This paper deals with the problem of fitting a discrete polynomial curve to 2D noisy data. We use a discrete polynomial curve model achieving connectivity in the discrete space. We formulate the fitting as the problem to find parameters of this model maximizing the number of inliers i.e., data points contained in the discrete polynomial curve. We propose a method guaranteeing inclusion-wise max...

A discrete polynomial curve is defined as a set of points lying between two polynomial curves. This paper deals with the problem of fitting a discrete polynomial curve to given integer points in the presence of outliers. We formulate the problem as a discrete optimization problem in which the number of points included in the discrete polynomial curve, i.e., the number of inliers, is maximized. ...

We construct Weakly Admissible polynomial Meshes (WAMs) on circular sections, such as symmetric and asymmetric circular sectors, circular segments, zones, lenses and lunes. The construction resorts to recent results on subperiodic trigonometric interpolation. The paper is accompanied by a software package to perform polynomial fitting and interpolation at discrete extremal sets on such regions....

Estimation of support frontiers and boundaries often involves monotone and/or concave edge data smoothing. This estimation problem arises in various unrelated contexts, such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programs of nuclear reactors. Very few constrained estimators of the support boundary of a bivariate distribution hav...

Though many past works have tried to cluster expressive timing within a phrase, there have been few attempts to cluster features of expressive timing with constant dimensions regardless of phrase lengths. For example, used as a way to represent expressive timing, tempo curves can be regressed by a polynomial function such that the number of regressed polynomial coefficients remains constant wit...