A Multivariate Mathematical Morphology Based on Orthogonal Transformation, Probabilistic Extrema Estimation and Distance Optimization
Mathematical morphology (MM) is a very popular image processing framework, which offers widely-used non-linear tools. It was introduced for binary and greylevel images, but recently, numerous approaches have been proposed for color or multivariate images. Many of these approaches are based on the lexicographical ordering, which respects the total ordering properties, thus making this approach a very robust solution. However, it also has disadvantages like the subjective prioritization of the components and the perceptual nonlinearities introduced due to color component prioritization. Within this paper, we introduce a new multivariate MM approach, derived from a probabilistic approach, through the optimization of the distance between the estimated pseudo-extrema and vectors within the initial data set. We compare the results generated using the two approaches and a generic lexicographic approach based on Principal Component Analysis as the axis prioritization criteria.
KeywordsMultivariate Mathematical Morphology Principal Component Analysis Color Image Segmentation
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