Advances in mathematical morphology applied to geoscience and remote sensing

By concentrating on the analysis of the spatial relationships between groups of pixels, mathematical morphology provides us with an image processing strategy complementary to those based on the analysis of the spectral signature of single pixels. A wide variety of morphological transformations are available for extracting structural information in spatial data. Accordingly, a stream of successful applications in geoscience and remote sensing have been reported since the mid-1980s as highlighted in a brief survey. However, recent advances in the theory of mathematical morphology still remain largely unexplored. We show in this paper that they can enhance methodologies for the processing and analysis of Earth observation data for tasks as diverse as filtering, simplification, directional segmentation and crest line extraction. We also address important issues overlooked in the past and concerning the applicability of a given morphological filter to Earth observation data. In particular, we point out that self-dual or even self-complementary filters are required in many applications to produce results independent of the local contrast of the searched image structures.

I. Introduction

Morphological image analysis or, more generally, mathematical morphology (MM) stems from the study of the geometry of binary porous media such as sandstones. They are binary in the sense that they are made up of two phases: the pores embedded in a matrix. This led Matheron and Serra to introduce in 1967 a set formalism for analyzing binary images [1] [2]–[4]. Indeed, one may consider the matrix as the set of object points and the pores as the complement of this set. Another set of carefully selected shape and size is then defined and translated over the image. This set is called the structuring element because it acts as a probe for extracting or suppressing specific structures of the image objects. The extraction or suppression is carried out by checking, for each position of the structuring element, whether it fits or not within the image objects. Hence, morphological operations are grounded on set operators such as union, intersection, complementation, and translation.