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研究生：	翁精鋒 Weng, Jing-Feng
論文名稱：	高穩健性濾波與相位展開演算法應用於數位影像中雜訊與孔洞之研究 Robust Filtering and Phase Unwrapping Algorithms for Noise and Holes in Digital Image Processing
指導教授：	羅裕龍 Lo, Yu-Lung
學位類別：	博士 Doctor
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	160
中文關鍵詞：	光斑、殘留雜訊、雜訊於高度不連續面、相位展開演算法、濾波演算法
外文關鍵詞：	speckle noise, residual noise, noise at the height discontinuities, phase unwrapping algorithm, filtering algorithm
相關次數：	點閱：124 下載：2
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表面輪廓干涉儀所拍得的二維干涉影像，最終可重建成三維立體影像(unwrapped phase map)。過程為二維干涉影像先轉換成相位圖(wrapped phase map)，再經由相位展開演算法(phase unwrapping algorithm)，最後可得三維立體影像(unwrapped phase map)。不幸的是，雜訊常出現於拍攝影像中，並使相位展開演算法(phase unwrapping algorithm)出錯，最後導致三維立體影像重建失敗。本論文將現今研究中常見的雜訊歸類成三種，分別為光斑(speckle noise)、殘留雜訊(residual noise)、雜訊於高度不連續面(noise at the height discontinuities)。現今研究只針對上述其中一種雜訊進行討論，相較之下，本研究同時針對三種雜訊進行討論。本研究提出新穎偵測演算法，名為雜訊與相位遷移偵測演算法(noise and phase jump detection scheme)，可同時偵測相位圖中的雜訊(noise)跟相位遷移(phase jump)，並分別標示於兩張圖中，名為雜訊圖(noise map)和相位遷移圖(phase jump map)。
不幸的是，雜訊強度過於密集或相位遷移過於不規則，會導致雜訊與相位遷移偵測演算法產生少許偵測錯誤(detection error)。為了濾除雜訊與偵測錯誤，本研究提出非線性濾波法，特點為結合雜訊與相位遷移偵測演算法和適應性中位數濾波法(adaptive median filter)。優點為可濾除雜訊和偵測錯誤，並減少相位遷移在2π與0兩處位置磨損(shifting error)。對於路徑獨立或路徑相依兩種不同類型的相位展開演算法，此濾波法皆能與之有效結合，同時進行相位展開與雜訊濾除兩種動作。
先執行濾波再執行相位展開為常見影像重建方式。然而，本研究顛覆傳統，改為先執行相位展開再執行濾波。先執行的相位展開演算法名稱為新穎旋轉演算法。此演算法有別於一般研究使用平移方式(shifting 2π method)將2π與0兩處黏合成連續相位，而改用旋轉方式黏合成連續相位。旋轉所需資訊，包括大小與方向，都是來自相位遷移圖。優點為相位遷移不會被磨損，同時保留雜訊與孔洞。相位展開結束後，被保留的雜訊可用濾波法移除，完成三維立體影像重建。
最後，本研究對雜訊與相位遷移偵測演算法中的相位遷移圖進行理論修正。一個相位遷移包含一個2π高處位置與0低處位置。不幸的是，此偵測演算法所得相位遷移圖，只能標出2π高處或0低處二者之一位置。幸運的是，修正後相位遷移圖(modified phase jump map)，可成功找出2π高處和0低處兩者位置，更能有效減少偵測錯誤產生。雜訊圖與修正後相位遷移圖可廣泛應用於相位展開演算法與濾波演算法，期望此研究對學術界做出一點微薄貢獻。

Interferometric system can capture the 2 dimensional interferograms, and then the captured images are converted into one 3 dimensional unwrapped phase map by using the image reconstruction process. The intact process is as follows. First, the 2 dimensional interferograms are converted into the wrapped phase map. Second, the wrapped phase map is unwrapped by the phase unwrapping algorithm. Finally, the 3 dimensional unwrapped phase map is obtained. Unfortunately, the noise which causes the phase unwrapping algorithm to fail usually occurs in the captured interferograms. This study classifies the common noise in current researches as three types of noise, namely speckle noise, residual noise, noise at the height discontinuities. The current researches focus on discussing one of these three types of noise. By contrast, this study discusses all of these three types of noise simultaneously. This study proposes the novel detection algorithm, namely the noise and phase jump detection scheme. This detection scheme can detect the noise and the phase jump positions in the wrapped phase map simultaneously, and then marks into two maps, namely the noise map and the phase jump map. Unfortunately, if the intensity of noise is too turbulent or the line of phase jump is too irregular, this detection scheme will produce the few detection errors.
