Some Studies on Mathematical Morphology in Remotely Sensed Data Analysis

Abstract

The application of Mathematical Morphology (MM) techniques has proven to be beneficial in the extraction of shapebased and texture-based features during remote sensing image analysis. The characteristics of these techniques, such as nonlinear adaptability and comprehensive lattice structure, make them useful for contextual spatial feature analysis. Despite the advancements, there are still persistent challenges, including the curse of dimensionality, maintaining spatial correlation, and the adaptability of morphological operators in higher dimensions. The focus of this thesis is to explore the potential of MM-based methods to analyse spatial features in addressing these challenges, specifically in the context of spatialcontextual feature analysis of hyperspectral images and Digital Elevation Models. This thesis explores the power of morphological distance in capturing spatial relationships and proposes a modified definition called "Dilation Distance" to address the "Dimensionality Curse" in hyperspectral images. By employing dilation-based distances, spatially separated objects can be identified, reducing redundancy and enhancing efficiency. Experimental trials demonstrate the superiority of the proposed approach. Additionally, the thesis introduces a new approach using morphological interpolation for terrain surface interpolation, preserving geometric structure while providing a smooth surface. The extension of conventional univariate morphological tools to hyperspectral images in a multivariate way is also explored, ensuring the concurrent application of operators while preserving the multivariate nature of the data. To achieve that a vector ordering strategy is proposed. Overall, these techniques have a profound impact on the progress of mathematical morphology in remotely sensed image analysis, offering valuable insights.