Processing Multispectral Images Via Mathematical Morphology

In this chapter, we illustrate how to process multispectral and hyperspectral images via mathematical morphology. First, according to the number of channels the data are embeded into a sufficiently high dimensional space. This transformation utilizes a special geometric structure, namely double hypersimplices, for further processing the data. For example, RGB-color images are transformed into points within a specific double hypersimplex. It is explained in detail how to calculate the supremum and infimum of samples of those transformed data to allow for the meaningful definition of morphological operations such as dilation and erosion and in a second step top hats, gradients, and morphological Laplacian. Finally, numerical results are presented to explore the advantages and shortcomings of the new proposed approach.