臺灣博碩士論文加值系統

本文提出一整套面像變換與合成的新技術，即四步法：（1）找尋臉部之內外邊界，（2）用光滑曲線描寫邊界，（3）形成調和變換，（4）用Splitting-integrating 法執行臉部影像的變換。可將臉部變形，產生不同的面部表情，更可將不同的影像圖片合成，例如可以預測夫妻未來的小孩模樣。文中亦提出新的數值常微分方法（ODE）以及數值方法，它能有效結合傳統的Spline插值與ODE數值方法。

This thesis is devoted to generating the boundary of face profile for face transformation in face combining, face resembling and face recognition. The face reformation can be carried by the geometric, harmonic model and numerical
methods, such as the splitting shooting method(SSM) and the splitting integrating methods(SIM) of image transformation. However, the harmonic model needs the boundary correspondence
in the Dirichlet condition. It is forbidding to
depict the pixel-pixel correspondence, but is necessary to find a few important, charactistic
point-point correspondences. Hence, we may seek the blending curves to establish the curve-curve correspondence. In this thesis, the formulation for the face boundary and profiles are explored by three methods: cubic spline, quadratic, spline, and the ordinary differential equation(ODE) approaches using Hermite interpolation. The latter is advantageous for handling different
boundary conditions in 2D clamped, simply support conditions and given curvature. The combined algorithms using both cubic splines
and the ODE methods are also developed. New mathematical algorithms of curves for given curvature on the boundary are proposed in this thesis, and the number of nonlinear equations
involved in curvature conditions can be reduced to two or three only. This thesis also displays the validity of the ODE approaches for 2D curves.
Graphical experiments are carried out to resembling face images of a young girl, based on the photos of her parents and her childhood.

1.Introduction
2.Curves for Face Boundary: Simple cases
3.Some Other Boundary Conditions
4.Combined and Nonlinear Blending Curves
5.Intermediate Pixel-pixel Correspondence between Two Face Boundaries
6.Splitting-Integrating Method for Harmonic Transformations
7.Numerical and Graphical Experiments

[1] K.E. Atkinson (1989), An Introduction to Numerical
Analysis(Second Ed.), John Wiley & Sons, New York, 1989.
[2] R. Brunelli and T. Poggio (1993), Face recognition: Features
versus templates, IEEE Trans. Patt. Anal. Machine Intell. Vol.
15, No. 10, pp. 1042-1052, 1993.
[3] R.L. Burden and J. Douglas Faires (1997), Numerical
Analysis(Sixth Ed.), Brooks/Cole Publishing Company, pp.
143-164, 1997.
[4] R. Chellappa, C.L. Wilson and S. Sirohey (1995), Human and
machine recognition of faces: A survey, Proc. IEEE Vol. 83, No.
5, pp. 705-740, 1995.
[5] T. Darrel, B. Moghaddam, and A.P. Pentland (1996), Active
face tracking and pose estimation in an interactive room, In
Proc. Computer Vision and Pattern Recognition, pp. 67-72, San
Francisco, California, Jun. 1996.
[6] E.R. Dougherty and C. R. Giardina (1987), Image
Processing-Continuous to Discrete, Vol.I, Geometric, Transform,
and Statistical Methods, Prentice-Hall Inc., Englewood Cliffs,
NJ 07632, 1987.
[7] G. Farin (1990), Curve and Surfaces for Computer Aided
Geometric Design, A Practical Guide,(Sec. Ed.) Academic Press,
1990.
[8] J.D. Foley, A van Dam, S.K. Feiner and J.K. Hughes (1990),
Computer Graphics, Principles and Practice(2nd Ed.),
Addison-Wesley, Reading, MA, 1990.
[9] R.C. Gonalez and R.E. Woods (1992), Digital Image
Processing, Addison Wesley Pub, 1992.
[10] V. Govindaraju, S.N. Srihari, and D.B. Sher (1990), A
computational model for face location, In Proc. Computer Vision
and Pattern Recognition, pp. 718-721, 1990.
[11] L.A. Hageman and D. M. Young (1981), Applied Iteration
Method, Academic Press, Boston, 1981.
[12] H.T. Huang and Z.C. Li (2002), Blending curves for blending
problems by numerical differential equations, III. Separation
techniques, accepted by Inter. J. Computer and Mathematics with
Application.
