Point Matching Constraints in Two and Three Views

Abstract

In the two-view case, point matching constraints are represented by the fundamental matrix. In the three-view case, the point matching constraints are indirectly represented by three trifocal tensors corresponding to the three camera matrices. A direct representation of the point matching constraints can be obtained by applying suitable transformations on the trifocal tensors. This paper discusses some issues related to point matching constraints. First, it presents a novel approach for deriving the constraints in terms of a generator space. Second, it shows that the resulting set of linearly independent constraints is 10- dimensional for the three-view case, a result which deviates from the literature on this subject. Third, in the case that the cameras have nonco-linear focal points, 9 of these 10 constraints can be obtained in a straight-forward way from the three fundamental matrices which we have in the three-view case. The last constraint can be obtained from the fundamental matrices but in a non-trivial way. The main result of the paper is a better understanding of the properties related to point matching constraints in three dimensions and how they are related to the corresponding two-view constraints.