In order to remove the noise and the detection errors, this study proposes the non-linear filtering algorithms, which combine the noise and phase jump detection scheme, and the adaptive median filter. Fortunately, the noise and the detection errors are effectively removed by the proposed filtering algorithms. In addition, the proposed filtering algorithms can reduce the degraded situation of smearing a phase jump located the 2π-high position and 0-low position, namely the shifting error. Importantly, the proposed filtering algorithms effectively combine with the two different types of phase unwrapping algorithms, namely path-dependent algorithms and path-independent algorithms, to remove the noise and unwrap the wrapped phase map simultaneously.
For the common image reconstruction, the filtering algorithm removes the noise in the wrapped phase map prior to the performance of the phase unwrapping algorithm. However, this study proposes the opposite method, using the novel rotation algorithm to unwrap the wrapped phase map prior to the performance of the filtering algorithm. Generally speaking, the common researches operate the phase jumps by shifting 2π, and eliminate the phase discontinuity between 2π-high and 0-low positions to become the continuous phase. By contrast, in this study, the rotation approach operates the phase jumps to obtain the continuous phase, rather than the approach of shifting 2π. The information of the rotation algorithm, including the magnitude and direction, is based on the phase jump map. It is noted that this rotation algorithm does not smear the phase jumps and saves the noise and holes. Finally, the filtering algorithm is used to remove the noise kept by this rotation algorithm, and the 3 dimensional reconstruction is completed.
Finally, this study modifies the theory of the noise and phase jump detection scheme, and proposes the modified phase jump map. One phase jump contains a 2π-high position and a 0-low position. Unfortunately, this original detection scheme only finds a 2π-high position and misses the corresponding 0-low position, or finds a 0-low position and misses the corresponding 2π-high position. The modified phase jump map is successfully capable of detecting both of 2π-high position and 0-low position. Moreover, it effectively reduces the detection error produced by the original detection scheme. The noise map and the modified phase jump map can be effectively applied to the phase unwrapping and filtering algorithms.

中文摘要 ...................................................................................................................................... i
Abstract ....................................................................................................................................... iii
Table of contents ..........................................................................................................................vi
List of Tables ............................................................................................................................... x
List of Figures .............................................................................................................................. xi
Notation ...................................................................................................................................... xx
Chapter 1. Introduction ..................................................................................................... 1
1 Three different types of noise ................................................................................... 1
2 Filtering algorithm.................................................................................................... 3
3 Phase unwrapping theory ......................................................................................... 5
4 Motivation and background (identifying three types of noise) ................................ 8
5 Method and purpose ............................................................................................... 12
6 Remainder .............................................................................................................. 16
7 Software and experimental setup ........................................................................... 18
Chapter 2. Proposed robust detection scheme presenting noise and phase jump ............ 20
1 Principles of proposed noise and phase jump detection scheme ............................ 21
1.1 Characteristics of Condition I pixels ............................................................. 24
1.2 Characteristics of Condition II pixels ........................................................... 25
2 Simulation results ................................................................................................... 28
2.1 Simulation Results on the 1st , 2nd , and 3rd positions by detection scheme.... 29
2.2 Noise map obtained from detection scheme .................................................. 32
2.3 Phase jump map obtained from detection scheme ......................................... 36
2.4 Choosing Suitable parameter of A 
from the noise and phase jump maps 37
3 Experimental setup and results ............................................................................... 40
3.1 Noise and phase jump map results ................................................................ 40
3.2 Phase unwrapping results ............................................................................. 43
3.3 Oblique angle with phase jump line and height discontinuities line ............. 45
3.4 Parallel with phase jump line and height discontinuity line ......................... 49
4 Summary ................................................................................................................ 50
Chapter 3. Proposed integration of image reconstruction based on detection scheme ... 52
1 Underlying principles of detection scheme and filtering operations ...................... 53
1.1 Filter A – application of detection scheme and adaptive median filter ......... 53
1.2 Filter B – detection scheme combined with noisy pixel replacement mechanism 54
