Digital watermarks on pictures are more useful when they are better able to survive image processing operations and when they cause less degradation of picture quality. Random geometric distortion is one of the most difficult kinds of image processing for watermarks to survive because of the difficulty of synchronizing the expected watermark patterns to the watermarks embedded in pictures. This paper proposes three methods to improve a previous method that is not affected by this difficulty but that is insufficient in maintaining picture quality and treating other problems in surviving image processing. The first method determines the watermark strength in L*u*v* space, where human-perceived degradation of picture quality can be measured in terms of Euclidian distance, but embeds and detects watermarks in YUV space, where the detection is more reliable. The second method, based on the knowledge of image quantization, uses the messiness of color planes to hide watermarks. The third method reduces detection noises by preprocessing the watermarked image with orientation-sensitive image filtering, which is especially effective in picture portions where pixel values change drastically. Subjective evaluations have shown that these methods improved the picture quality of the previous method by 0.5 point of the mean evaluation score at the representative example case. On the other hand, the watermark strength of the previous method could be increased by 30% through 60% while keeping the same picture quality. Robustness to image processing has been evaluated for random geometric distortion, JPEG compression, Gaussian noise addition, and median filtering and it was clarified that these methods reduced the detection error ratio to 1/10 through 1/4. These methods can be applied not only to the previous method but also to other types of pixel-domain watermarking such as the Patchwork watermarking method and, with modification, to frequency-domain watermarking.

Digital watermarks on pictures must have the ability to survive various image processing operations while not causing degradation of picture quality. Random geometric distortion is one of the most difficult kinds of image processing for a watermark to survive, and this problem has become a central issue in watermarking research. Previous methods for dealing with random geometric distortion have been based on searches, special watermark patterns, learning, or additional data such as original pictures. Their use, however, is accompanied by large computational overhead or by operational inconvenience. This paper therefore proposes a method based on embedding watermark patterns in two of the three color planes constituting a color picture so that these two planes have a specific covariance. The detection of the embedded information is based on the covariance between these two planes. Random geometric distortion distorts all the constituent color planes of a picture in the same way and thus does not affect the covariance between any two. The covariance-based detection is therefore immune to the distortion. The paper clarifies that detection error would occur whenever the inherent covariance (the covariance in the original picture) overrides the covariance made by watermarking. The two constituent planes having the minimum inherent covariance are therefore selected and their inherent covariance is reduced by shifting one of them and using a noise-reduction preprocess. Experimental evaluations using StirMark confirmed that 64 bits embedded in 256256-pixel pictures can be correctly detected without using searches, special patterns, learning, or additional data.