Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Numerical definition of drainage network and subcatchment areas from digital elevation models
Computers & Geosciences
Data-parallel procedures for drainage basin analysis
Computers & Geosciences
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
The image processing handbook (3rd ed.)
The image processing handbook (3rd ed.)
Proceedings of the sixth ACM symposium on Solid modeling and applications
The Medial axis of a union of balls
Computational Geometry: Theory and Applications
International Journal of Computer Vision
Pruning Discrete and Semiocontinuous Skeletons
ICIAP '95 Proceedings of the 8th International Conference on Image Analysis and Processing
Delete and insert operations in Voronoi/Delaunay methods and applications
Computers & Geosciences
The computational geometry of hydrology data in geographic information systems
The computational geometry of hydrology data in geographic information systems
A Mathematical Tool to Extend 2D Spatial Operations to Higher Dimensions
ICCSA '08 Proceeding sof the international conference on Computational Science and Its Applications, Part I
Proceedings of the twenty-fifth annual symposium on Computational geometry
Curve reconstruction from noisy samples
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
A simplex-based approach to implement dimension independent spatial analyses
Computers & Geosciences
Voronoi-Based curve reconstruction: issues and solutions
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part II
A Stable Voronoi-based Algorithm for Medial Axis Extraction through Labeling Sample Points
ISVD '12 Proceedings of the 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering
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The watersheds are commonly delineated from digital elevation models (DEM). This approach is not efficient when an accurate DEM is not available. Furthermore, since raster-based algorithms are employed, the computations for large areas are very time consuming and even may be impractical. This article investigates delineation of the watersheds from the medial axis of river networks: If the river network is sampled by a set of points, the medial axis of the sample points provides an approximation of the catchments, whose aggregation results in the watersheds. Although this idea has been already proposed in the literature, the complexities of the medial axis extraction prevent it from being practically used. A major issue is appearing extraneous branches in the media axis due to perturbations of the sample points, which must be filtered out in a pre- or post-processing step. This article improves a Voronoi-based medial axis extraction algorithm by using labeled sample points to automatically avoid extraneous branches. The proposed method is used in four case studies to delineate the watersheds. The results illustrate that the proposed method is stable, easy to implement and robust, even in presence of significant noises and perturbations. The results also indicate that the watersheds delineated using the proposed and the DEM-based methods are reasonably comparable.