A generalization of the Bookstein constraint to algebraic surfaces

Curve and surface fitting in image processing are considered. A data independent constraint on the coefficients of an algebraic surface, invariant to rotations and translations, is presented. The derivation is obtained by using tensor products in the form of Kronecker products. This constraint corresponds to the generalization of the Bookstein constraint to algebraic curves of arbitrary order p⩾1 in 2-D space, and algebraic surfaces of arbitrary order p⩾1 in N -dimensional real space, with N⩾3