A novel watermarking for DIBR 3D images with geometric rectification based on feature points

Abstract

Depth-image-based rendering (DIBR) has become an important technology in 3D displaying with its great advantages. As a result, more and more 3D products copyright problems turn out. Since either the center view with depth image or the synthesized virtual views could be illegally distributed, we need to protect not only the center views but also the synthesized virtual views. In this paper, a robust watermarking method for DIBR 3D images is proposed. After applying three-level DWT to the center image, we utilize spread spectrum technology to embed the watermark into suitable coefficients of the sub-blocks of the center image, by this way we make our method robust to typical signal distortions, such as JPEG compression, noise addition and median filter. Meanwhile, in order to make the proposed method robust to some common geometric distortion attacks, SIFT-based feature points are used for geometric rectification to eliminate the effect caused by geometric distortion attacks. As the experimental results shown, the proposed method is much more robust to the common signal distortion attacks with lower BER (bit error rate) compared with existing methods. With geometric rectification, our method also performs good robustness to some simple affine transformations. In addition, the proposed watermarking method also has good robustness to the common operations of DIBR processing system.

Appendix

Algorithm 1: Watermark embedding

Find common parts in center image using formula (2): img[M][N]

$BS=64\begin{array}{cc}\hfill :\hfill & \hfill \begin{array}{ccc}\hfill size\hfill & \hfill of\hfill & \hfill sub- block\left(64\times 64\right)\hfill \end{array}\hfill \end{array}$

Watermark: w[⌊M/BS⌋][⌊N/BS⌋]

Hadamard matrix: p[128][128]

k = 1

for i = 1 to [⌊N/BS⌋]

for j = 1 to [⌊N/BS⌋]

if w[i][j] == 1

Watermark_seq[k] = 1

Watermark_seq[k] = − 1

end

end

end

Scramble Watermark_seq[⌊(M/BS)⌋ × ⌊(N/BS)⌋]

num = 1

for i = 1 to M

for j = 1 to N

block = block(i : i + N − 1, j : j + N − 1)

block = 3 − DWT(block)

Choose LH ₃ and HL ₃ as cof[128]

$ip=\frac{\left\langle cof,\kern0.2em p\left[num\right]\right\rangle }{\left\langle p\left[num\right],\kern0.2em p\left[num\right]\right\rangle }$

for k = 1 to 128

cof[k] = cof[k] + (Watermark_seq[num] + 6 × ip) × p[num][k]

end

Change LH ₃ and HL ₃ with cof[128]

block = 3 − IDWT(block)

j = j + BS

num = num + 1

end

i = i + BS

end

Algorithm 2: Watermark extraction

Watermark: watermark[3]

BS = 64

Hadamard matrix: p[128][128]

for situation[k] in formula (6)

Find common parts in watermarked image using formula (6): img[M][N]

bit_seq[⌊(M/BS)⌋ × ⌊(N/BS)⌋]

for i = 1 to M

for j = 1 to N

block = block(i : i + N − 1, j : j + N − 1)

block = 3 − DWT(block)

Choose LH ₃ and HL ₃ as cof[128]

$ip=\frac{\left\langle cof,\kern0.2em p\left[num\right]\right\rangle }{\left\langle p\left[num\right],\kern0.2em p\left[num\right]\right\rangle }$

if ip > 0

bit_seq[num] = 1

else

bit_seq[num] = − 1

end

j = j + BS

num = num + 1

end

i = i + BS

end

watermark[k]= bit_seq

end

Similarity: NC[3]

for situation[k] in formula (6)

Compute NC[k] between watermark[k] and Watermark_seq

end

Select the watermark with biggest NC between as the final extracted watermark