Least-squares smoothing of 3D digital curves

In this paper an efficient procedure for 3D digital curve smoothing is presented. It is described by linear operators which allow to perform the constrained, position invariant, least-squares smoothing of 3D digital curves minimizing the undersampling, digitizing and quantizing error and to calculate various curve characteristics and invariants related to the original digitized curve. They are represented by sparse symmetric circulant Toeplitz matrices with integer coefficients which can be efficiently realized in serial as well as in parallel manner.