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
The adaptive pyramid: a framework for 2D image analysis
CVGIP: Image Understanding
Algebraic specification of a 3D-modeler based on hypermaps
CVGIP: Graphical Models and Image Processing
Topological Encoding of 3D Segmented Images
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Generalized map pyramid for multi-level 3d image segmentation
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
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
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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 of the hierarchy on the original image. Using the father-child relationship, global properties of a receptive field may be computed in O(log(m)) parallel processing steps where m is the diameter of the receptive field. 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.