On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
The Complexity of Rivers in Triangulated Terrains
Proceedings of the 8th Canadian Conference on Computational Geometry
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Image segmentation using topological persistence
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Bridge detection in grid terrains and improved drainage enforcement
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Flow computations on imprecise terrains
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Exact and approximate computations of watersheds on triangulated terrains
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Implicit flow routing on terrains with applications to surface networks and drainage structures
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Morse-Smale decompositions for modeling terrain knowledge
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
Watershed identification of polygonal patterns in noisy SAR images
IEEE Transactions on Image Processing
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Computing watersheds on triangulated terrain models in a robust manner is a difficult task as it is sensitive to noise that appears in the elevation values of the input. This is amplified by the existence of many very small watersheds (corresponding to spurious minima) that obscure the overall hydrological structure of the terrain. In the present work we perform an experimental evaluation of various algorithms that may help alleviate these problems: • We introduce and experimentally investigate algorithms for matching watersheds in different instances of a triangulated terrain that arise from adding noise to the elevations of the terrain model. These algorithms can be used to see which parts of a computed watershed map are reliable in the presence of noise. • We compare two methods for merging small watersheds into larger ones. We use these methods in combination with the watershed matching algorithms to assess which merging method is most effective in facilitating successful matching of watersheds. We have evaluated the performance of the studied methods using a software package that we developed for computing watersheds on triangulated terrains. To our knowledge, this package is the first to use a robust flow model together with exact arithmetic.