Bicubic B-Spline And Thin Plate Spline On Surface Appoximation
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Date
2017-03
Authors
Liew, Khang Jie
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
In real life, the available data points which are either 2D or 3D are normally
scattered and contaminated with noise. The noise is defined as the variation in a set
of data points. To fit these data points, the approximation methods are considered as
a suitable mean compared to the interpolation methods. It is important for the approximation
methods to preserve the shape and features of the model in the presence
of any noise. B-spline and thin plate spline approximation are being studied in this
thesis. The effectiveness of the modified B-spline approximation algorithm is investigated
in approximating the bicubic B-spline surface from the samples of scattered
data points taken from the point set model. The algorithm is used to determine the
unknown B-spline control points and followed by the construction of bicubic B-spline
surface patch. The experimental results show that the modified B-spline approximation
algorithm manages to construct the surfaces that resemble the shape of original
samples point set without going through the multilevel surface approximation. The
sharp edge preservation in bicubic B-spline surface is also being studied. On top of
that, an algorithm which is based on bootstrap averaging method is proposed and able
to achieve the sharp edge preservation. Further studies are carried out to investigate
the effect of noise with different noise levels in preserving the sharp edge. The approximation
scheme of the thin plate spline which is one of the radial basis functions
is also used to fit the data points in this study. A comparison is carried out to observe
the effect of noise in the bicubic B-spline surface fitting and the thin plate spline surface
fitting, which reveals that the B-spline surface is sensitive to the noise compared
to the thin plate spline.
Description
Keywords
Bicubic B-spline and thin plate spline , on surface appoximation