Subspace matching: Unique solution to point matching with geometric constraints

Finding correspondences between feature points is one of the most relevant problems in the whole set of visual tasks. In this paper we address the problem of matching a feature vector (or a matrix) to a given subspace. Given any vector base of such a subspace, we observe a linear combination of its elements with all entries swapped by an unknown permutation. We prove that such a computationally hard integer problem is uniquely solved in a convex set resulting from relaxing the original problem. Also, if noise is present, based on this result, we provide a robust estimate recurring to a linear programming-based algorithm. We use structure-from-motion and object recognition as motivating examples.