Computer Vision, Graphics, and Image Processing
Hierarchical Image Analysis Using Irregular Tessellations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Receptive fields within the combinatorial pyramid framework
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Geometrical, topological, and hierarchical structuring of overlapping 2-D discrete objects
Computers and Graphics
Hierarchical watersheds within the combinatorial pyramid framework
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are often used within the segmentation and the connected component analysis frameworks to detect meaningful objects together with their spatial and topological relationships. The graphs reduced in the pyramid may be region adjacency graphs, dual graphs or combinatorial maps. Using any of these graphs each vertex of a reduced graph encodes a region of the image. Using simple graphs one edge between two vertices encodes the existence of a common boundary between two regions. Using dual graphs and combinatorial maps, each connected boundary segment between two regions is associated to one edge. Moreover, special edges called loops may be used to differentiate a special type of adjacency where one region surrounds the other. We show in this article that the loop information does not allow to distinguish inside and outside of the loop by local computations. We provide a method based on the combinatorial pyramid framework which uses the orientation explicitly encoded by combinatorial maps to determine inside and outside with local calculus.