Morphological operations on 3D and 4D images: From shape primitive detection to skeletonization

Abstract

This paper describes a practical approach to mathematical morphology and ways to implement its operations. The first chapters treat a formalism thathas the potential of implementing morphological operations on binary images of arbitrary dimensions. The formalism is based on sets of structuring elements for hit-or-miss transforms whereas each structuring element actually describes a shape primitive. The formalism is applied to two and three dimensional binary images and the paper includes structuring elements for topology preserving thinning or skeletonization and various skeleton variants. The generation of shape primitive detecting masks is treated as well as their application in segmentation, accurate measurement and conditions for topology preserving. The formalism is expanded to four-dimensional images and elaborates on the extension of 3D skeletonization to 4D skeletonization. A short excursion was made to methods based on 3D and 4D Euler - cluster count methods. © Springer-Verlag Berlin Heidelberg 2000.