[13] S.H. Jeng, H.Y.M. Liao, C.C. Han, M.Y. Chern and Y.T. Liu (1998),
Facial feature detection using geometrical face model: An
efficient approach, Pattern Recognition, Vol. 31, No, 3, pp.
273-282, 1998.
[14] P. Juell and R. Marsh (1996), A hierarchical neural network
for human face detection, Pattern Recognition, Vol. 29, No. 5,
pp. 781-787, 1996.
[15] T.K. Leung, M.C. Burl, and P. Perona (1995), Finding faces in
clustered scenes using random labeled graph matching, In Proc.
Computer Vision and Pattern Recognition, pp. 637-644, Cambridge,
Mass., Jun. 1995.
[16] Z. C. Li (1990), Discrete techniques for computer
transformations of digital images and patterns, Pattern
Recognition[SCI], Vol. 23, No. 11, pp. 1249-1273, 1990.
[17] Z. C. Li, T. D. Bui, C. Y. Suen and Y. Y. Tang (1990a),
Splitting-shooting methods for nonlinear transformations of
digitized patterns, IEEE Pattern Anal. Machine Intell[SCI], Vol.
12, No. 7, pp. 671-682, 1990.
[18] Z. C. Li, Y. Y. Tang, T. D. Bui and C. Y. Suen (1990b), Shape
Transformation models and their applications in pattern
recognition, Int. J. Pattern Recognition and Artificial Intell,
Vol. 4, No. 1, pp. 65-94, 1990.
[19] Z. C. Li, Q. L. Gu, C. Y. Suen, and T. D. Bui (1990c), A
comparative study of nonlinear shape models for digital
processing and pattern recognition, IEEE, Trans. on Sys., Man
and Cybernetics[SCI], Vol. 20, No. 4, pp. 858-871, 1990.
[20] Q. L. Gu, C. Y. Suen. T. D. Bui and Z. C. Li (1991), Font
generation and shape design of character by mathematical models,
Computer Processing of Chinese and Oriental Languages, Vol. 5,
pp. 347-360, 1991.
[21] Z. C. Li, C. Y. Suen, T. D. Bui, T. D. Tang and Q. L. Gu (1992a),
Splitting-integrating methods for nonlinear images by inverse
transformations, IEEE, Trans. Pattern Anal. Machine Intell[SCI],
Vol. 14, pp. 678-686, 1992.
[22] 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[SCI], Vol. 54, pp.
198-209, 1992.
[23] Z.C. Li (1994), Advanced Splitting-integrating methods with
high convergence rates for restoring images and patterns, J. of
Scientific Computing, Vol. 9, pp. 149-172, 1994.
[24] Z.C. Li (1995), Splitting-integrating method for inverse
transformation of n-dimensional digital images, Numerical
Algorithms, Vol. 9, pp. 181-198, 1995.
[25] Z.C. Li (1996a), Splitting-integrating method for image
transformations T and T^{-1}T, Computers Math. Applies, Vol.
32, pp. 32-60, 1996.
[26] Z.C. Li(1996), Analysis of discrete techniques for image
transformations, Numerical Algorithms, Vol. 13, pp. 225-263,
1996.
[27] Z.C. Li(1998a), New discrete techniques for 3D image
transformations, Inter. J. Computers & Mathematics with
Application[SCI], Vol. 36, No. 4, pp. 77-109.
[28] Z. C. Li(1998b), Discrete techniques for 3-D digital images
and patterns, IEEE Trans. on Sys. Man and Cybern[SCI], Vol. 28,
No,6, pp. 883-894, 1998.
[29] Z.C. Li and Z.D.Bai(1998), Probabilistic analysis on the
splitting-shooting method for image transformations, J.
Computational and Applied Mathematics[JCR], Vol. 94, No. 2, pp.
69-121, 1998.
[30] Z.C. Li (1999), Advanced combinations of
splitting-shooting-integrating methods for digit image
transformations, Inter. J. Comp. and Appl. Math., Vol. 107, pp.
147-177, 1999.
[31] Z.C. Li and Y.C. Lin (2002), Image transformation by
numerical methods, Technical report, Department of Applied
Mathematics, National Sun Yat-sen University, Kaohsiung, 2002.
