A geometric dissimilarity criterion between Jordan spatial mosaics. Theoretical aspects and application to segmentation evaluation

Yann Gavet (1, 2, 3, 4) , Jean-Charles Pinoli (1, 2, 3, 4)

1 CIS-ENSMSE - Centre Ingénierie et Santé
2 DIM-ENSMSE - Département Imagerie et Morphologie
3 LPMG-EMSE - Laboratoire des Procédés en Milieux Granulaires
4 IFRESIS - Institut Fédératif de Recherche en Sciences et Ingénierie de la Santé

An image segmentation process often results in a special spatial set, called a mosaic, as the subdivision of a domain S within the n-dimensional Euclidean space. In this paper, S will be a compact domain and the study will be focused on finite Jordan mosaics, that is to say mosaics with a finite number of regions and where the boundary of each region is a Jordan hypersurface. The first part of this paper addresses the problem of comparing a Jordan mosaic to a given reference Jordan mosaic and introduces the (Epsilon) dissimilarity criterion. The second part will show that the (Epsilon) dissimilarity criterion can be used to perform the evaluation of image segmentation processes. It will be compared to classical criterions in regard to several geometric transformations. The pros and cons of these criterions are presented and discussed, showing that the dissimilarity criterion outperforms the other ones.

Mots clés: Dissimilarity criterion; Geometric distances; Spatial mosaics; Human visual perception; Supervised segmentation evaluation

Domaines: Génie des procédés; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Yann Gavet, Jean-Charles Pinoli. A geometric dissimilarity criterion between Jordan spatial mosaics. Theoretical aspects and application to segmentation evaluation. Journal of Mathematical Imaging and Vision, 2012, 42 (1), pp.25-49. ⟨10.1007/s10851-011-0272-4⟩. ⟨hal-00660178⟩