Constructing control points for Bézier interpolating surfaces using diagonal data points interpolation strategy and its application in image upscaling

• Main Authors: Fadhel, Mustafa Abbas, Omar, Zurni
• Format: Conference Proceeding
• Language: English
• Subjects: Bezier patches; Data points; Interpolation; Polynomials; Smoothness; Surface stability
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0177676

Interpolation is a mathematical technique employed for estimating unknown values between data points. This technique assures that the resulting polynomial passes through all data points. One of the most useful interpolation polynomials is the parametric interpolation polynomial. Bézier interpolating surfaces are parametric interpolation polynomials that produce smooth, flexible, and accurate functions. One of the most crucial parts in deriving Bézier interpolating surfaces is to construct control points. However, the control points constructed by most of the existing strategies produce partial smoothness functions with less accurate solutions. In this paper, a new strategy for constructing control points is proposed. This strategy interpolates diagonal data points to construct control points of three-dimensional (3D) datasets. The obtained control points are then employed to derive Bézier interpolating surfaces that preserve stability and smoothness. The newly derived Bézier interpolating surfaces are then applied in colour image upscaling. Not only do the derived Bézier interpolating surfaces produce sharper upscale images, the numerical results show that they also produce more accurate solutions than other existing methods.