Introduction to Solid Modeling
Introduction to Solid Modeling
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Hierarchical Image Analysis Using Irregular Tessellations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Functional specification and prototyping with oriented combinatorial maps
Computational Geometry: Theory and Applications
Generic Programming Techniques that Make Planar Cell Complexes Easy to Use
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Border Map: A Topological Representation for nD Image Analysis
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
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
Region merging with topological control
Discrete Applied Mathematics
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 new sub-pixel map for image analysis
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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Finite topological spaces are now widely recognized as a valuable tool of image analysis. However, their practical application is complicated because there are so many different approaches. We show that there are close relationships between those approaches which motivate the introduction of XPMaps as a concept that subsumes the important characteristics of the other approaches. The notion of topological segmentations then extends this concept to a particular class of labelings of XPMaps. We show that the new notions lead to significant simplifications from both a theoretical and practical viewpoint.