本篇論文係運用一度空間及二度空間立方樣條差補法（Cubic Spline Interpolation），並結合MPEG壓縮法，來達成對視訊影像做極低位元速率（very low bit-rate）壓縮以及可擴充視訊壓縮 (scalable video compression) 的新技術。
這種CSI插補法與其他插補法的不同之處，是其他插補法在資料取樣時，會直接捨去非取樣點上之原函數值，一但函數重建時會造成較多的誤差。而CSI插補法則在資料取樣時，先利用立方樣條插補函數以及最小平方法，來估算出與原函數之間誤差最小的取樣函數，並事先儲存估算出來誤差最小的取樣函數值，當資料重建時，再用立方迴旋插補法來計算重建函數，因此所獲得的重建函數和原來函數間的總誤差值，將比其它許多插補法來的小。
透過CSI技術配合MPEG-1壓縮標準，將可達成極低位元速率的影像壓縮，這不但能減輕MPEG在高壓縮比時所產生的方塊效應（blocking effect），同時在達成極低位元率的視訊壓縮時，還能保有一定的視訊品質。運用CSI技術亦可達成可擴充的視訊壓縮，這種動態改變資料傳輸速率的壓縮方式，將能有效應用在不同傳輸能力的網路環境之下。

This thesis applies the one-dimensional (1-D) and two-dimensional (2-D) cubic-spline interpolation (CSI) schemes to MPEG standard for very low-bit rate video coding. In addition, the CSI scheme is used to implement the scalable video compression scheme in this thesis.
The CSI scheme is based on the least-squares method with a cubic convolution function. It has been shown that the CSI scheme yields a very accurate algorithm for smoothing and obtains a better quality of reconstructed image than linear interpolation, linear-spline interpolation, cubic convolution interpolation, and cubic B-spline interpolation.
In order to obtain a very low-bit rate video, the CSI scheme is used along with the MPEG-1 standard for video coding. Computer simulations show that this modified MPEG not only avoids the blocking effect caused by MPEG at high compression ratio but also gets a very low-bit rate video coding scheme that still maintains a reasonable video quality. Finally, the CSI scheme is also used to achieve the scalable video compression. This new scalable video compression scheme allows the data rate to be dynamically changed by the CSI scheme, which is very useful when operates under communication networks with different transmission capacities.

中文摘要 …………………………………………………………… i
Abstract ……………………………………………………………. ii
Contents …………………………………………………………….. iii
List of Figures ………………………………………………………. iv
Chapter 1 Introduction ……………………………………………. 1
1.1 Motivation and Related Research ………………………………………… 1
1.2 Summary of the Thesis …………………………………………………… 4
1.3 Organization of The Thesis ………………………………………………. 6
Chapter 2 Technical Preliminaries ………………………………… 7
2.1 Interpolation Functions ……………………………………………………. 7
2.2 CSI Scheme for 1-D Signal ……………………………………………….. 9
2.3 CSI Scheme for 2-D Signal …………………...………………………….. 14
2.4 Reconstructed Function of 1-D CSI Scheme ….…………………………. 20
2.5 Reconstructed Function of 2-D CSI Scheme ….…………………………. 21
Chapter 3 Very Low Bit-Rate Video Coding Scheme …………….. 23
3.1 Modified MPEG Scheme …..……………………………………………… 23
3.1.1 Modified MPEG with 2-D CSI ………..……………………………… 24
3.1.2 Modified MPEG with 3-D CSI ………..……………………………… 25
3.2 Experimental Results …………………………………………………….. 26
3.2.1 Experimental for Modified MPEG with 2-D CSI ………..………….. 26
3.2.2 Experimental for Modified MPEG with 3-D CSI …………………… 36
3.3 The Experiment of H.263 Codec …………………………………………. 41
Chapter 4 Scalable Video Compression Scheme ………………… 45
4.1 New Scalable Video Compression Scheme ………………………………. 45
4.2 Experimental Results for New Scalable Video Compression Scheme ....… 49
Chapter 5 Conclusions and Further Research ……………………. 52
5.1 Conclusions ………………………………………………………………. 52
5.2 Further Research …………………………………………………………. 53
Bibliography ……………………………………………………….. 54

