A High Performance Multi-layer Reversible Data Hiding Scheme Using Two-Step Embedding Authors: Jinxiang Wang Jiangqun Ni Jinwei Pan

Outline Histogram Shifting on Pixel Differences  HS for single layer embedding  HS for multi-layer embedding Two-Step Embedding Framework (TSE) Improvement for Reduction the Location Map  Traditional location map generation  The improvement scheme for reduction location map size Embedding Process Extraction Process Experimental Results

Histogram shifting algorithm Traditional histogram shifting algorithm (HS) Traditional histogram shifting algorithm is based on the pixel values, which utilizes the redundancy of the host image statistical information to hide secret data, the sketch map is shown as follows. Grayscale value Frequency Peak point Lowest point non-zero point situation Zero point Grayscale value Frequency Grayscale value Frequency Peak point zero point situation Frequency Zero point Peak point w Embedding

Note: 1) The extraction is performed in the reverse order as the embedding process. 2) The side information (peak/zero points) should be additionally transmitted to the receiver for reversible recovery.——No blind 3) The histogram shifting is extended to the pixel differences or predictive errors to improve the performance

Histogram shifting on the pixel differences d Frequency Histogram shifting d’d’ Pixel differences calculation ‘d’ Generate the histogram of pixel differences Generate the marked pixel differences ‘d’’ Generate the marked pixel values ‘y’ Note: 1)P and Z should be additional transmitted to the receiver. 2)The process represents the single layer embedding

Multi-layer embedding When the size of secret data is large, the generated stego-image (stego-differences) is repeatedly considered as a new cover image (cover differences) to perform a new round histogram shifting to hide more message. The multi-layer embedding is described as follows. Stego- image Pixel differences Original image 1 th layer …… m th layer Marked pixel differences P1,Z1P1,Z1 Pm,ZmPm,Zm Note: the side information {P i,Z i | 1≤i ≤m} should be additional transmitted

Two-Step Embedding Framework Purpose : 1) To solve the issue of needing to transmit the side information additionally. —— No blind 2) To ensure the optimal peak/zero points selection among HS to improve the performance. TSE for single layer embedding A1 optimal selection histogram peak / zero points first LSB replacement Replaced LSBs Stego Image pixel differences Original image second Stego A2 Stego

TSE for multi-layer embedding Note: 1) TSE is employed in the final layer embedding; 2) The LSB substitution is performed on the stego-pixels. m th layer (TSE) A1 A2 Stego- image Pixel differences Original image 1 th layer …… (m-1) th layer Framework of two-step embedding for multi-layer embedding

The characteristic of TSE: 1) TSE is an improved LSB based scheme, which hides the side information in the LSBs of the chosen stego-pixels in A1 to achieve the blind requirement. 2) Without consuming some intact fixed area to hide side information in the traditional schemes, our scheme utilizes the LSB in the stego-pixels. 3) The flexible optimal peak/zero point ensures the better performance.

Improvement for Reduction the size of Location Map Location map: Due to the modification on the pixel differences to hide secret data, the marked differences may be not in the normal range [0, 255] for a 8-bit grayscale image. Thus the location map is needed to record the special overflow/underflowed pixels and embedded in the cover image together with the secret message. The location map can be recovered by the receiver to lossless restore the original image.

Traditional method for the location map generation Each layer HS embedding leads to at most 1 unit distortion between marked difference d i ’ and original difference d i. Thus, the difference between the stego-pixel and original pixel via m - layer embedding is The potentially overflowed/underflowed pixels (POPs) is in the range and should be specially handled as follows.

: POPs Cover image 1) Locate all the POPs in the interval 2) Use histogram narrowing technique (HN) to narrow the POPs to the middle grayscale value and generate a new narrowed cover image I’ 3) After m-layer embedding on the narrowed image I’, no overflow/underfow occurs. 4) Generate a same sized location map with ‘1’ and ‘0’ to indicate the narrowed pixels and non-narrowed pixels. 5) Compress the location map and hide the compressed version in the cover image.

