Image watermarking based on sequency and wavelet transforms

• US 7,742,619 B2
• Filed: 12/20/2006
• Issued: 06/22/2010
• Est. Priority Date: 12/21/2005
• Status: Active Grant

• Current Assignee: Texas Instruments, Inc.
• Original Assignee: Texas Instruments, Inc.
• Inventors: Kumar, Sanjeev, Jayaraman, Raghuram Karthik
• Primary Examiner(s): KIM, CHONG R
• Application Number:
  US11/613,261
• Publication Number:
  US 20070140524A1
• Time in Patent Office: 1,280 Days
• Field of Search: None
• US Class Current: 382/100
• CPC Class Codes: H04N 1/32154 Transform domain methods H04N1/32309 takes precedence
• CPC Class Codes: H04N 1/3217 using wavelet transforms
• CPC Class Codes: H04N 1/32187 with selective or adaptive application of the additional information, e.g. in selected frequency coefficients

Abstract

This invention is a new approach for the image watermarking in the wavelet transform domain based on sequency of the host and watermark image. For each sub-band a first transform level of the host image is thresholded and binarized. Sequencies of thresholded and binarized data host image are compared with sequencies of the discrete wavelet transformed watermark image to form a watermarking sequency mask. The watermarked wavelet domain data is formed by combining data elements of the discrete wavelet transformed host image with corresponding data elements of the wavelet transformed watermark image as filtered by the watermarking mask. A reverse process can extract the watermark with a high degree of accuracy even after attack upon the watermarked host image.

Claims

1. A method for embedding a binary watermark image into a gray scale host image comprising the steps of:

discrete wavelet transforming the host image;

discrete binary wavelet transforming the watermark image;

for each sub-band subb selected from the set of LL, LH, HL and HH of a first predetermined transform level of the host image and a second predetermined transform level to the watermark image

thresholding and binarizing data elements of the corresponding sub-band of the discrete wavelet transformed host image,

comparing sequencies of thresholded and binarized data elements of the discrete wavelet transformed host image with sequencies of the discrete wavelet transformed watermark image to form a watermarking sequency mask,

forming watermarked wavelet domain data by combining data elements of the corresponding sub-band of the discrete wavelet transformed host image with data elements of the corresponding sub-band of the wavelet transformed watermark image as filtered by the watermarking mask, and

inverse discrete transforming the watermarked wavelet domain data thereby forming a watermarked host image.

2. The method of claim 1, wherein:

said step of comparing sequencies generates a sequency key.

3. The method of claim 1, wherein:

said step of comparing sequencies to form a watermarking mask includes

calculating a binary host image sub-band sequency as follows;

$S_h=\left\{S_h<br><br>\left(i\right)\in <br><br>Z_i;<br><br>i=1,\mathrm{\dots <br><br>}<br><br><br><br>\frac{N}{8<br><br>}\right\},$

calculating a watermark image sub-band sequency as follows;

$S_w=\left\{S_w<br><br>\left(i\right)\in <br><br>Z_i;<br><br>i=1,\mathrm{\dots <br><br>}<br><br><br><br>\frac{N}{8<br><br>}\right\},$

forming said embedding mask ƒ

as follows;

$f_{\mathrm{subb}}=\left\{f<br><br>\left(1\right)=\left(j<br><br>\text{;<br><br>}<br><br><br><br>\min <br><br><br><br>S_h<br><br>\left(i\right)-S_w<br><br>\left(j\right)<br><br>\right\}\right\}$ $\forall <br><br>i<br><br><br><br>\mathrm{and}<br><br><br><br>j=1,\mathrm{\dots <br><br>}<br><br>,\frac{N}{8<br><br>}<br><br><br><br>\mathrm{where}<br><br><br><br>i,j\in <br><br>\left\{1,\mathrm{\dots <br><br>}<br><br>,\frac{N}{8<br><br>}\right\},$

where;

|X| is the Euclidian norm distance measure, and transforming the watermark image as follows;

ƒ

_subb;

W_subb(i,j)→

W_sub(ƒ

_subb(i),j)

where;

W_subb(i,j) is the watermark image; and

W_subb(ƒ

_subb(i),j) is the transformed watermark image after sequency mask transformation.

4. The method of claim 3, wherein:

said step of comparing sequencies to form a watermarking mask generates a mask key.

