隨著資訊科技的發展，各種演算法不斷被發表，使得影像追尋技術愈來愈進步。大部分的方式傾向物體特徵辨認，並過濾不符合此特徵的背景成份。
　　本文使用一種時空域平面共振遞迴濾波器，在未知運動物體特徵的情況下，仍可給定適當速度參數，使得濾波器強化該物體，並過濾移動速度與濾波器參數不同的物體。由於此濾波器無法過濾影像背景，因此導入同態濾波與快速光流估測法，辨認並分離連續影像中的背景與運動物體成份。本文同時考慮不同的三維頻寬參數，發展出一套系統方法來設計濾波器參數，以方便實務上之應用。

Along with rapid development of information technology, all kinds of algorithms have been presented, to achieve significant progress in image tracking. Most methods tend to identify features of moving objects, and filter out background components which do not meet these features.
This thesis uses a spatio-temporal planar-resonant filter to accomplish moving object tracking tasks. Under the condition without prior knowledge about features of moving objects, choosing appropriate filter’s parameters is able to enhance the object with a certain moving speed and reduce intensity of objects with different velocities. Nevertheless, this filter cannot solve the problem background filtering. Therefore, a homomorphic filtering with fast optical flow estimation is implemented to identify and separate the background and moving components in dynamic images. This thesis also considers different 3-D bandwidth parameters. To develop a systematic approach to design filter’s parameters for actual implementations.

List of Figures III
List of Tables VI
Notations VII
摘要 VIII
Abstract IX
Chapter 1 Introduction 1
1.1 Motivation and Goal 1
1.2 Literatures Review 3
1.3 Organization of the thesis 7
Chapter 2 Motion in Frequency Domain 8
2.1 Fourier Transform 8
2.2 Fourier Spectrum of 2-D Spatio-temporal Signal 14
2.3 Fourier Spectrum of 3-D Spatio-temporal Signal 20
Chapter 3 Digital Planar-resonant Recursive Filter 24
3.1 Circuit Analysis 24
3.2 Bilinear Transformation 33
3.3 Three-dimensional Planar-resonant Recursive Filter 35
3.4 Filter Design 44
Chapter 4 Background Extraction 47
4.1 Homomorphic Filtering 47
4.2 Fast Optical Flow Estimation 52
Chapter 5 Simulation Studies 58
5.1 Filtering with background extraction 58
5.2 Analysis of Filter Responses 62
5.3 Design of Filter’s parameters 67
Chapter 6 Conclusions 72
6.1 Thesis Summary 72
6.2 Future Outlook 74
Reference 75
Appendix A The output function for only one matched velocity component 79
Appendix B The output function for two unmatched velocity components 81

[1] A. B. Watson and A. J. Ahumanda, Jr. “A Look at Motion in the Frequency Domain,” NASA Technical Memorandum 84352, April 1983.
[2] E. H. Adelson and J. R. Bergen, “Spatiotemporal Energy Models for the Perception of Motion, ” Journal of Optical Society of America, Vol. 2, No. 2, pp. 284-299, February 1985.
[3] L. T. Bruton and N. R. Bartley, “Three-Dimensional Image Processing Using the Concept of Network Resonance,” IEEE Transactions on Circuits and Systems, Vol. 32, No. 7, pp. 664-672, July 1985.
[4] L. T. Bruton and N. R. Bartley, “The Enhancement and Tracking of Moving Objects in Digital Images Using Adaptive Three-Dimensional Recursive Filters,” IEEE Transactions on Circuits and Systems, Vol. 33, No. 6, pp. 604-613, June 1986.
[5] 丁士翔，以時空域為基礎之移動物體追尋，國立中山大學機械與機電工程研究所碩士論文，民國九十七年六月。
[6] B. P. Lathi, Signal Processing & Linear Systems, Oxford University Press, ISBN: 978-0195219173, February 2000.
[7] D. E. Dudgeon and R. M. Mersereau, Multidimensional Digital Signal Processing, Prentice-Hall, ISBN: 978-0136049593, September 1983.
[8] C. L. Phillips and H. T. Nagle, Digital Control System Analysis and Design (3rd Edition), Prentice-Hall, ISBN: 978-0133098327, November 1994.
[9] C. E. Erdem, G. Z. Karabulut, E. Yanmaz, and E. Anarim, “Motion Estimation in the Frequency Domain Using Fuzzy C-Planes Clustering, ” IEEE Transactions on Image Processing, Vol. 10, No. 12, pp. 1873-1879, December 2001.
[10] M. Pingault and D. Pellerin, “Motion Estimation of Transparent Objects in the Frequency Domain,” Signal Processing, Vol. 84, No. 4, pp. 709-719, April 2004.
[11] 黃婉婷，適用於物體追蹤一維時空域濾波器之設計與應用，國立臺灣大學電信工程學研究所碩士論文，民國九十四年六月。
[12] S. C. Pei, W. Y. Kuo, and W. T. Huang, “Tracking Moving Objects in Image Sequences Using 1-D Trajectory Filter,” IEEE Signal Processing Letters, Vol. 13, No. 1, pp. 13-16, January 2006.
[13] Y. Zhang and L. T. Bruton, “Applications of 3-D LCR Networks in the Design of 3-D Recursive Filters for Processing Image Sequences,” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 4, No. 4, pp. 369-382, August 1994.
[14] H. J. Kaufman and M. A. Sid-Ahmed, “Real-time 2-D Homomorphic Filter for Broadcast TV Signals,” IEEE Transactions on Consumer Electronics, Vol. 38, No. 2, pp. 48-56, May 1992.
[15] M. R. Asharif and H. Etemadnia, “Shadow identification by Image Components Separation Using Homomorphic System,” Bulletin of the Faculty of Engineering, University of the Ryukyus, No. 66, pp. 71-75, March 2004.
[16] J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of Optical Flow Techniques,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’92), Vol. 1, pp. 236-242, June 1992.
[17] 景雅新，光流技術在移動物體影像追尋上之應用，國立中山大學機械與機電工程研究所碩士論文，民國九十二年六月。
[18] M. Roth, K. Tanaka, C. Weissman, and W. Yerazunis, “Computer Vision for Interactive Computer Graphics,” IEEE Computer Graphics and Applications, Vol. 18, No. 3, pp. 42-53, May-June 1998.
[19] Y. Zhang and L. T. Bruton, “Differential-Type Three-Dimensional Recursive Ladder Filters Having Frequency-Planar- or Frequency-Beam-Shaped Passbands,” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 2, No. 3, pp. 297-305, September 1992.