Recursive morphological operators for gray image processing. Application in granulometry analysis

Abstract

This paper presents a new algorithm for an efficient implementation of morphological operations for gray images. It defines a recursive morphological decomposition method of convex structuring elements by only causal two pixel structuring elements. Whatever the element size, erosion or/and dilation can then be performed during a unique raster-like image scan, involving a fixed reduced analysis neighborhood. The resulting process offers a low computational complexity, combined with an easiness for describing the element form. The algorithm is exemplified with granulometry. Quantum dots are segmented using a multiscale morphologic decomposition. Our new algorithm is particularly well suited for this type of morphological treatments, as they use structuring elements with both a large size and a form fitting the object to extract, that is to say depending on the application.