Models and numerical methods in nonlinear diffusion equations for 2D/3D image and image sequence analysis (Q2718069)

In this survey paper, the authors propose nonlinear partial differential equations which combine spatial nonlinear selective smoothing of Perona--Malik type or geometrical diffusion of mean curvature type with Galilean invariant movie multiscale analysis of Alvarez, Guichar, Lions and Morel and discuss three models for image sequences that distinguish the noise from the contours of the different structures by using spatial and temporal coherence. Since these five models present different properties and performances, they require different numerical techniques in order to derive stability properties, error estimates and convergence. Computational results of 3D- and 2D-echocardiographic images are presented.