Geodesic Saliency of Watershed Contours and Hierarchical Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Auto-dual connected operators based on iterative merging algorithms
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Modelling and segmentation of colour images in polar representations
Image and Vision Computing
Partial Partitions, Partial Connections and Connective Segmentation
Journal of Mathematical Imaging and Vision
Constrained Connectivity and Transition Regions
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Orders on partial partitions and maximal partitioning of sets
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Orders on partial partitions and maximal partitioning of sets
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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Given a set E, the partitions of E are usually ordered by merging of classes. In segmentation procedures, this ordering often generates small parasite classes. A new ordering, called "grain building ordering", or GBO, is proposed. It requires a connection over E and states that A ≤ B, with A, B ⊆ E, when each connected component of B contains a connected component of A. TheGBO applies to sets, partitions, and numerical functions. Thickenings ψ with respect to the GBO are introduced as extensive idempotent operators that do not create connected components. The composition product ψγ of a connected opening by a thickening is still a thickening. Moreover, when {γi, i ∈ I} is a granulometric family, then the two sequences {ψγi, i ∈ I} and {γiψ, i ∈ I} generate hierarchies, from which semi-groups can be derived. In addition, the approach allows us to combine any set of partitions or of tessellations into a synthetic one.