Curve tting that minimizes the mean square of perpendicular distances from sample points

This paper presents a new method of curvetting to a set of noisy samples. In the case of tting a curved line (or a curved surface) to given sample points, it seems natural the curve is decided so as to minimize the mean square of perpendicular distances from the sample points. However it is di cult to get the optimal curve in the sense of this criterion. In this paper, the perpendicular distance is approximated by local linear approximation of function, and the algorithm for getting the near-optimal curve is proposed. Some simulation results are also shown.