Nonlocal and multivariate mathematical morphology

The generalization of mathematical morphology to multivariate images is addressed in this paper. The proposed approach is fully unsupervised and consists in constructing a complete lattice from an image as a rank transformation together with a learned ordering of vectors. This unsupervised ordering...

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Bibliographic Details
Main Authors: Lezoray, O., Elmoataz, A.
Format: Conference Proceeding
Language:English
Subjects:
Dictionaries
Image color analysis
Laplace equations
Lattices
manifold learning
Manifolds
Mathematical morphology
Morphology
multivariate
nonlocal
Vectors
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Summary:The generalization of mathematical morphology to multivariate images is addressed in this paper. The proposed approach is fully unsupervised and consists in constructing a complete lattice from an image as a rank transformation together with a learned ordering of vectors. This unsupervised ordering of vectors relies on three steps: dictionary learning, manifold learning and out of sample extension. In addition to providing an efficient way to construct a vectorial ordering, nonlocal configurations based on color patches can be easily handled and provide much better results than with classical local morphological approaches.
ISSN:1522-4880
2381-8549
DOI:10.1109/ICIP.2012.6466812