Shape Gradient for Image and Video Segmentation

Stéphanie Jehan-Besson (1) , Ariane Herbulot (2) , Michel Barlaud (3) , Gilles Aubert (4)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 LAAS-RAP - Équipe Robotique, Action et Perception
3 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe IMAGES-CREATIVE
4 LJAD - Laboratoire Jean Alexandre Dieudonné

In this chapter, we propose to concentrate on the research of an optimal domain with regards to a global criterion including region and boundary functionals. A local shape minimizer is obtained through the evolution of a deformable domain in the direction of the shape gradient. Shape derivation tools, coming from shape optimization theory, allow us to easily differentiate region and boundary functionals. We more particularly focus on region functionals involving region-dependent features that are globally attached to the region. A general framework is proposed and illustrated by many examples involving functions of parametric or non parametric probability density functions (pdfs) of image features. Among these functions, we notably study the minimization of information measures such as the entropy for the segmentation of homogeneous regions or the minimization of the distance between pdfs for tracking or matching regions of interest.

Mots clés: active contours; active regions; region functionals; boundary functionals; shape optimization; shape gradient; segmentation; tracking; Image statistics; non parametric statistics; parzen window; entropy; distance between pdfs

Domaines: Traitement des images [eess.IV]

Stéphanie Jehan-Besson, Ariane Herbulot, Michel Barlaud, Gilles Aubert. Shape Gradient for Image and Video Segmentation. Paragios Nikos, Chen Yunmei, Faugeras, Olivier. Handbook of Mathematical Models in Computer Vision, Springer US, pp.309-323, 2006, 978-0-387-28831-4. ⟨10.1007/0-387-28831-7_19⟩. ⟨hal-01206707⟩