Soft morphological filtering

Abstract

Stack filters are widely used nonlinear filters based on threshold decomposition and positive Boolean functions. They have shown to form a very large class of filters which includes rank-order operations as well as standard morphological operations. The stack filter representation of an order statistic filter provides an efficient tool for the theoretical analysis of the filter. Soft morphological filters form a large subclass of stack filters. They were introduced to improve the behavior of standard morphological filters in noisy conditions. In this paper, different properties of soft morphological filters are analysed and illustrated. Their connection to stack filters is established, and that connection is used in the statistical analysis of soft morphological filters. Soft morphological filters are less sensitive to additive noise than standard morphological filters. The deterministic properties of soft morphological filters are also analysed and it is shown that soft morphological filters form a class of filters with many desirable properties. For example, they preserve well details of images.