二合一秘密影像分享 (two-in-one secret image sharing; TiOSIS) 是植基於視覺密碼(Visual Cryptography Scheme; VCS)與多項式秘密影像分享(Polynomial-based Secret Image Sharing; PSIS)的秘密影像分享技術。視覺密碼(VCS)可以通過疊合子影像然後直接用進行視覺解碼，而基於多項式的秘密影像分享(PSIS)則可以通過多項式插值法無損地恢復秘密影像。結合上這兩個方案VCS與PSIS，TiOSIS有兩種的解碼選項。我們可以利用VCS做快速疊合簡單地支接解碼黑白秘密影像，同時子影像中的子像素 (註: 利用子像素的排列組合) 可以攜帶用於PSIS來回復無損失的灰階秘密影像。
一般而言，TiOSIS會有一張黑白的秘密影像用於VCS和一張灰階影像用於PSIS。TiOSIS的主要目的是共享灰階秘密影像，而VCS解碼的黑白秘密影像只是用來預覽、和驗證。事實上，只要能成功預覽可，我們並不需要非常清晰的VCS疊合結果。在本論文，我們提出了一種基於4方形點子像素的TiOSIS，4方形點子像素是一個2x2組成的四方形4個子像素圖案，我們使用三黑一白(3B1W)來代表黑，三白一黑(3W1B)來代表白，因為(3B1W)、與(3W1B)都各有4種不同的排列，所以我們可以用它們來代表用於PSIS的2(=⌊〖log〗_2^4 ⌋)個秘密影像位元。傳統的TiOSIS中是使用不同的黑白子向像素組合來隱藏秘密資訊，我們所提出的植基於4方形點子像素方法中，它可以攜帶的信息容量包括傳統方法的隱藏方式、還加上4方形點子像素的排列的2個位元。雖然基於4方形點子像素的TiOSIS有較大的子影像擴張，但平均下來的攜帶量是更大的更適合用於多媒體數據通訊。理論分析證明了我們的(k, n)-TiOSIS信息攜帶能力增加，實驗結果也呈現了我們機制的VCS預覽解碼的清晰度是在視覺可視的接受範圍。

A two-in-one secret image sharing (TiOSIS) is a hybrid using two SIS technologies: one is the visual cryptography scheme (VCS) and the other is polynomial-based secret image sharing scheme (PSIS). VCS can be used for visually decoding visual secret based on human visual system (HVS) by stacking shadow images. On the other hand, PSIS could recover lossless secret images via using polynomial interpolation. The TiOSIS based on VCS and PSIS has two decoding options. We could use the stacking-to-see property of VCS to easily and visually decode a black/white secret image, and meantime the subpixels in shadow images could carry information used for PSIS to reconstruct a lossless grayscale secret image.
Generally, TiOSIS will have a black/white secret image for VCS and a grayscale image for PSIS. The main purpose of TiOSIS is to share and recover a grayscale secret image, and the black/white secret image in VCS decoding is just for preview and authentication. Actually, we do not need very clear stacked result of VCS. We just need a visual quality of VCS for preview and authentication. In this thesis, we propose a 4 square-dot subpixel based TiOSIS, the 4-square dot pixel is a pattern composed of 2×2 pixels. We use three black and one white dots (3B1W) to represent “black” color, and three white and one black dots (3W1B) to represent “white” color. Since there are four different combinations of for (3B1W) and (3W1B), we can use 2(=⌊〖log〗_2^4 ⌋) to represent 2 secret bits used in PSIS. The conventional TiOSIS, uses different combinations of black and white sub-pixels to carry secret information. Our proposed TiOSIS carries the secret information like the conventional TiOSIS, and other 2 bits using 4-square dot pixel. Although the shadow size of our TiOSIS is expanded, the average carrying capacity is increased, on which it is more suitable for multimedia communication. Theoretical analyses the enhancement of carrying capacity for our TiOSIS, and experiments also demonstrate that the clarity of VCS decoding is enough for preview.

Chapter 1 Introduction 1
Chapter 2 Preliminary 5
2.1 VCS 5
2.2 PSIS 6
2.3 TiOSIS 6
Chapter 3 Motivation 11
Chapter 4 The Proposed TiOSIS Using 4 Square-Dot Subpixel 15
4.1 Infrastructure of Subpixel 15
4.2 Stacked Subpixels for the Conventional TiOSIS and the Proposed TiOSIS 18
4.3 Contrast and Security Conditions 20
4.4 Carrying Information in Shadow 21
Chapter 5 Construction of The Proposed TiOSIS 25
5.1 (2, n)-TiOSIS 25
5.2 (k, k)-TiOSIS 29
5.3 (3, n)-TiOSIS 32
Chapter 6 Monotonously Increasing Property in Contrast Condition for The Proposed (k, n)-TiOSIS 37
Chapter 7 Experiment and Comparison 43
7.1 Experimental Results 43
7.2 Discussion and Comparison 48
Chapter 8 Conclusions and Future Work 59
References 61

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