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
The adaptive pyramid: a framework for 2D image analysis
CVGIP: Image Understanding
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Logarithmic Tapering Graph Pyramid
Proceedings of the 24th DAGM Symposium on Pattern Recognition
Topological Encoding of 3D Segmented Images
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Pyramid segmentation algorithms revisited
Pattern Recognition
Real-time object tracking using bounded irregular pyramids
Pattern Recognition Letters
Hierarchical Matching Using Combinatorial Pyramid Framework
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
A novel approach for salient image regions detection and description
Pattern Recognition Letters
The construction of bounded irregular pyramids with a union-find decimation process
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 new sub-pixel map for image analysis
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Top-down tracking and estimating 3d pose of a die
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Each vertex of a reduced graph corresponds to a connected set of vertices in the level below. One connected set of vertices reduced into a single vertex at the above level is called the reduction window of this vertex. In the same way, a connected set of vertices in the base level graph reduced to a single vertex at a given level is called the receptive field of this vertex. The graphs used in the pyramid may be region adjacency graphs, dual graphs or combinatorial maps. This last type of pyramids are called Combinatorial Pyramids. Compared to usual graph data structures, combinatorial maps encode one graph and its dual within a same formalism and offer an explicit encoding of the orientation of edges around vertices. This paper describes the construction scheme of a Combinatorial Pyramid. We also provide a constructive definition of the notions of reduction windows and receptive fields within the Combinatorial Pyramid framework.