The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be solved in the least squares sense is then a rectangular Bernstein-Vandermonde matrix. In order to use the method based on the QR decomposition of A, the first stage consists of computing the bidiagonal decomposition ...

Usually, in image processing, edge detectors are mostly used as a basis for high level processing. In many cases, the edge detection gives erroneous and imprecise results, as incomplete or open contours. These inaccuracies mislead the subsequent processing. In this article, we propose a method to close contours of synthetic and real images. This method combines polynomial contour fitting with e...

A new signal processing method is developed for solving the multiline fitting problem in a two dimensional image. We first reformulate the former problem in a special parameter estimation framework such that a first order or a second order polynomial phase signal structure is obtained. Then, the recently developed algorithms in that formalism (and particularly the downsampling technique for hig...

As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet ...

A problem which often arises while fitting implicit polynomials to 2D and 3D data sets is the following: Although the data set is simple, the fit exhibits undesired phenomena, such as loops, holes, extraneous components, etc. Previous work tackled these problems by optimizing heuristic cost functions, which penalize some of these topological problems in the fit. This paper suggests a different ...

A trigonometric curve is a real plane curve where each coordinate is given parametri-cally by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can be also represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric repre...

For any finitely generated torsion-free graded module over a polynomial ring, there exists a homogeneous ideal fitting into an exact sequence similar to a Bourbaki sequence even though its height is not restricted to two.

When the number of objects in the training set is too small for the number of features used, most classification procedures cannot find good classification boundaries. In this paper, we introduce a new technique to solve the one class classification problem based on fitting an implicit polynomial surface to the point cloud of features to model the one class which we are trying to separate from ...

This paper addresses the problem of speaker-dependent isolate digits recognition using sole visual information. We employ intensity transformation and spatial filter to estimate the minimum enclosing rectangle of mouth in each frame. Thus, for each utterance, we can obtain two vectors composed of width and height of mouth, respectively. Then, we propose an approach to recognize the speech based...

This paper addresses the pointwise estimation of differential properties of a smooth manifold S —a curve in the plane or a surface in 3D— assuming a point cloud sampled over S is provided. The method consists of fitting the local representation of the manifold using a jet, and either interpolation or approximation. A jet is a truncated Taylor expansion, and the incentive for using jets is that ...