[1] Joan L. Mitchell, William B. Pennebaker, Chad E. Fogg, and Didier J. LeGall, MPEG Video Compression Standard, International Thomson Publishing.
[2] ISO/IEC JTC1/SC29/WG11 N3747, Overview of the MPEG-4 Standard, October 2000.
[3] Thomas Sikora, Senior Member, IEEE, “The MPEG-4 Video Standard Verification Model”, IEEE Trans. on Circuits and Systems for Video Technology, vol. 7, no. 1, pp. 19-31, February 1997.
[4] Video Coding for Low Bit Rate Communication, ITU-T Rec. H.263, January 1998.
[5] Karel Rijkse, KPN Research, “H.263:Video Coding for Low-Bit-Rate Communicaiton,” IEEE Communication Magazine, pp. 42-45, December 1996.
[6] Detlev Marpe and Hans L. Cycon, “Very Low Bit-Rate Video Coding Using Wavelet-Based Techniques,” IEEE Trans. on Circuit and Systems for Video Technology, vol. 9, no.1, pp. 85-94, February 1999.
[7] Jozsef Vass, Student Member, IEEE, Bing-Ging Chai, Member, IEEE, Kannappan Palaniappan, Member, IEEE, and Xinhua Zhuang, Senior Member, IEEE, “Significance-Linked Connected Component Analysis for Very Low Bit-Rate Wavelet Video Coding”, IEEE Trans. on Circuit and System for Video Technology, vol. 9, no. 4, pp. 630-647, June 1999.
[8] Jia Zhike, Cui Huijuan, and Tang Kun, “Adaptive quantization scheme for very low bit rate video coding,” Communications, 1999. APCC/OECC '99. Fifth Asia-Pacific Conference on ... and Fourth Optoelectronics and Communications Conference, Volume: 2 , 1999, Page(s): 940 -943 vol.2.
[9] Touradj Eerahimi, Member, IEEE, Emmanuel Reusens, and Wei Li, “New Trends in Very Low Bitrate Video Coding,” Proceedings of The IEEE, vol. 83, no. 6, June 1995.
[10] T. K. Truong, L. J. Wang, I. S. Reed, and W. S. Hsieh, “Image data compression using cubic convolution spline interpolation,” IEEE Trans. Image Processing, vol. 9, pp. 1988-1995,Nov. 2000.
[11] R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. on Acoustic, Speech, and Signal Processing, vol. ASSP-29, No.6, pp.1153-1160, Dec. 1981.
[12] H. S. Hou, and H. C. Andrews, “Cubic splines for image interpolation and digital filtering,” IEEE Trans. on Acoustic, Speech, and Signal Processing, vol. ASSP-26, No.6, pp.508-517, Dec. 1978.
[13] W. K. Pratt, Digital Image Processing, second edition, John Wiley & Sons, Inc., New York, 1991.
[14] C. de Boor, A Practical Guide to Splines. New York: Springer-Verlag, 1978.
[15] M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: Part II-Efficient design and applications,” IEEE Trans. Signal Processing, vol. 41, pp. 834-848, Feb. 1993.
[16] M. Unser, A. Aldroubi, and M. Eden, “Enlargement or Reduction of Digital Images with Minimum Loss of Information,” IEEE Trans. Image Processing, vol. 4, pp. 247-258, March 1995.
[17] I. S. Reed, Notes on Image Data Compression Using Linear Spline Interpolation, Department of Electrical Engineering, University of Southern California, Los Angeles, California, 90089-2565, U.S.A., Nov. 1981.
[18] I. S. Reed and A. Yu, Optimal Spline Interpolation for Image Compression, United States Patent, No. 5822456, Oct. 13, 1998.
[19] E. O. Brigham, The Fast Fourier Transform and its Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.
[20] A. V. Oppenheim, and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
[21] L. J. Wang, W. S. Hsieh, T. K. Truong, I. S. Reed, and T. C. Cheng, “A Fast Efficient Computation of Cubic-Spline Interpolation in Image Codec,” IEEE Trans. on Signal Processing, vol. 49, no. 6, June 2001.
[22] L. J. Wang, “A fast cubic-spline interpolation and its applications,” Ph.D. dissertation, National Sun Yat-Sen University, Taiwan, R.O.C., Mar, 2001.