Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
CVGIP: Graphical Models and Image Processing
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
A topological approach to digital topology
American Mathematical Monthly
Discrete Combinatorial Surfaces
Graphical Models and Image Processing
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Topological 3D-manifolds: a statistical study of the cells
Theoretical Computer Science
A topologically consistent representation for image analysis: the Topological Graph of Frontiers
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Abstraction Pyramids on Discrete Representations
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Topological Map Based Algorithms for 3D Image Segmentation
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Computer Vision and Image Understanding
Comparison and convergence of two topological models for 3D image segmentation
GbRPR'03 Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition
A new contour filling algorithm based on 2D topological map
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Pyramids of n-dimensional generalized maps
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
A Generic and Parallel Algorithm for 2D Image Discrete Contour Reconstruction
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
3D Topological Map Extraction from Oriented Boundary Graph
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
Signatures of Combinatorial Maps
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Efficient search of combinatorial maps using signatures
Theoretical Computer Science
A polynomial algorithm for submap isomorphism of general maps
Pattern Recognition Letters
Polynomial algorithms for subisomorphism of nD open combinatorial maps
Computer Vision and Image Understanding
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Measuring the distance of generalized maps
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
A generic and parallel algorithm for 2D digital curve polygonal approximation
Journal of Real-Time Image Processing
Digital Imaging: A Unified Topological Framework
Journal of Mathematical Imaging and Vision
From maximum common submaps to edit distances of generalized maps
Pattern Recognition Letters
A distance measure between labeled combinatorial maps
Computer Vision and Image Understanding
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In this paper, we define the three-dimensional topological map, a model which represents both the topological and geometrical information of a three-dimensional labeled image. Since this model describes the image's topology in a minimal way, we can use it to define efficient image processing algorithms. The topological map is the last level of map hierarchy. Each level represents the region boundaries of the image and is defined from the previous level in the hierarchy, thus giving a simple constructive definition. This model is an extension of the similar model defined for 2D images. Progressive definition based on successive map levels allows us to extend this model to higher dimension. Moreover, with progressive definition, we can study each level separately. This simplifies the study of disconnection cases and the proofs of topological map properties. Finally, we provide an incremental extraction algorithm which extracts any map of the hierarchy in a single image scan. Moreover, we show that this algorithm is very efficient by giving the results of our experiments made on artificial images.