Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Shading from shape, the eikonal equation solved by grey-weighted distance transform
Pattern Recognition Letters
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
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
Sub-pixel distance maps and weighted distance transforms
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
A fast level set based algorithm for topology-independent shape modeling
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Differential morphology and image processing
IEEE Transactions on Image Processing
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
A comparison of two tree representations for data-driven volumetric image filtering
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
The image ray transform for structural feature detection
Pattern Recognition Letters
Efficient and robust segmentations based on eikonal and diffusion PDEs
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
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The classical morphological segmentation paradigm is based on the watershed transform, constructed by flooding the gradient image seen as a topographic surface. For flooding a topographic surface, a topographic distance is defined from which a minimum distance algorithm is derived for the watershed. In a continuous formulation, this is modeled via the eikonal PDE, which can be solved using curve evolution algorithms. Various ultrametric distances between the catchment basins may then be associated to the flooding itself. To each ultrametric distance is associated a multiscale segmentation; each scale being the closed balls of the ultrametric distance.