Optimal curve fitting approach to represent outlines of 2D shapes

Abstract

A new outline capturing system is presented in this paper. It employs Bezier curve for curve approximation. Approximation starts with an initial estimation of control points positions, which is updated iteratively based on computed error. Consequently, the control points converge to an optimum position. The segments obtained after corner detection are initially approximated with Bezier curve of lowest degree, i.e. degree 1. The degree of approximating curve is then increased iteratively until the error comes under the user specified limit. This ensures optimal fit with least number of control points. Shape representation results of proposed algorithm are compared with existing techniques. Experimental results show that proposed algorithm can approximate the 2D shapes with considerably less number of control points, when compared with existing techniques. Computational efficiency is another advantage of proposed algorithm. Presented algorithm can have very useful applications in CAD/CAGD and real-time computer vision algorithms.

Systematic Digitized Treatment of Engineering Line-Diagrams

“…This paper describes a new system wh ich is capable of getting of the manual inspection of graphs and synthesizing this process with 3 different curve fitt ing processes: the cubic spline Function, Neural Net work Methods, and a curve fitting approach based on Grey Models. The cubic spline function has been widely used in line graph modeling and is easily applied [4][5][6][7][8]. Neural networks can intrinsically model mult i-curve graphs and in thought to have greater accuracy and higher processor efficiency [9].…”

“…In order to resolve these issues, some research wo rks have been carried out, which allo w semi-automatic data extraction, followed by data interpolation using more sophisticated curve fitting techniques, e.g. Least square method, Lagrange interpolation, Newton difference quotient, Cubic Spline Method, Quintic Sp line Method, and Neural Network Methods [1,2,[4][5][6][7][8][9]. This paper describes a new system wh ich is capable of getting of the manual inspection of graphs and synthesizing this process with 3 different curve fitt ing processes: the cubic spline Function, Neural Net work Methods, and a curve fitting approach based on Grey Models.…”