This issue of JMIV is the result of a Call For Papers sent to all selected speakers of the third conference on Mathematics and Image Analysis (MIA'00) which took place in Paris on September 25-27, 2000. The first two meetings were organized in Luminy, near Marseilles, France, in November 1997 and April 1999. These conferences were initiated by the committee of the French research cluster called GDR MSPC, for Mathematics of Cognitive and Perceptive Systems, created by Robert Azencot (ENS Cachan). The first two conferences were organized mainly by Laurent Younes (ENS Cachan), Alain Trouvé (University Paris 13), and myself.

The MIA'00 conference took a larger scale and was organized jointly with the research cluster called GDR ISIS, for Information, Signal, Images and ViSion. We also had two industrial sponsors, Airsys department of Thomson-CSF, now called Thales, and DGA. There were about 170 participants attending the 22 talks, among which five long talks. Most participants were from France, but about half of the talks were from abroad in Europe, Israel, USA and Canada. The Organizing Committee of MIA'00 was composed of Frédéric Barbaresco (Thomson-CSF Airsys), Laurent Cohen (Ceremade, University of Paris 9 Dauphine), Nicolas Rougon (INT), Alain Trouvé (University Paris 13) and Laurent Younes (ENS Cachan). The complete list of speakers with abstracts and program committee is available on the web site http://www.ceremade.dauphine.fr/~cohen/mia2000.

The goal of these conferences and the research cluster (GDR) behind is to enhance a trend which started about 15 years ago to give a mathematical framework to many fields of computer vision. This involves nowadays researchers all around the world at the interface between applied mathematics and new developments in various areas of computer vision.

Concerning this special issue, all papers submitted were reviewed as usual for JMIV by two referees, and eight papers were selected. We thank by the way all the referees that helped in the editorial work to realize this special issue.
The papers presented make use of either variational methods and Partial Differential Equations or Statistical Methods.

The first five papers use Partial Differential Equations and deal with regularization problems for signal, image and shape smoothing (Sochen et al., Tek and Kimia), minimal paths for perceptual grouping, shape from shading and path planning (Cohen, Kimmel and Sethian) and motion estimation from a sequence of images (Weickert and Schnorr).

The last three papers use statistical methods and deal with motion estimation for video indexing (Fablet and Bouthemy), edge detection (Desolneux et al.) and shape recognition (Dahmen et al.).