5. The method of claim 1, wherein:

said step of forming watermarked wavelet domain data includes

combining the host image and the watermarking mask as follows

Ĥ

_subb(i,j)=H_subb(i,j)+α

_subb*S(H_—

R_subb(i,j)*{tilde over (W)}_subb(ƒ

_subb(i),j)

where;

H_subb(i,j) is the discrete wavelet transformed host image for the sub-band subb;

α

_subb is a constant watermark strength for the respective sub-band given by;

α

_subb=[α

_LL3,α

_LH3,α

_HL3,α

_HH3]^T,

=[2,1,1,1]^T

with [x]^T the transpose of a column vector x;

S(H_—

R_subb(i,j)=(2*√

{square root over (K_subb*abs(H_—

R_subb(i,j)))}+G_subb(i,j),

which is a parabolic function of H_R_subb(i,j);

abs(x) is the absolute value of x;

G_subb(i,j)={2*√

{square root over (max(H_—

R_subb(i,j)*K_3sub)}+ε

}

which is a maximum weight factor of embedding with strength S which is function of H_R_subb(i,j);

H_R_subb(i,j) is the autocorrelation of the pixel(i,j) of the wavelet transformed host image sub-band H_subb;

abs (x) is absolute value of x;

ε

is a predetermined constant;

K₃ is given by;

K₃=[K_3(LL),K_3(LH),K_3(HL),K_3(HH)]^T=[20,10,10,10]^T.

6. The method of claim 5, wherein:

ε

is equal to 5.

7. The method of claim 1, further comprising:

pseudo randomizing rows of said discrete wavelet transformed watermark image before comparing said sequencies.

8. The method of claim 7, wherein:

said step of pseudo randomizing rows of said discrete wavelet transformed watermark image generates a pseudo randomization key.

9. The method of claim 1, further comprising:

extracting said watermark from a watermarked host image including

discrete wavelet transforming said watermarked image,

for each sub-band subb selected from the set including LL, LH, HL and HH of said first predetermined transform level of the watermarked host image

calculating a weight factor Ŝ

as follows;

Ŝ

(Ĥ

_—

R_subb(i,j)=(2*√

{square root over (K_subb*abs(Ĥ

_—

R_subb(i,j)))}+Ĝ

_subb(i,j),

where;

Ĝ

_subb(i,j)={2*√

{square root over (max(Ĥ

_—

R_subb(i,j)*K_sub)}+ε

};

Ĥ

_R_subb(i,j) is the autocorrelation of the pixel(i,j) of the wavelet transformed host image sub-band Ĥ

_subb; and

ε

is a predetermined constant,

determining individual pixels (i,j) of an extracted wavelet domain watermark image from M_subb(i,j), N_subb(i,j), R_subb(i,j) and D_subb as follows;

If ((D_subb>

0 AND M_subb<

D_subb>

N_subb) OR (D_subb<

0 AND R_subb<

D_subb>

N_subb)

Then Ŵ

_subb(ƒ

_subb(i),j)=1

Else Ŵ

_subb(ƒ

_subb(i),j)=0

where;

$\begin{array}{c}{T}_1=<br><br>0.75<br><br><br><br>\mathrm{and}\\ T_2=<br><br>1.25\\ M_{\mathrm{sub}}<br><br>\left(i,j\right)=<br><br>\left(T_1+0.75*\mathrm{\Delta <br><br>}<br><br><br><br>\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{sub}}<br><br>\left(i,j\right)\right)/2\\ N_{\mathrm{subb}}<br><br>\left(i,j\right)=<br><br>\left(5*T_2+0.75*\mathrm{\Delta <br><br>}<br><br>\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{subb}}<br><br>\left(i,j\right)\right)/2\\ R_{\mathrm{subb}}<br><br>\left(i,j\right)=<br><br>\left(T_1-0.75*\mathrm{\Delta <br><br>}<br><br>\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{subb}}<br><br>\left(i,j\right)\right)/2;<br><br>\mathrm{and}\end{array}$ $D_{\mathrm{subb}}=\frac{\mathrm{abs}<br><br>\left(\hat{H}<br><br>\mathrm{\_subb}<br><br>\left(i,j\right)-\mathrm{H\_subb}<br><br>\left(i,j\right)\right)}{{\mathrm{\alpha <br><br>}}_{\mathrm{subb}}*\hat{S}(\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{subb}}<br><br>\left(i,j\right)},\mathrm{and}$

 

inverse discrete binary wavelet transforming the extracted wavelet domain watermark image thereby forming an extracted watermark image.

