Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two Dimensions

Abstract This paper proposes a way of better approximating continuous, two-dimensional morphology in the discrete domain, by allowing for irregularly sampled input and output signals. We generalize previous work to allow for a greater variety of structuring elements, both flat and non-flat. Experimentally we show improved results over regular, discrete morphology with respect to the approximation of continuous morphology. It is also worth noting that the number of output samples can often be reduced without sacrificing the quality of the approximation, since the morphological operators usually generate output signals with many plateaus, which, intuitively do not need a large number of samples to be correctly represented. Finally, the paper presents some results showing adaptive morphology on irregularly sampled signals.