Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Merging in maps and in pavings
Theoretical Computer Science
An optimal algorithm for extracting the regions of a plane graph
Pattern Recognition Letters
Symbol Recognition by Error-Tolerant Subgraph Matching between Region Adjacency Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Marked Subgraph Isomorphism of Ordered Graphs
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
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
Topological Map Based Algorithms for 3D Image Segmentation
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 3)-Volume 3 - Volume 3
Computer Vision and Image Understanding
A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topological model for 3D image representation: Definition and incremental extraction algorithm
Computer Vision and Image Understanding
A Polynomial Algorithm for Submap Isomorphism
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Signatures of Combinatorial Maps
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Insertion and expansion operations for n-dimensional generalized maps
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
First results for 3D image segmentation with topological map
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
AllDifferent-based filtering for subgraph isomorphism
Artificial Intelligence
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
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
Part-based object detection into a hierarchy of image segmentations combining color and topology
Pattern Recognition Letters
Polynomial algorithms for open plane graph and subgraph isomorphisms
Theoretical Computer Science
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Combinatorial maps describe the subdivision of objects in cells, and incidence and adjacency relations between cells, and they are widely used to model 2D and 3D images. However, there is no algorithm for comparing combinatorial maps, which is an important issue for image processing and analysis. In this paper, we address two basic comparison problems, i.e., map isomorphism, which involves deciding if two maps are equivalent, and submap isomorphism, which involves deciding if a copy of a pattern map may be found in a target map. We formally define these two problems for nD open combinatorial maps, we give polynomial time algorithms for solving them, and we illustrate their interest and feasibility for searching patterns in 2D and 3D images, as any child would aim to do when he searches Wally in Martin Handford's books.