Yahya, Zainor Ridzuan
(2013)
Representation Of Rational Bézier
Quadratics Using Genetic Algorithm,
Differential Evolution And Particle
Swarm Optimization.
PhD thesis, Universiti Sains Malaysia.
Abstract
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.
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