Vector field restoration by the method of convex projections

In this paper, the theory of image restoration by projections onto closed convex sets is applied to the restoration of vector elds. 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 elds computed between successive views of a scene. They also nd applications in the restoration of vector elds 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 elds. P. Y. Simard was with the Institut de G enie Biom edical Ecole Polytechnique, C. P. 6079, Succ A, Montr eal, P.Q., Canada, H3C 3A7. He is now with the Department of Computer Science, University of Rochester, Rochester, NY 14627. G. E. Mailloux is with the Institut de G enie Biom edical Ecole Polytechnique, C. P. 6079, Succ A, Montr eal, P.Q., Canada, H3C 3A7.