existence theorem for a
solution to this problem and its uniqueness are proved. Examples of conditions under which a
solution does not exist or is not unique are given. An algorithm for the approximate search of
all possible solutions to the problem under certain conditions is also proposed. The problem
considered in the article arises when constructing three-dimensional models of objects from their
photograph.