On least-squares digital contour smoothing

In this paper an efficient procedure for constrained least-squares smoothing for digital contours is presented. It is described by linear operators represented by circulant Toeplitz matrices with integer coefficients which can be efficiently implemented. They allow to calculate several characteristics and invariants related to the corresponding original digitized contour and also to estimate its derivatives and corresponding invariants. The use of the smoothed values and the values of estimated first derivatives obtained by the described procedure for the problem of length estimation of digitized contours is discussed.