A survey of thresholding techniques
Computer Vision, Graphics, and Image Processing
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computers and Biomedical Research
Picture Segmentation by a Tree Traversal Algorithm
Journal of the ACM (JACM)
The watershed transform: definitions, algorithms and parallelization strategies
Fundamenta Informaticae - Special issue on mathematical morphology
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Surface tiling with differential topology
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Extraction and simplification of iso-surfaces in tandem
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Shape recovery algorithms using level sets in 2-D/3-D medical imagery: a state-of-the-art review
IEEE Transactions on Information Technology in Biomedicine
SMI 2012: Short Dimension-independent multi-resolution Morse complexes
Computers and Graphics
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We describe an algorithm for segmenting three-dimensional medical imaging data modeled as a continuous function on a 3-manifold. It is related to watershed algorithms developed in image processing but is closer to its mathematical roots, which are Morse theory and homological algebra. It allows for the implicit treatment of an underlying mesh, thus combining the structural integrity of its mathematical foundations with the computational efficiency of image processing.