Robust Light Field Watermarking by 4D Wavelet Transform

Abstract

Unlike common 2D images, the light field representation of a scene delivers spatial and angular description which is of paramount importance for 3D reconstruction. Despite the numerous methods proposed for 2D image watermarking, such methods do not address the angular information of the light field. Hence the exploitation of such methods may cause severe destruction of the angular information. In this paper, we propose a novel method for light field watermarking with extensive consideration of the spatial and angular information. Considering the 4D innate of the light field, the proposed method incorporates 4D wavelet for the purpose of watermarking and converts the heavily-correlated channels from RGB domain to YUV. The robustness of the proposed method has been evaluated against common image processing attacks.

An Improved Hybrid DCT-DWT Blind Watermarking Technique for Securing Multimedia Images

“…The 3D perception of the watermarked LF is very well preserved which provides appreciable robustness against Guassian noise, median filtering, JPEG compression, and JPEG 2000. It was discovered that utilizing too few or too many DCT coefficients as well as too small block dimensions lowers the performance [12] [33].…”

4D Dual-Tree Complex Wavelets for Time-Dependent Data

“…This is especially advantageous in higher dimensions where most of the computational load is on the first decomposition level. For example in 4D every subsequent level is only 1 16 𝑡ℎ of the size of the previous one.…”

“…The adjoint of the analysis operator is also known as the synthesis operator. Since the orthogonal wavelet systems used for levels 𝑗 2 use the same filters (just time-reversed) for the inverse, the adjoint is the inverse but scaled by 1 2 (instead of the normalization factor 1 4 in equations ( 8) and ( 9)): namely, it has the same normalization factor of decomposition operator. However, for the first level the dual filters 𝐻, 𝐿 also need to be replaced by the time-reversed decomposition filters 𝐻, 𝐿.…”

“…It is clear from figure 3 that dual-tree complex wavelets (left) produce a remarkably cleaner representation of the edges 1 For example, the asymptotic decay rate remains O ( 𝑁 −1 ) in 2D [20] and…”

“…While 4D real-valued wavelets have been considered in applications (e.g., [1,15]), to our knowledge a 4D complexvalued wavelet system has not been proposed before. In addition different extensions of wavelets using quaternions [6] (which are 4D in a different sense) and hypercomplex numbers [5] have been introduced but the actual implementations have so far been limited to 2D and 3D setting.…”