Reversible watermarking Wu Dan

Introduction What?

Introduction Why? Military data Medical data How? Data compression

Difference expansion Histogram bin shifting

Reversible Data Embedding using a Difference Expansion Jun Tian IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL.13 NO.8 AUGUST 2003

How to measure a reversible data embedding algorithm? Payload capacity (bpp) Visual quality (PSNR) Complexity

A simple example of the difference expansion x=206, y=201; b=1. l: the integer average h: difference DE: difference expansion The new values:

Reversible data embedding Reversible integer transform The inverse transform: To prevent the overflow and underflow :

Expandable and changeable difference values Expandable: (for both b=1,0) Changeable: (for both b=0,1)

By definition, we can find that: If h is changeable, h ’ is still changeable. If h is expandable, h is changeable. After the DE, the expanded difference value h ’ is changeable. if h=0 or -1, the conditions on expandable and changeable are equivalent.

Data embedding algorithm : 1. The original image is grouped into pairs of pixels values. Then compute the difference values h. 2. Create four disjoint sets of difference values: EZ, EN, CN, and NC EZ: contains all expandable h=0 and expandable h=-1. EN: contains all expandable h EZ

CN: contains all changeable NC: contains all non-changeable h. 3. Create a location map of selected expandable difference values.

4. Collect original LSBs of difference values in EN2 and CN. However for those h=1 or h=-2 in EN2 and CN, their LSBs will be not collected. 5. The location map will be losslessly compressed. The compressed bit stream is denoted as L. Embed L, the original LSBs C, and a payload P. 6. Apply the inverse integer transform to obtain the embedded image.

Discussions: Capacity: Threshold:

The scanning order: Non-changeable: Scanning order :

Non-changeable:

decoding : 1. Calculate the difference values h. 2. Create two disjoint sets of difference values: CH and NC changeable and non-changeable 3. Collect LSBs of all difference values in CH, and form a binary bit stream B. 4. Decode the location map from B, and restore the original values of differences as follows:

Experimental results:

Alattar Jun Tian Chin-chen Chang Dinu Coltuc

Reversible data hiding Zhicheng Ni, Yun-Qing,Nirwan Ansari, and Wei Su IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, March 2006

Algorithm Zero point and peak point

Embedding: Generate the histogram H(x). In the histogram, find the zero point H(a) and peak point H(b). If H(b)>0,record the coordinate of those pixels. Assume a<b. Scan the image. If x ∈ (a,b),x+1; leaving the value a+1 empty. If w=0, a=a; if w=1,a=a+1.

Pure payload: C=H(a) - H(b) Multiple pairs of Maximum and minimum points:

Extraction algorithm: ( Assume the zero point and peak points are a,b ) Scan the image in the same order as in the embedding procedure. If the value is a+1,w=1; if the value is a, w=0. Scan the image again, if the grayscale value x ∈ (a,b], x-1. If the overhead information found in the extracted data, set the pixel grayscale value as b.

Lower bound of the PSNR of a Marked image The total embedding time is just 100ms.

Experimental results

Discussion: 1) How to get the peak point and zero point for verifier? 2) How to use the a and a+1?

Reversible watermark using the difference expansion of a generalized integer transform Adnan M.Alattar, Member, IEEE, IEEE TRANSACTIONS ON IMAGE PROCESSING, AUGUST 2004

Generalized difference expansion Vector: Reversible integer transform:

return

A difference expansion oriented data hiding scheme for restoring the original host images Chin-Chen Chang, Tzu-Chuen Lu The Journal of systems and software, May 2006

return

Very Fat Watermarking by Reversible Contrast Mapping Dinu Coltuc and Jean-Marc Chassery IEE SIGNAL PROCESSING LETTERS, APRIL 2007

Reversible contrast mapping:

Dc: the domain without the odd pixels pairs. Embedding: 1 partition the entire image into pairs. 2 for each pair: a) if (x,y) is even pixel pair, set the LSB x ’ to 1, the LSB of y ’ is the watermark. b) if (x,y) ∈ Dc, set the LSB of x to 0, and the LSB of y is the watermark. c) if (x,y) Dc, set the LSB of x to 0, and save the ture value. return