© 2000 Eastman Kodak Company Data Embedding Using Phase Dispersion Chris Honsinger and Majid Rabbani Imaging Science Division Eastman Kodak Company Rochester, NY USA Abstract A method of data embedding based on the convolution of message data with a random phase carrier is presented. The theory behind this method is reviewed and it is shown that the technique can be used to hide both pictorial and non-pictorial data. The details of the procedures used for carrier design, message template optimization, message extraction optimization, block synchronization, and rotation and scale correction are discussed. Finally, the algorithm’s benchmark results using Stirmark are presented. 1. Introduction An important aspect of our technique is that it can be used to embed either a grayscale iconic image or binary data. Examples of iconic images are trademarks, corporate logos or other arbitrary small images. Since the algorithm performance generally decreases as the message energy increases, it is preferable to use the edge maps of an icon as a message as shown in Figure 1a. When embedding binary data, the one and zero bits are represented by positive and negative delta functions that are placed in predefined and unique locations across the message image (referred to as the message template) as shown in Figure 1b. Common examples of binary data are the 32-bit representations of URL’s or copyright notices. Figure 1. Examples of iconic and binary message images The following notation is adopted throughout this paper. The original image is represented by the two dimensional array, I(x,y) the watermarked image (the image containing the embedded data) by I’(x,y), the message image by M(x,y), the carrier image by C(x,y), and the message template by T(x,y). With these definitions, the message embedding process is defined by the following equation: ) , ( )) , ( ) , ( ( ) , ( y x I y x C y x M y x I * α = ′ Eq. (1) where the symbol, * , represents cyclic convolution and α is an arbitrary constant chosen to make the embedded message simultaneously invisible and robust to common processing. From Eq. (1) it is clear (a) Example of a 128x128 binary iconic message (b) Example of a 64-bit binary message comprising of 1’s (white) and 0’s (black)