Determinant‐Constrained Affine Transformations

ABSTRACT We study the problem of estimating an affine transformation with prescribed determinant from point pairs in dimension . The determinant constraint is nonconvex and challenging to handle. We propose a method to reformulate the problem into a system of quadratics and one polynomial of degree in unknowns. We propose a solution method for this system and a procedure to retrieve the single or multiple affine transformation solutions. We show that the related problem of finding the closest ‐simplex of prescribed volume and orientation to a given arbitrary ‐simplex is solved as a special case of the proposed method. We report experimental results demonstrating the use of the proposed transformations in three applications.