Univariate cubic L1 spline fits have been successful to preserve the shapes of 2D data with abrupt changes. The reason is that the minimization of L1 norm of the data is considered, as opposite to L2 norm. While univariate L1 spline fits for 2D data are discussed by many, bivariate L1 spline fits for 3D data are yet to be fully explored. This thesis aims to develop bicubic L1 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 L1 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 L 1 interpolation. In the second level, the absolute error (i.e. L1 norm) will be minimized using an iterative gradient search. This study may be extended to higher dimensional cubic L 1 spline fits research.
Some files may require a special program or browser plug-in. More Information
|Advisor:||Wang, Ziteng, Damodaran, Purushothaman|
|Commitee:||Moraga, Reinaldo, Nguyen, Christine|
|School:||Northern Illinois University|
|Department:||Industrial and Systems Engineering|
|School Location:||United States -- Illinois|
|Source:||MAI 57/06M(E), Masters Abstracts International|
|Subjects:||Computer Engineering, Industrial engineering|
|Keywords:||3d spline surface, Algorithm, Bicubic interpolation, L1 approximation, Spline, Terrain modeling|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be