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.
Vector directional filters (VDF) for multichannel image processing are introduced and studied. These filters separate the processing of vector-valued signals into directional processing and magnitude processing. This provides a link between single-channel image processing where only magnitude processing is essentially performed, and multichannel image processing where both the direction and the magnitude of the image vectors play an important role in the resulting (processed) image. VDF find applications in satellite image data processing, color image processing, and multispectral biomedical image processing. Results are presented here for the case of color images, as an important example of multichannel image processing. It is shown that VDF can achieve very good filtering results for various noise source models.
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.
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