# nD generalized map pyramids: definition, representations and basic operations

Pattern Recognition, Volume 39, Number 4, pages 527-538 - April 2006

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 generalized maps. This extends the previous works to any dimension, and generalizes them in order to represent any type of pyramid built by using any removal and/or contraction operations. We give basic algorithms that allow to build an n-dimensional generalized pyramid that describes a multi-level segmented image. A pyramid of n-dimensional generalized maps can be implemented in several ways. We propose three possible representations and give conversion algorithms.

## BibTex references

@Article{SDL2006_959,

}

author | = {Simon, C. and Damiand, G. and Lienhardt, P.}, | |

title | = {nD generalized map pyramids: definition, representations and basic operations.}, | |

journal | = {Pattern Recognition}, | |

number | = {4}, | |

volume | = {39}, | |

pages | = {527-538}, | |

month | = {April}, | |

year | = {2006}, | |

keywords | = {Irregular pyramid; Hierarchical data structure; Pyramid of generalized maps; Multi-level segmented image}, | |

url | = {http://dx.doi.org/10.1016/j.patcog.2005.10.004}, |