警方偵辦連續性犯罪常藉不同現場間鞋印紋路的比對，篩選遺留具備相似鞋印紋路的案件，並自關聯案件中指紋及生物性跡證來確認犯嫌身分。現場鞋印多使用相機翻拍，實務上礙於地物環境限制，常以手持相機方式取代架設三腳架進行拍攝，無可避免因手持拍照產生拍攝角度偏斜會造成鞋印影像變形，並衍生後續鞋印影像關聯比對的困難。
對於刑案現場攝影，每張鞋印照片內除了鞋印主體外還會放置參考物L形比例尺(L-shape scale ruler)用來標記影像的大小及形變情形。本篇論文探討，藉由比較形變鞋印影像中的參考物，來模擬適當的Homography矩陣，並校正變形之鞋印影像。
在現今運算能力大幅提升及新穎類神經網路興起的時代，本篇論文探討利用全卷積網路先將參考物與背景分離，再以分割後的參考物影像，應用空間變換網路循環迭代，逐次逼近適當的Homography矩陣，還原因拍攝角度偏斜的鞋印影像，使鞋印影像便於後續刑案現場鞋印資料庫建檔及分析。

When investigating the serial criminal cases, police frequently links the different cases with similar shoeprint patterns and then adopt the fingerprints or the bodily fluids, such as blood, to identify the criminals. Practically, most of the shoeprints are collected by photographing. However, due to the obstacles of the various environments in each crime scene, the camera is usually held in hands instead of setting on a well-adjusted tripod when photographing the shoeprints. There is no denying that both pitch and yaw around the x,y-axes will cause the deformed shoeprint images and make the consequent forensic examination on shoeprint images become more difficult.
As for the criminal photography, each shoeprint image not only has the shoeprint marks but also accompanies with the reference object. The reference object frequently used to indicate the actual scale and the level of the deformation in the shoeprint evidence is L-shape scale ruler. In this paper, we focus on evaluating the deformation of the reference object to predict the suitable homography matrix H, which can rectify the deformed reference object and shoeprint marks in the shoeprint image.
In the era of the significant improvement on the computing ability and thriving of the brand-new neural network structure, this paper uses the convolutional neural network to segment the reference object from the shoeprint image and then applies recurrent spatial transformation structure to keep rectifying the deformed reference object little by little until obtaining adequate H to make the deformed reference object deformation-free and facilitate the following shoeprint database constructing and analysis.

摘要 I
Abstract II
誌謝 IV
Table of Contents VI
Figure of Contents VIII
Table of Contents XII
Chapter 1 Introduction 1
1.1 Motivation 4
1.2 Related Works 9
1.3 System Setup and Framework 11
1.4 Contributions 13
Chapter 2 Shoeprint Database Preparation and Labeling 15
2.1 Framework 15
2.2 System Hardware: Specification 17
2.3 Shoeprint Preparation 19
2.4 Shoeprint Database Rectification 23
Chapter 3 Scale Ruler Segmentation using Fully Convolutional Autoencoder Network 26
3.1 Generate Scale Ruler Patch and Data Augmentation 28
3.2 Training Process 31
3.3 Testing Process 33
3.4 Physical Meaning 34
Chapter 4 Shoeprint Image Rectification using Recurrent Spatial Transformation Network 36
4.1 Generate Scale Ruler Image and Data Augmentation 40
4.2 Spatial Transformer Network 43
4.3 Training Process 47
4.4 Testing Process 56
4.5 Physical Meaning 56
Chapter 5 Experimental Results 58
5.1 Scale Ruler Segmentation using Fully Convolutional Network 58
5.2 Shoeprint Image Rectification using Recurrent Spatial Transformation Network 62
Chapter 6 Conclusion and Future Work 75
Reference 76
Appendix A. 2D Planar Transformation 78
Appendix B. The Homography Matrix 80
Appendix C. Homography Decomposition 81
C.1 Homography Decomposition 81
C.2 Proposed Homography Model 83
C.3 Proposed Homography Decomposition 89

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