An algebraic approach for morphological operations on 2D and 3D images

摘要

This paper describes an algebraic approach to morphological operations on 2D and 3D images. For 2D images, a matching algorithm based on mathematical morphology is given. For 3D images represented by voxels, algorithms are developed for the shape decomposition and thinning. The possible advantages of the algebraic approach are indicated by showing that a considerable speedup takes place (for large-sized templates) if the Fast Fourier Transform (FFT) is used to compute the convolutions.