The hierarchy of the cocoons of a graph and its application to image segmentation

A set of particular subgraphs of a valued graph, called cocoons, is introduced. Within the image segmentation framework, the cocoons represent a model of contrasted regions. It is shown that the cocoons are organized into a hierarchy which is a sub-hierarchy of the one produced by the standard clustering algorithm of complete linkage. This result thus offers a new point of view on what the complete linkage algorithm achieves when it is applied on image data. For segmentation purposes, the hierarchy is built on a region adjacency graph valued with a dissimilarity function. It's construction is efficient, parameter free, and robust towards monotone transformations of the dissimilarities. It is illustrated that the simplest cut criterion in these hierarchies, based on thresholding an associated ultrametric distance, already produces meaningful segmentations.

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