Bicubic L1 Spline Fits for 3D Data Approximation

• Main Author: Zaman, Muhammad Adib Uz
• Language: EN
• Published: Northern Illinois University 2018
• Subjects: Computer engineering|Industrial engineering
• Online Access: http://pqdtopen.proquest.com/#viewpdf?dispub=10751900

<p> Univariate cubic <i>L</i>¹ spline fits have been successful to preserve the shapes of 2D data with abrupt changes. The reason is that the minimization of <i>L</i>¹ norm of the data is considered, as opposite to <i>L</i>² norm. While univariate <i>L</i>¹ spline fits for 2D data are discussed by many, bivariate <i>L</i>¹ spline fits for 3D data are yet to be fully explored. This thesis aims to develop bicubic <i>L</i>¹ spline fits for 3D data approximation. This can be achieved by solving a bi-level optimization problem. One level is bivariate cubic spline interpolation and the other level is <i> L</i>¹ error minimization. In the first level, a bicubic interpolated spline surface will be constructed on a rectangular grid with necessary first and second order derivative values estimated by using a 5-point window algorithm for univariate <i>L</i>¹ interpolation. In the second level, the absolute error (i.e. <i> L</i>¹ norm) will be minimized using an iterative gradient search. This study may be extended to higher dimensional cubic <i>L</i>¹ spline fits research.</p><p>