Least squares orthogonal distance fitting of implicit curves and surfaces

Abstract

Curve and surface fitting is a relevant subject in computer vision and coordinate metrology. In this paper, we present a new fitting algorithm for implicit surfaces and plane curves which minimizes the square sum of the orthogonal error distances between the model feature and the given data points. By the new algorithm, the model feature parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. The form parameters determine the shape of the model feature, and the position/rotation parameters describethe rigid body motion of the model feature. The proposed algorithmis applicable to any kind of implicit surface and plane curve.