A method is developed for fitting a hyperplane to a set of data by least-squares, allowing for independent uncertainties in all coordinates of each data point, and including an error analysis. Note: This paper is adapted from a technical report I wrote as a graduate student in the Department of Physics, University of California, Berkeley, in 1976. Copyright c ©2002, by Robert K. Moniot. All rig...

A parameter estimation problem for ellipsoid fitting in the presence of measurement errors is considered. The ordinary least squares estimator is inconsistent, and due to the nonlinearity of the model, the orthogonal regression estimator is inconsistent as well, i.e., these estimators do not converge to the true value of the parameters, as the sample size tends to infinity.A consistent estimato...

This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4 2 1 the new method incorporates the ellipticity constraint into the normalization factor. The new method combines several advantages: (i) It is ellipse-specific so th...

A technique for reconstructing a class of quadric surfaces from 3D data is presented. The technique is driven by a linear least-squaresbased fitting mechanism. Previously, such fitting was restricted to recovery of central quadrics; here, extension of that basic mechanism to allow recovery of one commonly-occurring class of non-central quadric, the elliptic paraboloids, is described. The extens...

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The ...

Reduced rank approximation of matrices has hitherto been possible only by unweighted least squares. This paper presents iterative techniques for obtaining such approximations when weights are introduced. The techniques involve criss-cross regressions with careful initialization. Possible applications of the approximation are in modelling, biplotting, contingency table analysis, fitting of missi...

We describe a new method for the fitting of differentiable fuzzy model functions to crisp data. The model functions can be either scalar or multidimensional and need not be linear. The data are n-component vectors. An efficient algorithm is achieved by restricting the fuzzy model functions to sets which depend on a fuzzy parameter vector and assuming that the vector has a conical membership fun...

We consider the problem of fitting a set of points in Euclidean space by an algebraic hypersurface. We assume that points on a true hypersurface, described by a polynomial equation, are corrupted by zero mean independent Gaussian noise, and we estimate the coefficients of the true polynomial equation. The adjusted least squares estimator accounts for the bias present in the ordinary least squar...