Median and robust polynomial filters for multivariate image data

This paper addresses the problems of image enhancement and restoration in the case of multivariate image data. Multivariate generalizations of median filtering are studied. The robustness properties of two such techniques are investigated using the influence function approach. Robust polynomial filters are introduced for applications where the original image has to be restored with high fidelity. Filtering examples are given using multivariate noise processes with equal component variances, unequal component variances, correlated noise components, and in the presence of outliers. Both simulated data and multivariate data from a range imaging sensor are used