Adaptive stack-filters towards a design methodology for morphological filters

Interest in non-linear signal/image-processing techniques has been growing. The lack of design tools in this area, however, has severely hindered development. In addition, nonlinear techniques such a stack-filtering, morphology, and order-statistic filters have been seen a separate disconnected methods, rather than as a unified class of filters. Morphological operators have found a range of applications, giving excellent results in areas such a noise reduction. Their design methods however, leave a great deal to be desired. Stack-filters, on the other hand appear to be more suitable for mathematical analysis and offer fast implementation via the threshold decomposition property. Stack-filters and morphological-filters have been shown to be subsets of each other. The present authors attempt to determine a set of stack-filters which are able to emulate morphological filters their noise-suppression and retain structural preservation properties. Hence they take the first step towards a design methodology for morphological filters. The methods developed are demonstrated on two application areas; 1-D ECG signals and ultrasound images