A relationship between quantization and watermarking rates in the presence of additive Gaussian attacks

A system which embeds watermarks in n-dimensional Gaussian data and distributes them in compressed form is studied. The watermarked/compressed data have to satisfy a distortion constraint, and the watermark has to be recoverable in a private scenario (in which the original data are available at the watermark detector). The performance of the system in the presence of additive Gaussian attacks is considered, and the region of achievable quantization and watermarking rate pairs (R/sub Q/,R/sub W/) is established. Moreover, two surprising facts are demonstrated: (1) at low R/sub Q/, the maximum achievable R/sub W/ is the same as when there are no attacks; and (2) at high (but finite) R/sub Q/, the maximum achievable R/sub W/ is the same as when there is no compression (R/sub Q/=/spl infin/). Finally, the performance of related schemes is also discussed.     

Directional processing of color images: theory and experimentalresults

The processing of color image data using directional information is studied. The class of vector directional filters (VDF), which was introduced by the authors in a previous work, is further considered. The analogy of VDF to the spherical median is shown, and their relation to the spatial median is examined. Moreover, their statistical and deterministic properties are studied, which demonstrate their appropriateness in image processing. VDF result in optimal estimates of the image vectors in the directional sense; this is very important in the case of color images, where the vectors' direction signifies the chromaticity of a given color. Issues regarding the practical implementation of VDF are also considered. In addition, efficient filtering schemes based on VDF are proposed, which include adaptive and/or double-window structures. Experimental and comparative results in image filtering show very good performance measures when the error is measured in the L*a*b* space. L*a*b* is known as a space where equal color differences result in equal distances, and therefore, it is very close to the human perception of colors. Moreover, an indication of the chromaticity error is obtained by measuring the error on the Maxwell triangle; the results demonstrate that VDF are very accurate chromaticity estimators.     

Generalized multichannel image-filtering structures

Recent works in multispectral image processing advocate the employment of vector approaches for this class of signals. Vector processing operators that involve the minimization of a suitable error criterion have been proposed and shown appropriate for this task. In this framework, two main classes of vector processing filters have been reported in the literature. Astola et al. (1990) introduce the well-known class of vector median filters (VMF), which are derived as maximum likelihood (ML) estimates from exponential distributions. Trahanias et al. (see ibid., vol.2, no.4, p.528-34, 1993 and vol.5, no.6, p.868-80, 1996) study the processing of color image data using directional information, considering the class of vector directional filters (VDF). We introduce a new filter structure, the directional-distance filters (DDF), which combine both VDF and VMF in a novel way. We show that DDF are robust signal estimators under various noise distributions, they have the property of chromaticity preservation and, finally, compare favorably to other multichannel image processing filters.