Split-and-merge algorithms defined on topological maps for 3D image segmentation

Authors:
Guillaume Damiand;Patrick Resch
Affiliations:
IRCOM-SIC, bât SP2MI, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France;LIRMM, 161 rue Ada, 34392 Montpellier Cedex 5, France
Venue:
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Year:
2003

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Abstract

Split-and-merge algorithms define a class of image segmentation methods. Topological maps are a mathematical model that represents image subdivisions in 2D and 3D. This paper discusses a split-and-merge method for 3D image data based on the topological map model This model allows representations of states of segmentations and of merge and split operations. Indeed, it can be used as data structure for dynamic changes of segmentation. The paper details such an algorithmic approach and analyzes its time complexity. A general introduction into combinatorial and topological maps is given to support the understanding of the proposed algorithms.