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

Shotaro Akaho

doi:10.1117/12.164998

1 December 1993 Curve fitting that minimizes the mean square of perpendicular distances from sample points

Shotaro Akaho

Proceedings Volume 2060, Vision Geometry II; (1993) https://doi.org/10.1117/12.164998
Event: Optical Tools for Manufacturing and Advanced Automation, 1993, Boston, MA, United States

Abstract

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.

Citation Download Citation

Shotaro Akaho "Curve fitting that minimizes the mean square of perpendicular distances from sample points", Proc. SPIE 2060, Vision Geometry II, (1 December 1993); https://doi.org/10.1117/12.164998

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