Résumé en anglais

This article presents the Δ-distance, a family of distances between images recursively decomposed into segments and represented by multi-level feature vectors. Such a structure is a quad, a quin or a nona-tree resulting from a fixed and arbitrary image partition or from an image segmentation process. It handles positional information of image features (e.g. color, texture or shape). Δ-distance is the generalized form of dissimilarity measures between multi-level feature vectors. Using different weights on tree nodes and different distances between nodes, distances between trees or visual similarity between images can be computed based on the general definition of Δ. In this article, we present three Δ-based distance families: two families of distances between tree structures, called {T}-distance{T}for Tree) and {S}-distance for Segment), and a family of visual distances between images, called {V}for Visual). The {V)-distance visually compares two images using their tree representation and the other two distances compare the tree structures resulting from image segmentation. Moreover, we show how existing distances between multi-level feature vectors appear to be particular cases of the Δ-distance.