Finite topology as applied to image analysis
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
Introduction to Combinatorial Pyramids
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Contraction kernels and combinatorial maps
Pattern Recognition Letters - Special issue: 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
Equivalence between Closed Connected n-G-Maps without Multi-Incidence and n-Surfaces
Journal of Mathematical Imaging and Vision
A First Step toward Combinatorial Pyramids in n-D Spaces
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Insertion and expansion operations for n-dimensional generalized maps
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
A causal extraction scheme in top-down pyramids for large images segmentation
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Invariant representative cocycles of cohomology generators using irregular graph pyramids
Computer Vision and Image Understanding
Generalized map pyramid for multi-level 3d image segmentation
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
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Graph pyramids are often used for representing irregular image pyramids. For the 2D case, combinatorial pyramids have been recently defined in order to explicitly represent more topological information than graph pyramids. The main contribution of this work is the definition of pyramids of n-dimensional (nD) generalized maps. This extends the previous works to any dimension, and generalizes them in order to represent any type of pyramid constructed by using any removal and/or contraction operations. We give basic algorithms that allow to build an nD generalized pyramid that describes a multi-level segmented image. A pyramid of nD generalized maps can be implemented in several ways. We propose three possible representations and give conversion algorithms.