Optimization of middle control points of cubic Bézier curve for handwriting representation using whale optimization algorithm

This study concerns the issue of curve representation of the handwriting image using a computational method namely the Whale Optimization Algorithm (WOA). The WOA is a novel nature-inspired meta-heuristic algorithm that mimics the social behavior of humpback whales. Optimization results based on structural and mathematical optimization problems previously proved that the WOA very competitive compared to the state-of-the-art optimization methods. The handwriting representation technique plays an important role in the recognition of handwriting characters. The accuracy of curve representation will affect the recognition results. Thus, this study deals with a curve fitting process to handle the accuracy issue of the curve representation. The handwriting curve representation involved a process of curve fitting which are boundary extraction, corner point detection, parameterization and parametric curve fitting. The research objective is to approximate the original handwriting curve by optimizing the location of middle control points of the cubic Bézier curve. The middle control points will change the whole shape of each Bézier curve. Thus, at the last phase of curve fitting, the WOA identifies the optimum middle control points of the cubic Bézier curve. These points give an accurate approximation of the original handwriting boundary curve. Sum of Squared Error (SSE) has been used to calculate the error between the two curves namely original handwriting and the new parametric curves. By using the chosen middle control points, the optimum smooth curve that minimizes the SSE between the original data and new representation data is then obtained. The curve fitting results of 191 handwriting boundaries by using the WOA have been compared with the direct method of curve fitting known as Least Square Approximation (LSA). It is confirmed that the WOA has a better performance in fitting the parametric curve compared to the LSA method.