Vector Ordering Algorithms for Morphological Multi-Valued Operators Using Improved F-score Technique and Numeral Systems

Mathematical morphology (MM) is an effective tool for modeling the spatial information and characterizes objects present in a satellite image. Morphological operators were initially defined for mono-band images (panchromatic images) where each pixel image is a scalar value. A simple solution to extend scalar morphological tools to multi-band images, in which the pixel is represented by a vector, is to apply separately the scalar morphological operator to each image band. However, this approach has two disadvantages: it neglects a correlation between image bands and creates new pixel vectors that do not exist in the original image. Several works have been proposed to extend the scalar morphological tools to multi-band images. The common point of these studies is the necessity to use an efficient vector ordering algorithm in the morphological transformation to apply morphological operators on all image bands simultaneously. This paper proposes two new vector ordering algorithms to extend the classical mono-band morphological tools to multi-band images. The first one is based on the Improved F -Score Technique. The second method is based on numeral systems to design a vector ranking algorithm. The two proposed vector ordering algorithms are integrated into the morphological features extraction process to validate the vectorial version of the scalar morphological operators.