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博碩士論文 etd-0713104-102812 詳細資訊
Title page for etd-0713104-102812
論文名稱
Title
用有限體積法(Delaunay劃分之臉型變換)
Face Transformation by Finite Volume Method with Delaunay Triangulation
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
72
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2004-05-28
繳交日期
Date of Submission
2004-07-13
關鍵字
Keywords
有限體積法、臉型變換、分裂投射法、Delaunay三角劃分、分裂積分法、Laplace方程
the splitting-shooting method, face transformation, blending curves, finite volume method, Delaunay triangulation, Laplace equation, the splitting-integration method
統計
Statistics
本論文已被瀏覽 5701 次,被下載 2229
The thesis/dissertation has been browsed 5701 times, has been downloaded 2229 times.
中文摘要
這篇論文中,在調和模型之臉型變換下我們主要是利用Delaunay三角劃分的有限體積法去求解Laplace方程,其優點是容易公式化成代數方程組、保持好的幾何和物理性質和減少CPU運算時間。而最後的數值實驗的結果,我們用女的臉型變換到男的臉型之後再還原回來,所得到計算誤差符合其理論分析。反之,用男的臉型變換到女的臉型之後再還原回來結果亦符合。
Abstract
This thesis presents the numerical algorithms to carry out the face transformation. The main efforts are denoted to the finite volume method (FVM) with the Delaunay triangulation to solve the Laplace equations in the harmonic transformation undergone in face images. The advantages of the FVM with the Delaunay triangulation are: (1) Easy to formulate the linear algebraic equations, (2) Good to retain the geometric and physical properties, (3) less CPU time needed. The numerical and graphical experiments are reported for the face transformations from a female to a male, and vice versa. The computed sequential and absolute errors are and , where N is division number of a pixel into subpixels. Such computed errors coincide with the analysis on the splitting-shooting method (SSM) with piecewise constant interpolation in [Li and Bui, 1998c].
目次 Table of Contents
1. Introduction 1
2. Harmonic Model 6
3. Blending Techniques for Face Boundary 12
4. Splitting Methods in Digitized Images 16
5. Numerical Techniques for Dirichlet Boundary Condition 29
6. Numerical and Graphical Experiments 33
參考文獻 References
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[18] Z. C. Li, C. Y. Suen, T. D. Bui and Q. L. Gu(1992b), Harmonic models of shape transformations in digital images and patterns, Computer Vision, Graphs and Image Processing, Vol. 54, pp.198-209, 1992.
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[22] Z. C. Li(2003), Improved splitting-integration methods for image geometric transformations, invited talk, International Conference on Numerical Infomation Processing at Institude for Mathematical Science, National University of Singapore, December 19-21, 2003.
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[26] M. C. Yang(1999), The Application of Delaunay Triangulation to Face Recognition, Master Thesis, Dept. of Appl. Math. National Sun Yat-sen University, Kaohsiung, 1999.
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