This work deals with fitting 2D and 3D implicit polynomials (IPs) to 2D curves and 3D surfaces, respectively. The zero-set of the polynomial is determined by the IP coefficients and describes the data. The polynomial fitting algorithms presented in this paper aim at producing polynomials that are robust to coefficient errors. Special emphasis is given here to errors due to coefficient quantizat...

Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional kernel estimators, these estimators are often of simpler form and possess some better properties. In th...

A newmethod for segmenting intensity images into smooth surface segments is presented. The main idea is to divide the image into flat, planar, convex, concave, and saddle patches that coincide as well as possible with meaningful object features in the image. Therefore, we propose an adaptive region growing algorithm based on low-degree polynomial fitting. The algorithm uses a new adaptive thres...

Combining implicit polynomials and algebraic invariants for representing and recognizing complicated objects proves to be a powerful technique. However, a basic requirement for using implicit polynomials for affine invariant recognition is to have an affine invariant fitting algorithm. In this paper, we study the problem of affine invariant fitting of an implicit polynomial to data. Received Ja...

To automate the multiresolution procedure of Kuhl and Wilson for modeling and simulating arrival processes that exhibit long-term trends and nested periodic effects (such as daily, weekly, and monthly cycles), we present a statistical-estimation method that involves the following steps at each resolution level corresponding to a basic cycle: (a) transforming the cumulative relative frequency of...

Using Polynomial Contour Fitting Internal Report R. F. Walker Signal Processing Research Centre Queensland University of Technology GPO Box 2434 Brisbane Q 4001 Australia

In this paper, I describe the implementation details of some functional, triangular data fitting schemes. The schemes in question use derivative information to find initial settings of control points, giving a C, piecewise polynomial surface with a high degree of polynomial precision. The interior control points are then modified to increase the continuity between patches without decreasing the...

We present in this paper a polynomial fitting method applicable to segments of footprints measured by the Geoscience Laser Altimeter System (GLAS) to estimate glacier thickness change. Our modification makes the method applicable to complex topography, such as a large mountain glacier. After a full analysis of the planar fitting method to characterize errors of estimates due to complex topograp...