<title>A variety of multichannel sigma filters</title>

Abstract

The smoothing function of widely used vector filters such as vector median (VMF), basic vector directional filter (BVDF) and directional distance filter (DDF) is designed to perform the fixed amount of smoothing. It may become the undesired property, because in some image areas these filters introduce too much smoothing and blur thin details and image edges. In general, the common problem is how to preserve some desired signal features while the noise elements are removed. An optimal situation would arise if the filter could be designed so that the desired features were invariant to the filtering operation and only noise would be affected. In case of the impulsive noise corruption, the problem is stated often as searching for the switching function that allows to reduce the filter effect only to noisy samples. In this paper, a new nonlinear filtering scheme for the removal of impulsive noise in multichannel digital images is presented. A new class of multichannel sigma filters is based on the combination of the standard sigma-filter concept provided by Lee and the robust order-statistics theory. With respect to a variety of the measures (e.g. vector distance expressed through Minkowski metric, angular distance or their combination) for quantification of the distance between multichannel samples, we provide a rich class of adaptive vector sigma filters taking advantages of the threshold structure with the approximation of the standard deviation and also the fully adaptive filter structure. Thus, by adaptive switching between the smoothing function and the identity operation, the behavior of the proposed method is attractive for filtering of image environments degraded by impulsive noise, bit errors and outliers. The new filtering scheme is computationally efficient and able to achieve excellent balance between the image detail preservation and the noise suppression. The achieved results show that the new filtering class has excellent preservation capabilities and provides significant improvement in comparison with well-known vector filters such as VMF, BVDF and DDF in terms of all commonly used quality measures.