Nonlinear multivariate image filtering techniques

In this paper, nonlinear multivariate image filtering techniques are proposed to handle color images corrupted by noise. First, we briefly review the principle of reduced ordering (R-ordering) and then define three R-orderings by selecting different central locations. Considering noise attenuation, edge preservation, and detail retention, R-ordering based multivariate filters are designed by combining the R-ordering schemes. To implement color image filtering more effectively, we develop them into a locally adaptive version. The output of the adaptive filter is the closest sample to a central location that is a weighted linear combination of the mean, the marginal median, and the center sample. As a result, we study an adaptive hybrid multivariate (AHM) filter consisting of the mean filter, the marginal median filter, and the identity filter. The performance of the two adaptive filtering techniques is compared with that of some nonadaptive ones. The examples of color image filtering show that the adaptive multivariate image filtering gives a rather good performance improvement.