Computer Science

Digital printers use digital halftoning, a technique that relies on only a handful of colors to create images that appear to have many colors. This process operates on pixels in color spaces, such as grayscale or red-green-blue (RGB). IBM Research has developed a flexible image embedding algorithm by generalizing digital halftoning to operate on Cartesian products of image color spaces. More specifically, the embedding algorithm embeds m images into n images by considering the n+m images as a single extended image whose pixels lay in the Cartesian product of n+m color spaces. This extended image is halftoned using pixels that satisfy constraints relating the pixels between the two groups of images. These constraints are imposed by the extraction algorithm that recovers the m images from the n images. The output of the embedding algorithm will be n images in the corresponding portion of the halftoned extended image. The constraints and thus the extraction algorithm are chosen according to the application. We show three applications where this algorithm can be applied. First, consider a case where a scrambled version of the image is embedded into the same image. This image is subsequently tampered with, as shown in Fig. 1a. The embedded image can be used to detect and localize the tampering. Furthermore, the embedded image can be used to reverse the tampering and recover the original image, as shown in Fig. 1b.

Figure 1: A watermarked image that has been changed
(b) The change is detected and the original image is recovered.

In another application, a watermark image is embedded into two halftone images. The extraction of the embedded watermark is accomplished by superimposing or combining these two watermarked images. This is useful in cases where the watermark extraction mechanism is computationally simple. As shown in Fig. 2, performing the XOR operation pixel by pixel on each of the color planes on the top two halftone images results in the bottom third image, which is the watermark image. Another operation that can be used for extracting the watermark is the OR operation which corresponds to simply overlaying the two images. One advantage over previous watermarking algorithms of this type is that the extracted watermark image can be of high complexity and fidelity.

Figure 2: Performing the XOR operation on each of the color channels on the top two images results in the bottom watermark image.

In the third application, we exploit the fact that a pixel on a twisted-nematic (TN) mode Liquid-Crystal Display (LCD) (commonly used in laptops, PDAs and digital cameras) incurs a large change in color and luminance when the viewing angle is changed. This allows us to create images which look different when viewed at different angles relative to the display. An example of this is shown in Fig. 3a and 3b, where the same image appears completely different on a TN mode LCD display when viewed at different angles. When the two embedded images are the same, this technique can be used to enhance the viewing angle characteristics of TN mode LCD displays.