Some Morphological Operators in Graph Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Morphology on Graphs and Minimum Spanning Trees
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Milena: Write Generic Morphological Algorithms Once, Run on Many Kinds of Images
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Collapses and Watersheds in Pseudomanifolds
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
A tensorial framework for color images
Pattern Recognition Letters
Segmentation of 4D cardiac MRI: Automated method based on spatio-temporal watershed cuts
Image and Vision Computing
Some links between extremum spanning forests, watersheds and min-cuts
Image and Vision Computing
Artwork 3D model database indexing and classification
Pattern Recognition
Ridge detection with a drop of water principle
ACM SIGGRAPH ASIA 2010 Posters
On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds
Journal of Mathematical Imaging and Vision
Incremental algorithm for hierarchical minimum spanning forests and saliency of watershed cuts
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Surface reconstruction using power watershed
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Iterated graph cuts for image segmentation
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
Analysis of Scalar Maps for the Segmentation of the Corpus Callosum in Diffusion Tensor Fields
Journal of Mathematical Imaging and Vision
Morphological filtering on graphs
Computer Vision and Image Understanding
A region-based method for sketch map segmentation
GREC'11 Proceedings of the 9th international conference on Graphics Recognition: new trends and challenges
Dense subgraph mining with a mixed graph model
Pattern Recognition Letters
Hi-index | 0.14 |
We study the watersheds in edge-weighted graphs. We define the watershed cuts following the intuitive idea of drops of water flowing on a topographic surface. We first establish the consistency of these watersheds: They can be equivalently defined by their "catchment basins” (through a steepest descent property) or by the "dividing lines” separating these catchment basins (through the drop of water principle). Then, we prove, through an equivalence theorem, their optimality in terms of minimum spanning forests. Afterward, we introduce a linear-time algorithm to compute them. To the best of our knowledge, similar properties are not verified in other frameworks and the proposed algorithm is the most efficient existing algorithm, both in theory and in practice. Finally, the defined concepts are illustrated in image segmentation, leading to the conclusion that the proposed approach improves, on the tested images, the quality of watershed-based segmentations.