We present an approach for representing digital image by using B-spline curve fittings to the segmented digital image. The image is first segmented to form isolated contours and regions. Each region’s boundary (contour) is thereafter approximated by a B-spline curve. A cubic B-spline curve is used instead of a far higher degree Bezier curve to approximate the boundary because it has a local con...

A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve lies inside the convex hull of the control points, and the segments of the broken line connecting the control points are tangent to the curve. To construct the...

Ghandmjit L. Bajaj t Department of Computer Science, Purdue University, West Lafayette, IN 47907 In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained by different characterizations of the zero contours of the Bernstein-Bezier (BB) form of bivariate po...

Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortio...

Abstract Although existing super-resolution networks based on deep learning have obtained good results, it is still challenging to achieve an ideal visual effect for irregular texts, especially spatially deformed ones. In this paper, we propose a robust Bezier Curve-based image network (BCSR), which can efficiently handle the degradation caused by deformations. Firstly, arbitrarily shaped text ...

The aim of this paper is to apply the Said Ball curve (SBC) find approximate solution fractional differential-algebraic equations (FDAEs). This method can be applied solve various types order differential equations. Convergence theorem proved. Some examples are presented show efficiency and accuracy method. Based on obtained results, SBC more accurate than Bezier