影像資料隱藏技術 (Data Hiding; DH) 是將秘密資訊隱藏於封面影像 (Cover Image) 中，隱藏秘密後的影像稱之為偽裝影像 (Stego Image)。隱藏所嵌入的信息容量、與不可察覺性是資料隱藏研究的重點。當解回隱藏信息時，若偽裝影像能復原回封面影像，我們稱之為可逆式資料隱藏 (Reversible DH; RDH)。但是，若只能回復至幾乎與原封面影像差異不大的影像，則稱之為部分可逆式資料隱藏 (Partial RDH; PRDH)。
漢明碼是經常使用於資料隱藏的的一種技術。傳統植基於漢明碼的資隱藏，通常是將 k 個秘密位元嵌入於 (2^k − 1) 像素的最低有效位位元(LSB)中。以最常使用的(7, 4)漢明碼為例，就是將每3個秘密位元嵌入7個像素的LSB。然而，這樣的信息嵌入率並不令人滿意。本論文"最小像素差的漢明碼之部分可逆式資料隱藏機制"，是研究部分可逆式資料隱藏機制。為了大幅提高嵌入的信息容量，我們不再是像傳統的(7, 4)漢明碼在每7個像素的LSB嵌入秘密。我們提出了一種基於漢明碼的利用像素差異的隱藏方法。本論文討論兩種方式的隱藏機制，第一種方法是每次從2個像素分別取出4個LSB與3個LSB建構成(7, 4)漢明碼。在這個漢明碼中，嵌入3個秘密位元。此時，與傳統(7, 4)漢明碼不同，我們不在指考慮更動最多一個位置來嵌入信息 (註: 因為現在這個漢明碼不再是7個像素的LSB，而是兩個像素中的4個LSB與3個LSB)。所以我們採用最小像素差的條件來進行信息嵌入。我們的第二個方法是將2個像素擴張至m個像素的通式架構，其中m可以是1 ~ 7。當m=2時，此通式架構則為第一個方法，m=7則此通式架構則為傳統(7, 4)漢明碼的嵌入方法。若是m值愈小，信息嵌入容量愈大但是偽裝影像的PSNR差。反之，m值愈大，嵌入容量小但是偽裝影像的PSNR好。第二個方法的通式架構可在嵌入量與PSNR之間取得平衡與妥協。實驗和理論結果證明了這兩種方法的可行性和其各別優勢。

The image data hiding (DH) hides the secret data into the cover image, and the embedded image is called as the stego image. Embedding capacity and imperceptibility are the main research issues about DH. When the secret data is extracted, the stego image can be recovered to the cover image, we call the DH as the reversible DH (RDH). However, the recover image cannot be recovered to the original image, and can only recovered to an image that is almost the same as original image, this RDH is referred to as partial RDH (PRDH).
Hamming code approach is often adopted to embed secret data in DH. In general, Hamming code based DH may embed k secret bits into the least significant bit (LSB) of (2^k−1) pixels. Consider using (7, 4) Hamming code as an example. We may embed 3 secret bits into the LSB of 7 pixels. However, such message embedding rate is not very high. In the thesis "Partial Reversible Data Hiding by Minimum-Pixel-Difference Hamming Code" is dedicated on studying PRDH. To enhance embedding capacity, we do not use the conventional approach like the (7, 4) Hamming code based DH. Here, we use the notion of pixel difference to use Hamming code for embedding secret data. Two approaches are prosed n this thesis. The first approach deals with every two pixels each time. We first use 4 LSBs and 3 LSBs from 2 pixels, respectively, to form as a (7, 4) Hamming code, and then embed 3 secret bits into the (7, 4) Hamming code based on the condition that these two pixels have the minimum pixel difference. Therefore, we do not modify at most one bit in (7, 4) Hamming code like the traditional (7, 4) Hamming code based DH. In the second approach, using 2 pixels is extended to using m=1~7 pixels to design a general framework of PRDH. When using m=2, the general framework is reduce as the first approach, and using m=7, the general framework is the same as the traditional (7, 4) Hamming code. It is observed that the smaller m may have the higher embedding capacity, is degrades the PSNR of stego image. On the other hand, if the larger m is adopted, we have the less embedding capacity and the better PSNR of stego image. There is a trade-off between embedding capacity and PSNR for the general framework. Experimental and theoretical results demonstrate the effectiveness of these two approaches, and their respective advantages.

Chapter 1 Introduction 1
1.1 Background 1
1.2 Contribution of the Thesis 3
1.3 Organization of the Thesis 4
Chapter 2 Hamming Code 6
Chapter 3 The proposed scheme 8
3.1 Image transformation phase 9
3.2 Data hiding phase 13
3.3 Data extraction and image recovery phase 16
3.4 A general framework for PRDH 18
Chapter 4 Theoretical Investigation 25
4.1 Evaluation 25
4.2 Theoretical estimation 26
Chapter 5 Experimental Results 45
5.1 Visual examples 45
5.2 Embedding capacity and visual performance 47
Chapter 6 Conclusion and Future Work 50
References 53

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