ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Fundamenta morphologicae mathematicae
Fundamenta Informaticae - Special issue on mathematical morphology
Mathematical morphology on complete semilattices and its applications to image processing
Fundamenta Informaticae - Special issue on mathematical morphology
Inf-Semilattice Approach to Self-Dual Morphology
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Connected Operators Based on Region-Tree Pruning Strategies
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Journal of Mathematical Imaging and Vision
Adjacency lattices and shape-tree semilattices
Image and Vision Computing
Reconstructing masks from markers in non-distributive lattices
Applicable Algebra in Engineering, Communication and Computing
Fast computation of a contrast-invariant image representation
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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This paper presents a tree-based framework for producing self-dual morphological operators, based on a tree-representation complete inf-semilattice (CISL). The idea is to use a self-dual tree transform to map a given image into the above CISL, perform one or more morphological operations there, and map the result back to the image domain using the inverse tree transform. We also present a particular case of this general framework, involving a new tree transform, the Extrema-Watershed Tree (EWT). The operators obtained by using the EWT in the above framework behave like classical morphological operators, but in addition are self-dual. Some application examples are provided: pre-processing for OCR and dust and scratch removal algorithms, and image denoising. We also explore first steps towards obtaining tree transforms that induce a CISL on the image domain as well.