Complete lattice learning for multivariate mathematical morphology

•Extends mathematical morphology to multivariate vectors.•Proposes an efficient strategy for complete lattice learning.•Requires no prior assumption on background/foreground.•Can integrate supervised information.•Enables to perform patch-based morphological operations.

The generalization of mathematical morphology to multivariate vector spaces is addressed in this paper. The proposed approach is fully unsupervised and consists in learning a complete lattice from an image as a nonlinear bijective mapping, interpreted in the form of a learned rank transformation together with an 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, the proposed approach can become a supervised ordering by the integration of pairwise constraints. The performance of the approach is illustrated with color image processing examples.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (97 K)Download as PowerPoint slide