1.3 Implementation of CA algorithm using array processor and additional sub-map area (using in Path III) .............................................................................................. 55
2 Integration of filtering and phase unwrapping algorithms for image reconstruction ............................................................................................................................... 57
3 Simulation results ................................................................................................... 59
3.1 Application of Filter A to noisy wrapped phase map .................................... 61
3.2 Path I using application of Filter B to noise-reduced wrapped phase map .. 62
3.3 Path II using application of Filter B to noise-reduced wrapped phase map . 64
3.4 Path III using application of Filter B to noise-reduced wrapped phase map 67
3.5 Summary of simulation results for Paths I, II and III Table 3-2 ................... 69
3.6 Effect of Filter B on Path III reconstruction performance ............................ 71
4 Experimental results ............................................................................................... 73
4.1 Precision evaluation of three reconstruction paths using sample with perpendicular phase jump lines ............................................................................................... 73
4.2 Robustness evaluation of three reconstruction paths using sample with non-straight phase jump lines .................................................................................................. 80
4.3 Sensitivity evaluation of Path I and Path III reconstruction paths using
sample with two different height discontinuities ...................................................................... 85
5 Summary ................................................................................................................ 89
Chapter 4. Proposed rotation unwrapping algorithm based on detection scheme ........... 93
1 Principles of proposed rotation algorithm .............................................................. 94
1.1 2D noise and phase jump detection scheme .................................................. 94
1.2 2D and 3D additional phase jump detection scheme for the proposed
rotation algorithm .................................................................................................................... 95
1.3 Rotation phase unwrapping scheme .............................................................. 97
1.4 First rotation procedure ................................................................................ 98
1.5 Second rotation procedure .......................................................................... 101
1.6 Stitching process .......................................................................................... 103
2 Effect of proposed rotation algorithm on noise errors, hole errors and phase
shifting errors ............................................................................................................................. 105
2.1 Characteristic of angle fix  given above errors ....................................... 106
2.2 Advantage of vector 1 2 CC in proposed rotation algorithm ..................... 107
3 Simulation results ................................................................................................. 108
3.1 2D non-noisy linear case (demonstrating total process in Section 4.1 and
presenting case in Figure 4-5(a)): Finding all of phase jumps .............................................. 108
3.2 2D non-noisy linear case (demonstrating total process in Section 4.1 and
presenting case in Figure 4-5(a)): Performing rotation scheme ............................................ 109
3.3 2D noisy linear case (containing speckle noise, residual noise, and holes,
and presenting cases in Figure 4-5(a) and Figure 4-5(b)) .................................................... 114
3.4 2D filtered linear case (presenting shifting error in Figure 4-5(c)) ............ 117
3.5 2D non-noisy non-linear case (presenting sine-wave case) ........................ 118
3.6 Discussion of rotation angles ...................................................................... 119
4 Experimental results ............................................................................................. 123
4.1 Retention of holes in proposed rotation algorithm ...................................... 123
4.2 Retention of noise in proposed rotation algorithm ...................................... 124
4.3 Robustness of proposed rotation algorithms toward noise ......................... 124
5 Summary .............................................................................................................. 127
Chapter 5. Proposed modified detection scheme .......................................................... 129
1 Principle of modified detection algorithm ............................................................ 130
1.1 Modified detection scheme for phase jumps ................................................ 130
1.2 Functions of High  and Low  ................................................................. 134
2 Simulation results ................................................................................................. 136
3 Experimental results ............................................................................................. 140
4 Discussion of High  and Low  in simulations and experiments .................... 143
5 Summary .............................................................................................................. 145
Chapter 6. Conclusions ................................................................................................. 147
Reference ................................................................................................................................. 151
List of publications .................................................................................................................. 157
Vita .......................................................................................................................................... 160
                                    

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