Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Partitioning 3D Surface Meshes Using Watershed Segmentation
IEEE Transactions on Visualization and Computer Graphics
The Complexity of Rivers in Triangulated Terrains
Proceedings of the 8th Canadian Conference on Computational Geometry
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
The complexity of flow on fat terrains and its i/o-efficient computation
Computational Geometry: Theory and Applications
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
Flow on noisy terrains: an experimental evaluation
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Morphologically-aware elimination of flat edges from a TIN
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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The natural way of modeling water flow on a triangulated terrain is to make the fundamental assumption that water follows the direction of steepest descent (dsd). However, computing watersheds and other flow-related structures according to the dsd model in an exact manner is difficult: the dsd model implies that water does not necessarily follow terrain edges, which makes designing exact algorithms difficult and causes robustness problems when implementing them. As a result, existing software implementations for computing watersheds are inexact: they either assume a simplified flow model or they perform computations using inexact arithmetic, which leads to inexact and sometimes inconsistent results. We perform a detailed study of various issues concerning the exact or approximate computation of watersheds according to the dsd model. Our main contributions are the following. • We provide the first implementation that computes watersheds on triangulated terrains following strictly the dsd model and using exact arithmetic, and we experimentally investigate its computational cost. Our experiments show that the algorithm cannot handle large data sets effectively, due to the bit-sizes needed in the exact computations and the computation of an intermediate structure called the strip map. • Using our exact algorithm as a point of reference, we evaluate the quality of several existing heuristics for computing watersheds. We also investigate hybrid methods, which use heuristics in a first phase of the algorithm and exact computation in a second phase. The hybrid methods are almost as fast as the heuristics, but give significantly more accurate results. • We describe and theoretically analyze a new exact algorithm for computing watersheds, which avoids the computation of the strip map.