Curve fitting that minimizes the mean square of perpendicular distances from sample points
Shotaro Akaho · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
This paper presents a new method of curve-fitting to a set of noisy samples. In the case of fitting 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 difficult 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.