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Nonlinear Multiscale Analysis Models for Filtering of 3D + Time Biomedical Images

  • A. Sarti
  • K. Mikula
  • F. Sgallari
  • C. Lamberti
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

We review nonlinear partial differential equations (PDEs) in the processing of 2D and 3D images. At the same time we present recent models introduced for processing of space-time image sequences and apply them to 3D echocardiography. The nonlinear (degenerate) diffusion equations filter the sequence with a keeping of space-time coherent structures. They have been developed using ideas of regularized Perona-Malik anisotropic diffusion and geometrical diffusion of mean curvature flow type, combined with Galilean invariant movie multiscale analysis of Alvarez, Guichard, Lions and Morel. A discretization of space-time filtering equations is discussed. Computational results in processing of 3D echocardiographic sequences obtained by rotational acquisition technique and by Real-Time 3D Echo Volumetrics aquisition technique are presented.

Keywords

Image Sequence Neumann Boundary Condition Multiscale Analysis Nonlinear Filter Motion Coherence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A. Sarti
    • 1
  • K. Mikula
    • 2
  • F. Sgallari
    • 3
  • C. Lamberti
    • 1
  1. 1.DEISUniversity of BolognaItaly
  2. 2.Department of MathematicsSlovak University of TechnologyBratislavaSlovakia
  3. 3.Department of MathematicsUniversity of BolognaItaly

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