On the mathematic modeling of non-parametric curves based on cubic B\'ezier curves

TL;DR

This paper introduces a new method for approximating non-parametric image outline segments with cubic Bézier curves, achieving higher accuracy and compression than previous techniques.

Contribution

It presents a novel technique for determining control points of cubic Bézier curves that improves approximation accuracy and reduces error in modeling non-parametric curves.

Findings

Higher accuracy in curve approximation

Reduced error compared to previous methods

Improved compression rate

Abstract

B\'ezier splines are widely available in various systems with the curves and surface designs. In general, the B\'ezier spline can be specified with the B\'ezier curve segments and a B\'ezier curve segment can be fitted to any number of control points. The number of control points determines the degree of the B\'ezier polynomial. This paper presents a method which determines control points for B\'ezier curves approximating segments of obtained image outline(non-parametric curve) by using the properties of cubic B\'ezier curves. Proposed method is a technique to determine the control points that has generality and reduces the error of the B\'ezier curve approximation. Main advantage of proposed method is that it has higher accuracy and compression rate than previous methods. The cubic B\'ezier spline is obtained from cubic B\'ezier curve segments. To demonstrate the various performances of the proposed algorithm, experimental results are compared.