Vector field restoration by the method of convex projections

Abstract

In this paper, the theory of image restoration by projections onto closed convex sets is applied to the restoration of vector fields. A set of useful projection operators is presented together with a linear time numerical implementation. These projection operators can be used to restore from partial information the velocity or deformation fields computed between successive views of a scene. They also find applications in the restoration of vector fields of physical quantities as those encountered in mechanics, hydrodynamics, or electromagnetism. The method is compared with the variational approach and illustrated by restoring simulated vector fields.