System and method for the generation of multiple angle correlation-based digital watermarks
Disclosed are systems and methods directed to the generation of digitally watermarked grayscale images having a watermark embedded at different arbitrary Rotation Angles. A single public key can be used to retrieve the otherwise invisible watermarks from the watermarked images when overlaid atop the images at Orientation Angles corresponding to the Rotation Angles.
1. A method creating digital watermarks in grayscale images, comprising:
receiving the first image to be watermarked;
determining the first watermark to be embedded in the first image;
embedding the first watermark into the first image by halftoning the first image using a three-dimensional threshold array having a phase shift value as an input and a first halftone structure defined by the spatial vectors V a1 (x a1 , y a1 ) and V b1 (x b1 , y b1 );
outputting a first watermarked grayscale image containing the first digital watermark embedded with the first halftone structure;
receiving the second image to be watermarked;
determining the second watermark to be embedded in the second image;
embedding the second watermark into the second image by halftoning the second image with a three-dimensional threshold array having a phase shift value as an input and a second halftone structure defined by the spatial vectors V a2 (x a2 , y a2 ) and V b2 (x b2 , y b2 ), wherein the interior angle between the two vectors V a1 (x a1 , y a1 ) and V b1 (x b1 , y b1 ) of the first halftone structure is equal to the interior angle between the two vectors V a2 (x a2 , y a2 ) and V b2 (x b2 , y b2 ) of the second halftone structure, the vector amplitude |V a1 (x a1 , y a1 )| of the first vector of the first halftone structure is equal to the vector amplitude |V a2 (x a2 , y a2 )| of the first vector of the second halftone structure, and the vector amplitude |V b1 (x b1 , y b1 )| of the second vector of the first halftone structure is equal to the vector amplitude |V b2 (x a2 , y b2 )| of the second vector of the second halftone structure; and
outputting a second watermarked grayscale image containing the second watermark embedded with the second halftone structure.
2. The method defined in claim 1 further comprising:
creating a public key by using the first halftone structure defined by the spatial vectors V a1 (x a1 , y a1 ) and V b1 (x b1 , y b1 ) for retrieving the digital watermark from the first and second image prints.
3. The method defined in claim 2 further comprising;
retrieving the first digital watermark from the first watermarked image using the public key without rotation.
4. The method defined in claim 3 further comprising;
retrieving the second digital watermark from the second image print using the public key oriented with respect to the second watermarked image with a Rotation Angle equal to the angle between the first vector V a1 (x a1 , y a1 ) of the first halftone structure and the first vector V a2 (x a2 , y a2 ) of the second halftone structure.
5. The method defined in claim 1 wherein the embedding steps further comprise conducting pixel-wise haltoning of the image to be watermarked using the three-dimensional threshold array
T ( x,y )=128−127·{cos [ k π( x·y a +y·x a )+ s ]+cos [ k π( x·y b +y·x b )+ s]}/ 2
where s is the phase shift in radians.
6. The method defined in claim 5 wherein s=g·π/N where g is the gray level of the watermark and N is the total number of gray levels contained in the watermark.
7. The method defined in claim 1 wherein the spatial vectors V a (x a , y a ) and V b (x b , y b ) do not have to be defined by integers.
8. The method defined in claim 1 wherein the spatial vectors represent a 45 degree 106 LPI (line-per-inch) cluster screen for a 600 DPI (dot-per-inch) printer.
9. A method of creating a plurality of grayscale images each having a retrievable invisible digital watermark comprising:
receiving the grayscale image to be watermarked;
determining the grayscale watermark to be embedded in the image; and
creating a plurality of digital watermarked grayscale images by embedding a digital watermark into the image by halftoning the image with different halftone structures each defined by the spatial vectors V a (x a , y a ) and V b (x b , y b ) having the same interior angle α, the same vector amplitudes |V a (x a , y a )| and |V a (x a , y a )|, and a different Rotation Angle, wherein the watermark can be retrieved from the plurality of images using a single public key.
10. The method defined in claim 9 wherein the step of creating a plurality of digital watermarked images includes embedding the digital watermark into the image by halftoning the image using a three-dimensional threshold array having a phase shift value as an input value.
11. The method defined in claim 9 further comprising:
creating the single public key defined by spatial vectors V a (x a , y a ) and V b (x b , y b ) having the interior angle α and the same vector amplitudes |V a (x a , y a )| and |V a (x a , y a )| as the halftone structures used for embedding the digital watermark into the image.
12. The method defined in claim 11 further comprising:
retrieving the digital watermark from each of the digital watermarked images using the single public key.
13. The method defined in claim 12 wherein the retrieving step further comprises:
orienting the single public key with respect to the watermarked images at different Orientation Angles for retrieving the watermark.
14. The method defined in claim 9 wherein the spatial vectors represent a 45 degree 106 LPI (line-per-inch) cluster screen for a 600 DPI (dot-per-inch) printer.
15. The method defined in claim 14 wherein the halftone structures are defined by the spatial vectors V a45 (5.657, 0) and V b45 (0, 5.657) for a Rotation Angle of 45 degrees, V a30 (1.464, 5.464) and V b30 (−5.464, 1.464) for a Rotation Angle of 30 degrees, V a15 (2.828, 4.899) and V b15 (−4.899, 2.828) for a Rotation Angle of 15 degrees, and V a0 (4, 4) and V b0 (−4, 4) for a Rotation Angle of 0 degrees.
16. A system for digital watermarking of an image, comprising:
an input image source;
image memory for storing the input image to be watermarked;
watermark memory for storing the watermark to be embedded in the image; and
an image processor including a three-dimensional threshold array where at least one input thereto is a phase shift value for embedding an invisible digital watermark into the image by halftoning the image with the three-dimensional threshold array using a plurality of halftone structures each defined by the spatial vectors V a (x a , y a ) and V b (x b , y b ) having the same interior angle α, the same vector amplitudes |V a (x a , y a )| and |V a (x a , y a )|, and a different Rotation Angle to produce a plurality of digitally watermarked output images.
17. A method for retrieving a watermark image from a plurality of digitally watermarked grayscale images, each formed by halftoning an image with a halftone structure having a different arbitrary Rotation Angle comprising:
overlaying a single public key transparency having halftone frequencies and angles matching the halftone structure used for forming the plurality of digital watermarked grayscale images atop each of the watermarked images and orienting the key with respect to the watermarked images at Orientation Angles matching the Rotation Angles used for embedding the watermark image into the corresponding digitally watermarked images to retrieve the watermark image.
18. The method defined in claim 17 wherein the public key transparency includes a checkerboard pattern.
19. The method defined in claim 18 wherein the watermark image was embedded into the digitally watermarked images a using a three-dimensional threshold array having phase shift value as an input.