10. The method of claim 9, further comprising:

modeling the effect of attacks on the watermarked host image and deciding threshold values in the extraction as follows;

Δ

Ĥ

_—

R_subb(i,j)=Ĥ

_—

R_subb(i,j)*H_—

R_subb(i,j)

where;

H_R_subb(i,j) is the autocorrelation of the pixel(i,j) of the wavelet transformed host image sub-band H_subb.

11. The method of claim 9, wherein:

ε

is equal to 5.

12. The method of claim 9, further comprising:

pseudo randomizing rows of said discrete wavelet transformed watermark image before comparing said sequencies and generating a pseudo randomization key; and

said step of extracting said watermark from a watermarked host image includes reverse pseudo randomizing rows of the extracted wavelet domain watermark image using said pseudo randomization key before inverse discrete wavelet transforming the extracted wavelet domain watermark image.

13. The method of extracting a watermark from a watermarked host image comprising the steps of:

discrete wavelet transforming said watermarked image,

for each sub-band subb selected from the set including LL, LH, HL and HH of said first predetermined transform level of the watermarked host image

calculating a weight factor Ŝ

as follows;

Ŝ

(Ĥ

_—

R_subb(i,j)=(2*√

{square root over (K_subb*abs(Ĥ

_—

R_subb(i,j)))}+Ĝ

_subb(i,j),

where;

Ĝ

_subb(i,j)={2*√

{square root over (max(Ĥ

_—

R_subb(i,j)*K_sub)}+ε

};

Ĥ

_R_subb(i,j) is the autocorrelation of the pixel(i,j) of the wavelet transformed host image sub-band Ĥ

_subb;

and ε

is a predetermined constant,

determining individual pixels (i,j) of an extracted wavelet domain watermark image from M_subb(i,j), N_sub(i,j), R_sub(i,j) and D_subb as follows;

If ((D_subb>

0 AND M_subb<

D_subb>

N_subb) OR (D_subb<

0 AND R_subb<

D_subb>

N_subb)

Then Ŵ

_subb(ƒ

_subb(i),j)=1

Else Ŵ

_subb(ƒ

_subb(i),j)=0

where;

$\begin{array}{c}{T}_1=<br><br>0.75<br><br><br><br>\mathrm{and}\\ T_2=<br><br>1.25\\ M_{\mathrm{sub}}<br><br>\left(i,j\right)=<br><br>\left(T_1+0.75*\mathrm{\Delta <br><br>}<br><br><br><br>\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{sub}}<br><br>\left(i,j\right)\right)/2\\ N_{\mathrm{subb}}<br><br>\left(i,j\right)=<br><br>\left(5*T_2+0.75*\mathrm{\Delta <br><br>}<br><br>\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{subb}}<br><br>\left(i,j\right)\right)/2\\ R_{\mathrm{subb}}<br><br>\left(i,j\right)=<br><br>\left(T_1-0.75*\mathrm{\Delta <br><br>}<br><br>\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{subb}}<br><br>\left(i,j\right)\right)/2;<br><br>\mathrm{and}\end{array}$ $D_{\mathrm{subb}}=\frac{\mathrm{abs}<br><br>\left(\hat{H}<br><br>\mathrm{\_subb}<br><br>\left(i,j\right)-\mathrm{H\_subb}<br><br>\left(i,j\right)\right)}{{\mathrm{\alpha <br><br>}}_{\mathrm{subb}}*\hat{S}(\hat{H}<br><br>{\mathrm{\_R}}_{\mathrm{subb}}<br><br>\left(i,j\right)},\mathrm{and}$

 

inverse discrete binary wavelet transforming the extracted wavelet domain watermark image thereby forming an extracted watermark image.

14. The method of claim 13, further comprising:

modeling the effect of attacks on the watermarked host image and deciding threshold values in the extraction as follows;

Δ

Ĥ

_—

R_subb(i,j)=Ĥ

_—

R_subb(i,j)*H_—

R_subb(i,j)

where;

H_R_subb(i,j) is the autocorrelation of the pixel(i,j) of the wavelet transformed host image sub-band H_subb.

15. The method of claim 13, wherein:

ε

is equal to 5.

16. The method of claim 13, further comprising:

reverse pseudo randomizing rows of the extracted wavelet domain watermark image using a pseudo randomization key before inverse discrete binary wavelet transforming the extracted wavelet domain watermark image.