[32] Z.C. Li, T.D. Bui, Y.Y. Tang and C.Y. Suen (1989), Computer
transformation of Digital Images and Patterns, World Scientific,
Singapore, New Jersey, London 1989.
[33] Z.C. Li and H.T. Huang (2000), Blending curves for blending
problems by numerical differential equations, II. Numerical
methods, Computer and Mathematics with Applications, Vol. 39,
pp. 165-187, 2000.
[34] Z. C. Li, C. Y. Suen, T. D. Bui, T. D. Tang and Q. L. Gu(1992a),
Splitting-integrating methods for nonlinear images by inverse
transformations, IEEE, Trans. Pattern Anal. Machine Intell, Vol.
14, pp. 678-686, 1992.
[35] 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.
[36] B.S. Manjunath (1992), A feature based approach to face
recognition, In Proc. Computer Vision and Pattern Recognition,
pp. 373-378, Champaign, Illinois, Jun. 1992.
[37] A. Pentland, B. Moghaddam, and T. Starner (1993), View-based
and modular eigenspaces for face recognition, Technical report
245, MIT Media Lab Vismod, 1993.
[38] J.F. Poliakoff, Y.K. Wong and P.D. Thomas (1999), An
automated curve fairing algorithm for cubic eta-spline
curves, J. CAM, Vol. 102, pp. 73-85, 1999.
[39] W.K. Pratt (1991), Digital Image Processing(Sec. Ed.), John
Wiley & Sons Inc., 1991.
[40] D.F. Rogers and J.A. Adames (1990), Mathematical Elements for
Computer Graphs(Sec. Ed.), McGraw Hill. Company, 1990.
[41] M.A. Shackleton and W.J. Welsh (1991), Classification of
facial features for recognition, In Proc. Computer Vision and
Pattern Recognition, pp. 573-579, Lahaina, Maui, Hawaii, Jun.
1991.
[42] K. Sobottka and I. Pitas (1996), Extraction of facial regions
and features using color and shape information, In Proc. 13th
International Conference on Pattern Recognition, pp. 421-425,
Vienna, Austria, Aug. 1996.
[43] B.Q. Su and D. Y. Liu (1989), Computational Geometry--Curve
and Surface Modelling, Academic Press, Boston, 1989.
[44] K.K. Sung and T. Poggio (1994), Example-based learning for
view-based human face de-tection, In Proc. Image Understanding
Workshop, pp. 843-850, Monterey, Calif., Nov. 1994.
[45] M. Turk and A. Pentland (1991), Eigenfaces for recognition,
Journal of Cognitive Neuro-science, Vol. 3, No. 1, pp. 71-86,
1991.
[46] J.S. Vandergraft (1983), Introduction to Numerical
Computations, Academic Press, Inc., pp. 136-138, 1983.
[47] J.J. Weng and D.L. Swets (1999), Face recognition, Chapter 3 in
Biometrics, Personal Identification in Networked Society,
Ed. by A.K. Jain and R. Bolle and S. Pankanti, Kluwer Academic
Publishers, 1999.
[48] H. Wu, Q. Chen, and M. Yachida (1995), An application of
fuzzy theory: Face detection, In Proc. International Workshop on
Automatic Face and Gesture Recognition, pp. 26-28, Zurich,
Switzerland, Jun. 1995.
[49] H. Wu, Q. Chen, and M. Yachida (1996), Facial feature
extraction and face recognition, In Proc. 13th International
Conference on Pattern Recognition, pp. 484-488, Vienna, Austria,
Aug. 1996.
[50] G. Yang and T.S. Huang (1994), Human face detection in a
complex background, Pattern Recognition, Vol. 27, No. 1, pp.
53-63, 1994.
[51] L. Sirovich and M. Kirby (1987), Low-dimentional procedure
for the characterization of human faces, J. Opt. Soc. Am. A, Vol.
4, No. 3, 1987.
[52] C. Yao and J.G. Rohne (1999), An integral linear
interpolation approach to the design of incremental line
algorithms, J. CAM, Vol. 102, pp. 3-19, 1999.
[53] C. Zhang and F. Cheng (1999), Constructing partametric
quadratic curves, J. CAM, Vol. 102, pp. 21-36, 1999.