A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to Solid Modeling
Introduction to Solid Modeling
Finite topology as applied to image analysis
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
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
XPMaps and Topological Segmentation - A Unified Approach to Finite Topologies in the Plane
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Subpixel-Precise Extraction of Watersheds
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Construction of combinatorial pyramids
GbRPR'03 Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition
Deriving topological representations from edge images
Proceedings of the 11th international conference on Theoretical foundations of computer vision
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
The GeoMap: a unified representation for topology and geometry
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
A topological sampling theorem for Robust boundary reconstruction and image segmentation
Discrete Applied Mathematics
Annotated Contraction Kernels for Interactive Image Segmentation
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
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Planar maps have been proposed as a powerful and easy-to-use representation for various kinds of image analysis results, but so far they are restricted to pixel accuracy. This leads to limitations in the representation of complex structures (such as junctions, triangulations, and skeletons) and discards the sub-pixel information available in grayvalue and color images. We extend the planar map formalism to sub-pixel accuracy and introduce various algorithms to create such a map, thereby demonstrating significant gains over the existing approaches.