Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A critical view of pyramid segmentation algorithms
Pattern Recognition Letters
Region representation: quadtrees from boundary codes
Communications of the ACM
Region representation: boundary codes from quadtrees
Communications of the ACM
Digital Picture Processing
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
Border Map: A Topological Representation for nD Image Analysis
DCGI '99 Proceedings of the 8th International Conference 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
Receptive Fields within the Combinatorial Pyramid Framework
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
Introduction to combinatorial pyramids
Digital and image geometry
Receptive fields within the combinatorial pyramid framework
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Construction of combinatorial pyramids
GbRPR'03 Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition
Computing homology for surfaces with generalized maps: application to 3d images
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
GbRPR'05 Proceedings of the 5th IAPR 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
Topological map: an efficient tool to compute incrementally topological features on 3d images
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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In this paper we define the 3d topological map and give an optimal algorithm which computes it from a segmented image. This data structure encodes totally all the information given by the segmentation. More, it allows to continue segmentation either algorithmically or interactively. We propose an original approach which uses several levels of maps. This allows us to propose a reasonable and implementable solution where other approaches don't allow suitable solutions. Moreover our solution has been implemented and the theoretical results translate very well in practical applications.