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Hiding depth information in compressed 2D image/video using reversible watermarking

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Abstract

In this paper, a novel joint coding scheme is proposed for 3D media content including stereo images and multiview-plus-depth (MVD) video for the purpose of depth information hiding. The depth information is an image or image channel which reveals the distance of scene objects’ surfaces from a viewpoint. With the concern of copyright protection, access control and coding efficiency for 3D content, we propose to hide the depth information into the texture image/video by a reversible watermarking algorithm called Quantized DCT Expansion (QDCTE). Considering the crucial importance of depth information for depth-image-based rendering (DIBR), full resolution depth image/video is compressed and embedded into the texture image/video, and it can be extracted without extra quality degradation other than compression itself. The reversibility of the proposed algorithm guarantees that texture image/video quality will not suffer from the watermarking process even if high payload (i.e. depth information) is embedded into the cover image/video. In order to control the size increase of watermarked image/video, the embedding function is carefully selected and the entropy coding process is also customized according to watermarking strength. Huffman and content-adaptive variable-length coding (CAVLC), which are respectively used for JPEG image and H.264 video entropy encoding, are analyzed and customized. After depth information embedding, we propose a new method to update the entropy codeword table with high efficiency and low computational complexity according to watermark embedding strength. By using our proposed coding scheme, the depth information can be hidden into the compressed texture image/video with little bitstream size overhead while the quality degradation of original cover image/video from watermarking can be completely removed at the receiver side.

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Correspondence to Jiying Zhao.

Appendices

Appendix A: Derivation of Laplacian PDF in discrete domain

Given the continuous Laplacian PDF as shown in (2), the discrete Laplacian PDF is derived as follows.

$$\begin{array}{@{}rcl@{}} P(Y=k)&=&\frac{p(k)}{\sum\limits_{j=-\infty}^{+\infty}p(j)}=\frac{\exp(-|k|/\sigma)}{\sum\limits_{j=-\infty}^{+\infty}\exp(-|j|/\sigma)}\\ &=&\frac{m^{|k|}}{\sum\limits_{j=-\infty}^{+\infty}m^{|j|}}=\frac{m^{|k|}}{1+2\sum\limits_{j=1}^{+\infty}m^{j}}\\ &=&\frac{m^{|k|}}{1+2\frac{m}{1-m}}=\frac{1-m}{1+m}m^{|k|},\quad k,j\in Z\\ \end{array} $$

where k is the discrete coefficient value, p is the Laplacian PDF in continuous domain, \(m=\exp (-\frac {1}{\sigma })\).

Appendix B: Entropy calculation for original and watermarked QDCT coefficients

Before watermarking, original QDCT coefficients obey the discrete Laplacian distribution as shown in (3). The entropy of these coefficients can be calculated as follows.

$$\begin{array}{@{}rcl@{}} H(Y_{o})&=& E(-\log_{2}P(Y=k))\\ &=& \sum\limits_{k=-\infty}^{+\infty}-(\frac{1-m}{1+m}m^{|k|})(\log_{2}\frac{1-m}{1+m}+|k|\log_{2}m)\\ &=& (\log_{2}\frac{1-m}{1+m})(-\frac{1-m}{1+m})\sum\limits_{k=-\infty}^{+\infty}m^{|k|}+ \\ & &(2\log_{2}m)(-\frac{1-m}{1+m})\sum\limits_{k=1}^{+\infty}km^{k}\\ &=& -\log_{2}\frac{1-m}{1+m}-2\log_{2}m(\frac{1-m}{1+m})\frac{m}{(1-m)^{2}}\\ &=& -\log_{2}\frac{1-m}{1+m}-\frac{2m\cdot \log_{2}m}{1-m^{2}} \end{array} $$

where k is the discrete coefficient value before watermarking, \(m=\exp (-\frac {1}{\sigma })\).

After watermarking, the original PDF are stretched. And the even values and odd values still obey discrete Laplacian distribution respectively. If we denote

$$\begin{array}{@{}rcl@{}} P^{1} &=& P(Y=2k+sgn(k)) = \frac{1}{2}\frac{1-m}{1+m}m^{|k|}, ~ k \in Z\\ P^{2} &=& P(Y=2k) = \frac{1}{2}\frac{1-m}{1+m}m^{|k|}, ~ k \in Z \end{array} $$

where k is the discrete coefficient value before watermarking, s g n(x) = x/|x| is the sign function, \(m=\exp (-\frac {1}{\sigma })\).

The entropy of the watermarked QDCT coefficients is calculated as follows.

$$\begin{array}{@{}rcl@{}} H(Y_{w})&=& E(-\log_{2}P^{1})+E(-\log_{2}P^{2})\\ &=& 2\sum\limits_{k=-\infty}^{+\infty}-\frac{1}{2}(\frac{1-m}{1+m}m^{|k|})(-1+\log_{2}\frac{1-m}{1+m}+|k|\log_{2}m)\\ &=& \sum\limits_{k=-\infty}^{+\infty}\frac{1-m}{1+m}m^{|k|}+ \\ & & \sum\limits_{k=-\infty}^{+\infty}-(\frac{1-m}{1+m}m^{|k|})(\log_{2}\frac{1-m}{1+m}+|k|\log_{2}m)\\ &=& 1+H(Y_{o}) \end{array} $$

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Wang, W., Zhao, J. Hiding depth information in compressed 2D image/video using reversible watermarking. Multimed Tools Appl 75, 4285–4303 (2016). https://doi.org/10.1007/s11042-015-2475-y

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