A lattice-based approach to mathematical morphology for greyscale and colour images

Mathematical morphology (MM) is a theory for the analysis of spatial structures, based on set-theoretical notions and on the concept of translation. MM has many applications in image analysis such as edge detection, noise removal, object recognition, pattern recognition and image segmentation in a.o. geosciences, materials science, the biological and medical world [13, 15]. MM was originally developed for binary images only. The basic tools of MM are the morphological operators, which transform an image A we want to analyse, using a structuring element B into a new image P(A, B) in order to obtain additional information about the objects in A like shape, size, orientation, image measurements. Apart from the threshold and umbra approach, binary morphology can be extended to morphology for greyscale images using fuzzy set theory, called fuzzy morphology. In this work we will present a new vector-based approach for the extension of MM for greyscale images to colour morphology. We will extend the basic morphological operators dilation and erosion based on the threshold and fuzzy set approach to colour images. Finally in the last section we illustrate an image denoising method using MM to reduce stripes' artefacts in satellite images