General idea: we exchange the histogram narrowing technique into the final layer embedding process and only indicate the actually overflowed/underflowed pixels (AOPs), which is a subset of the POPs. Thus the improved location map with less ‘1’ in it will be easier to be compressed. The detailed TSE for the reduction of the location map is described as follows. Improvement for Reduction the size of Location Map

R_POPs in A2 w={w(1), w(2), w(3)} w(1) w(2) LM + SI POPs R_POPs in A1 A1 HS embedding LSB replacement HS embedding LM LSBs AOPs : POPs A1 A2 Cover image Pixel differences HS embedding A1 A2 w(3)+LSBs The sketch map of TSE for location map reduction

Embedding Process 1) Calculate the pixel differences 2) Determine the embedding layer ‘m’ 3) Identify the POPs in cover image with gray value in the range 4) Perform the front (m-1)-layer embedding 5) Implement the TSE in the final layer embedding. Note: Among the process, the compressed location map and side information for each layer are together hidden in the image in step 5. Moreover, the histogram narrowing technique is utilized in the same step.

Extraction Process 1) Divide the stego-image into A1 and A2 as did in embedding side, and collect the side information from the LSBs of the marked pixels in A1. 2) Decompress and generate the location map to indicate the actually overflowed/underflowed pixels (AOPs). Perform the inverse HN operation on the AOPs. 3) Perform the m-layer extraction operation in the inverse order and recover the original cover image.

The TSE framework extended to other prediction errors One prediction model: (a) (b) The multilayer embedding is iteratively performed between the ‘cross’ set and ‘round’ set. And the successive prediction utilizes the generated stego- pixels in opposite set. The (i+1) th layer embedding process is illustrated.

Experimental Results The Efficiency for Location Map Reduction between the traditional method and our improved scheme Where LM t and LM i denote the size of traditional and improved location map, respectively.

Cover image (512×512) chosen schemes Lena Traditional location map [18]20 Improved location map20 Overflow/UnderflowNNNNN E_Map-- Peppers Traditional location map [18] Improved location map Overflow/UnderflowYYYYY E_Map0%9.1%19.4%63.6%108.6% Baboon Traditional location map [18] Improved location map Overflow/UnderflowYYYYY E_Map600%633.3%785.7%755.6%935.3% F16 Traditional location map [18]20 Improved location map20 Overflow/UnderflowNNNNN E_Map-- Goldhill Traditional location map [18]20 Improved location map20 Overflow/UnderflowNNNNN E_Map-- Boat Traditional location map [18] Improved location map Overflow/UnderflowYYYYY E_Map11.1%50%73.9%112.9%282.1%

Comparison Between the TSE in Pixel Differences, in Predictive Errors and Other Schemes TSE_PD_TM: TSE + Pixel differences + traditional location map TSE_PD_IM: TSE + Pixel differences + improved location map TSE_PE_IM: TSE + prediction errors + improved location map [18] Tai W. L., Yeh C. M., Chang C. C.: Reversible Data Hiding Based on Histogram Modification of Pixel Differences. IEEE Trans. Circuits Syst. Video Technol., vol. 19, no. 6, pp (2009) [19] Luo L., Chen Z., Chen M., Zeng X., Xiong Z.: Reversible Image Watermarking Using Interpolation Technique. IEEE Trans. Inf. Forensics Security, vol. 5, no. 1, pp.187–193 (2010) [13] Hwang J., Kim J., Choi J.: A Reversible Watermarking Based on Histogram Shifting. In: Proc. International Workshop on Digital Watermarking. pp Jeju Island, Korea (2006)

Conclusion 1) The proposed scheme exploits TSE to solve the problem of communicating side information. The TSE framework also ensures the adoption of optimal peak and zero point pair in each layer for high performance reversible data hiding. 2) An improved location map, which indicates only the actual overflow/underflow pixels, is constructed to facilitate the compression of location map and further increase the embedding capacity.

Thank you!