Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watershed of a continuous function
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Geodesic Saliency of Watershed Contours and Hierarchical Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
The watershed transform: definitions, algorithms and parallelization strategies
Fundamenta Informaticae - Special issue on mathematical morphology
Order independent homotopic thinning for binary and grey tone anchored skeletons
Pattern Recognition Letters
IFT-Watershed from Gray-Scale Marker
SIBGRAPI '02 Proceedings of the 15th Brazilian Symposium on Computer Graphics and Image Processing
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Quasi-Linear Algorithms for the Topological Watershed
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Quasi-Linear Algorithms for the Topological Watershed
Journal of Mathematical Imaging and Vision
Image and Vision Computing
Uniquely-Determined Thinning of the Tie-Zone Watershed Based on Label Frequency
Journal of Mathematical Imaging and Vision
Fusion Graphs: Merging Properties and Watersheds
Journal of Mathematical Imaging and Vision
Weighted fusion graphs: Merging properties and watersheds
Discrete Applied Mathematics
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Computer Vision and Image Understanding
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In this paper, we investigate the links between the flooding paradigm and the topological watershed. Guided by the analysis of a classical flooding algorithm, we present several notions that lead us to a better understanding of the watershed: minima extension, mosaic, pass value and separation. We first make a detailed examination of the effectiveness of the divide set produced by watershed algorithms. We introduce the mosaic to retrieve the altitude of points along the divide set. A desirable property is that, when two minima are separated by a crest in the original image, they are still separated by a crest of the same altitude in the mosaic. Our main result states that this is the case if and only if the mosaic is obtained through a topological thinning. We investigate the possibility for a flooding to produce a topological watershed, and conclude that this is not feasible. This leads us to reverse the flooding paradigm, and to propose a notion of emergence. An emergence process is a transformation based on a topological criterion, in which points are processed in decreasing altitude order while preserving the number of connected components of lower cross-sections. Our main result states that any emergence watershed is a topological watershed, and more remarkably, that any topological watershed of a given image can be obtained as an emergence watershed of the image.