Geodesic Saliency of Watershed Contours and Hierarchical Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Constrained Connectivity for Hierarchical Image Decomposition and Simplification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Partial Partitions, Partial Connections and Connective Segmentation
Journal of Mathematical Imaging and Vision
Adjunctions on the lattices of partitions and of partial partitions
Applicable Algebra in Engineering, Communication and Computing
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Mathematical morphology on bipolar fuzzy sets: general algebraic framework
International Journal of Approximate Reasoning
Journal of Mathematical Imaging and Vision
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The segmentation of a function on a set can be considered as the construction of a maximal partial partition of that set with blocks satisfying some criterion for the function. Several order relations on partial partitions are considered in association with types of operators and criteria involved in the segmentation process. We investigate orders for which this maximality of the segmentation partial partition is preserved in compound segmentation with two successive criteria. Finally we consider valuations on partial partitions, that is, strictly isotone functions with positive real values; this gives an alternative approach where the valuation, not the partial partition, should be maximized.