Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Hierarchical Image Analysis Using Irregular Tessellations
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Introduction to the Special Section on Graph Algorithms in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Object Matching on Irregular Pyramid
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
nD generalized map pyramids: Definition, representations and basic operations
Pattern Recognition
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
A polynomial algorithm for submap isomorphism of general maps
Pattern Recognition Letters
Hierarchical interactive image segmentation using irregular pyramids
GbRPR'11 Proceedings of the 8th 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
Receptive fields for generalized map pyramids: the notion of generalized orbit
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
A distance measure between labeled combinatorial maps
Computer Vision and Image Understanding
Multimedia Tools and Applications
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Graph pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids overcome the main limitations of their regular ancestors. The graphs used in the pyramid may be region adjacency graphs, dual graphs or combinatorial maps. Compared to usual graph data structures, combinatorial maps offer an explicit encoding of the orientation of edges around vertices. Each combinatorial map in the pyramid is generated from the one below by a set of edges to be contracted. This contraction process is controlled by kernels that can be combined in many ways. This paper shows that kernels producing a slow reduction rate can be combined to speed up reduction. Conversely, kernels decompose into smaller kernels that generate a more gradual reduction. We also propose one sequential and one parallel algorithm to compute the contracted combinatorial maps.