臺灣博碩士論文加值系統

在過去二十年，小波轉換在視訊處理、電腦視覺及資料壓縮等領域已變成了一種標準的處理技術。這些應用所處理的往往都是取樣後的訊號，因此離散小波轉換已成為一廣泛被採用的計算工具。在電腦視覺的應用上，光流計算是一重要的課題。本論文探討如何由小波方法，從一連串的影像中精確的找出運動物體的光流資訊並將之應用於影像切割、影像追蹤等方面。

本論文實現不同的尺度函數的小波光流估測。我們比較D4、 D6、CDF 6/2(6)、CDF 9/7(7)、CDF 9/7(9)尺度函數在小波方法上的表現。我們計算2個合成影像Translating Tree and Yosemitec與4個實際影像Rubik cube、Hamburg Taxi、Coastguard、Football的光流。對合成影像，Daubechies 4小波基底沒利用降解析的角度平均誤差分別為19.85o、34.23o並需要130.6、156.8秒的計算時間;實際影像分別需要144.4、182.9、238.1、181.5秒的計算時間。Daubechies 6小波基底沒利用降解析的角度平均誤差分別為0.701o、5.136o並需要153.5、200.0、163.0、199.9、256.3、197.8秒的計算時間。Daubechies 6/2(6) 小波基底沒利用降解析的角度平均誤差分別為0.633o、5.369o並需要149.7、202.1、163.6、198.8、255.3、197.5秒的計算時間。Daubechies 9/7(7) 小波基底沒利用降解析的角度平均誤差分別為0.644o、5.073o並需要180.9、249.9、180.1、238.7、308.0、233.4秒的計算時間。Daubechies 9/7(9) 小波基底沒利用降解析的角度平均誤差分別為0.661o、4.475o並需要265.4、318.5、209.0、253.1、315.7、250.5秒的計算時間。然後比較垂直與偶垂直基底時，我們可以知道偶垂直基底有比垂直基底有更好的表現。且因我們利用了降解析與原有的小波方法合併，大大減少了原有的計算時間。

Over the past twenty years, the wavelet transform has become a standard technique in many fields such as signal processing, computer vision and data compression. In these applications, the signals to be processed are usually sampled, so the discrete wavelet transform (DWT) is used extensively. Optical flow calculation is an essential problem in computer vision. This thesis investigates how to obtain accurate optical flow of moving objects from image sequences by using wavelets.

This thesis reports the computation time and accuracy of optical flow calculation using different scaling functions. We compare the performance of the Daubechies D4, D6, CDF , CDF and CDF scaling functions employed in the wavelet-based optical flow estimation. We estimated the optical flow from two kinds of synthetic sequences: Translating Tree and Yosemitec and four kinds of real sequences: Rubik’s cube, Hamburg Taxi, Coastguard and Football. The average errors and computation time of the D4 are 19.85o, 34.23o degrees and 130.6, 156.8, 144.4, 182.9, 238.1 and 181.5 seconds without resolution reduction. The average errors and computation time of the D6 are 0.701o, 5.136o degrees and 153.5, 200.0, 163.0, 199.9, 256.3 and 197.8 seconds without resolution reduction. The average errors and computation time of the CDF are 0.633o, 5.369o degrees and 149.7, 202.1, 163.6, 198.8, 255.3 and 197.5 seconds without resolution reduction. The average errors and computation time of the CDF are 0.644o, 5.073o degrees and 180.9, 249.9, 180.1, 238.7, 308.0 and 233.4 seconds without resolution reduction. The average errors and computation time of the CDF are 0.661o, 4.475o degrees and 265.4, 318.5, 209.0, 253.1, 315.7 and 250.5 seconds without resolution reduction. When compared with the orthogonal bases the biorthogonal bases, have better performance. Finally, we reduce the computation time by combining the wavelet-based method and resolution reduction.

摘要 i
Abstract iii
誌謝 v
Contents vi
Figure Captions viii
Table Captions x

CHAPTER 1 Introduction 1
1.1 Motivation 1
1.2 Related Works 1
1.3 Gist of the Thesis 3

CHAPTER 2 Wavelet Theory 4
2.1 Multiresolution Analysis 4
2.2 Connection between DWT and Filter Bank 11
2.3 2-D Discrete Wavelet Transform 15

CHAPTER 3 Optical Flow Estimation 18
3.1 Optical Flow and Image Flow 18
3.2 Optical Flow Methods 19
3.2.1 Horn and Schunck Method 19
3.2.2 Wavelet-Based Method 28
CHAPTER 4 The Characteristic of Scaling Functions and Their Connection Coefficients 41
4.1 Characteristics of Orthogonal, Linear Phase and FIR Scaling Functions 41
4.2 Scaling Functions of Compact Support 42
4.2.1 Orthogonal Scaling Functions 42
4.2.2 Biorthogonal Scaling Functions 44

CHAPTER 5 Experiments and Results 53
5.1 Experimental description 53
5.2 Synthetic Image Sequences 53
5.3 Real Image Sequences 60
5.4 Real Application 72

CHAPTER 6 Conclusion 77

References 79

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