Morphological bandpass decomposition of images

Abstract

The concept of a morphological size distribution is well known. It can be envisioned as a sequence of progressively more highly smoothed images which is a nonlinear analogue of scale space. Whereas the differences between Gaussian lowpass filtered images in scale space form a sequence of approximately Laplacian bandpass filtered images, the difference image sequence from a morphological size distribution is not bandpass in any usual sense for most images. This paper presents a proof that a strictly size band limited sequence can be created along one dimension in an n dimensional image. This result is used to show how an image time sequence can be decomposed into a set of sequences each of which contains only events of a specific limited duration. It is shown that this decomposition can be used for noise reduction. This paper also presents two algorithms which create from morphological size distributions, (pseudo) size bandpass decompositions in more than one dimension. One algorithm uses Vincent grayscale reconstruction on the size distribution. The other reconstructs the difference image sequence.