Computing Multivalued Mathematical Morphology on Multiband Images Using Algorithms for Multicriteria Analysis

Mathematical morphology (MM) is a powerful tool for spatial multispectral and hyperspectral image analyses. However, MM was originally developed for single-band images in which each pixel is represented by a numerical value. The most commonly used method for extending MM to multiband images is to process each band independently without considering its correlations with other bands. This can lead to the creation of artificial false spectral signatures and result in object misidentification. Therefore, extending MM to multiband images requires the use of an adequate vector ordering strategy to fully exploit its potential. This work proposes new vector ordering algorithms for the computation of multivalued MM. A multicriteria analysis (MCA) system is used as a tool for establishing an ordering of vectors. Two MCA approaches, namely, an "analytic hierarchy process" and a "preference ranking organization method for enrichment evaluation," are developed to define ordering relations between vectors. To ensure the validity of the proposed vector ordering algorithms, the computed multivalued morphological profiles are compared using the proposed vector ordering approaches and conventional schemes. The results of applying the proposed vector ordering algorithms for computing morphological profiles show that good classification accuracies were achieved for urban structures in ROSIS hyperspectral images.