Representation Of Rational Bézier Quadratics Using Genetic Algorithm, Differential Evolution And Particle Swarm Optimization - Yahya, Zainor Ridzuan (2013)
Data representation is a challenging problem in areas such as font reconstruction, medical image and scanned images. Direct mathematical techniques usually give smallest errors but sometime take a much longer time to compute. Alternatively, artificial intelligence techniques are widely used for optimization problem with shorter computation time. Besides, the usage of artificial technique for data representation is getting popular lately. Thus, this thesis is dedicated for the representation of curves and surfaces. Three soft computing techniques namely Genetic Algorithm (GA), Differential Evolution (DE) and Particle Swarm Optimization (PSO) are utilized for the desired manipulation of curves and surfaces. These techniques have been used to optimize control points and weights in the description of spline functions used. Preprocessing components such as corner detection and chord length parameterization are also explained in this thesis. For each proposed soft computing technique, parameter tuning is done as an essential study. The sum of squares error (SSE) is used as an objective function. Therefore, this is also a minimization problem where the best values for control points and weights are found when SSE value is minimized. Rational Bézier quadratics have been utilized for the representation of curves. Reconstruction of surfaces is achieved by extending the rational Bézier quadratics to their rational Bézier bi-quadratic counterpart. Our proposed curve and surface methods with additional help from soft computing techniques have been utilized to vectorize the 2D and 3D shapes and objects.