影像補繪的應用包括了物件移除、照片修補與抓痕移除等等。在本論文中我們提出了一個改良式的多層次影像補繪技術與一個使用類神經網路以學習為基礎的補繪方法。
多層次的影像補繪方法混合了影像分割、邊緣估測與以範例為基礎的影像補繪方法。影像分割是為了在目標區域之外找到影像的邊緣並且將影像分成數個同質性高的區塊。影像分割之後，我們使用邊緣估測來計算在目標區域的曲線去將整張影像分成許多不同的區塊。再使用以範例為基礎的影像補繪方法分開去填補在不同區塊內的目標區域。
以範例為基礎的影像補繪技術使用材質合成與範例區塊的填補順序來填補目標區域。範例區塊是由與目標區域鄰近的區域中找出來的，而範例區塊的填補順序是依照填補前緣上的等輻透線向量值和範例影像區塊密度來決定。
以學習為基礎的技術是一個新的技術。此技術結合了機器學習與填補順序的的觀念。我們使用類神經網路去學習在目標區塊附近的資料。在訓練完之後，我們依照填補順序去填補目標區塊。
由模擬結果來看，多層次的影像補繪在大物件移除上可以得到非常好的結果，而以學習為基礎的技術在移除中型物件於灰階影像上可以得到很好的結果。

Application of Image inpainting ranges from object removal, photo restoration, scratch removal, and so on. In this thesis, we will propose a modified multi-scale method and learning-based method using artificial neural networks for image inpainting.
Multi-scale inpainting method combines image segmentation, contour estimation, and exemplar-based inpainting. The main goal of image segmentation is to separate image to several homogeneous regions outside the target region. After image segmentation, we use contour estimation to estimate curves inside the target region to partition the whole image into several different regions. Then we fill those different regions inside the target region separately by exemplar-based inpainting method.
The exemplar-based technique fills the target region via the texture synthesis and filling order of exemplary patches. Exemplary patches are found near target region and the filling order is determined by isophote and densities of exemplary patches.
Learning-based inpainting is a novel technique. This technique combines machine learning and the concept of filling order. We use artificial neural networks
to learn the structure and texture surrounding the target region. After training, we fill the target region according to the filling order.
From our simulation results, very good results can be obtained for removing large-size objects by using the proposed multi-scale method, and for removing medium-size objects of gray images.

誌謝 …………………………………………………………………………… i
摘要 ……………………………………………………… ii
ABSTRACT ………………………..…………....................................... iii
GLOSSARY OF SYMBOLS ……………………………………………………. v
LIST OF FIGURES ……………………............................................................... vi

CHAPTER 1 INTRODUCTION …………………............................................. 1

1.1 Motivation ……………………………………………………... 1
1.2 Brief Sketch of the Contents …………………………………... 4

CHAPTER 2 REGION-BASED SEGMENTATION …...................................... 7

2.1 Pre-processing ……………………………………………….… 8
2.2 Method of Felzenszwalb and Huttenloche ……………………… 9
2.3 Post-processing ………………………………………………. 13
2.4 Algorithm ……………………………….……………………. 13

CHAPTER 3 CONTOUR ESTIMATION ……………………..……………... 16

3.1 Introduction ……………………...…………………………… 16
3.2 Contour Merging and Contour Growing ………………..…..... 19
3.3 Algorithm …………………………………………………….. 26

CHAPTER 4 EXEMPLAR-BASED INPAINTING ………………………….. 29

4.1 Pre-processing ………………………………………………... 29
4.2 Mathematical Notation …..………………...…………………. 30
4.3 Exemplar-based Inpainting …..……………..……………...... 32
4.4 Algorithm…………………..…………………………………... 36

CHAPTER 5 LEARNING-BASED INPAINTING …………………………... 39

5.1 Artificial Neural Network ……...…...……..…………………. 39
5.2 Learning-based Inpainting ……………...……..…………….. 42

CHAPTER 6 EXPERIMENTAL RESULTS ……...………………………….. 48

6.1 Multi-scale Inpainting ……..….…….………………………... 48
6.2 Learning-based Inpainting ………………………………….. 53

CHAPTER 7 CONCLUSION AND DISCUSSION ………………………….. 58

REFERENCES ……………………………………………………...…............. 61

[Ber.1] M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, “Image Inpainting,” In Proceedings of SIGGRAPH 2000, New Orleans, USA, 2000.
[Bert.1] D.P. Bertsekas, Nonlinear Programming. Second Edition, Belmont, MA: Athena Scientific, 1999.
[Chen.1] W.C. Chen, “A Multi-Scale Approach for Image Inpainting,” M.S. Thesis, Department of Electrical Engineering, Tatung University, Taiwan, 2004.
[Chi.1] C.Y. Chi, “A New Watershed-based Color Image Segmentation Algorithm,” M.S. Thesis, Department of Electrical Engineering, National Cheng Kung University, Taiwan, 2004.
[Cri.1] A. Criminisi, P. P