Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
A critical view of pyramid segmentation algorithms
Pattern Recognition Letters
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
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
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
Inside and outside within combinatorial pyramids
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
Topological operators on cell complexes in arbitrary dimensions
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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A hierarchical structure is a stack of successively reduced image representations. Each basic element of a hierarchical structure is the father of a set of elements in the level below. The transitive closure of this father-child relationship associates to each element of the hierarchy a set of basic elements in the base level image representation. Such a set, called a receptive field, defines the embedding of one element on the original image. Combinatorial pyramids are defined as a stack of successively reduced combinatorial maps, each combinatorial map being defined by two permutations acting on a set of half edges named darts. The basic element of a combinatorial pyramid is thus the dart. This paper defines the receptive field of each dart within a combinatorial pyramid and study the main properties of these sets.