Evolutionary partial differential equations for biomedical image processing

Authors:
Alessandro Sarti;Karol Mikula;Fiorella Sgallari;Claudio Lamberti
Affiliations:
Department of Mathematics, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA and DEIS, University of Bologna, Viale Risorgimento, 2 I 40136 Bologna, Italy;Department of Mathematics, Slovak University of Technology, Radlinskeho 11, 813 68 Bratislava, Slovakia;Department of Mathematics, University of Bologna, Italy;DEIS, University of Bologna, Viale Risorgimento, 2 I 40136 Bologna, Italy
Venue:
Computers and Biomedical Research
Year:
2002

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Abstract

We are presenting here a model for processing space-time image sequences and applying them to 3D echo-cardiography. The non-linear evolutionary equations filter the sequence with keeping space-time coherent structures. They have been developed using ideas of regularized Perona-Malik an-isotropic diffusion and geometrical diffusion of mean curvature flow type (Malladi-Sethian), combined with Galilean invariant movie multi-scale analysis of Alvarez et al. A discretization of space-time filtering equations by means of finite volume method is discussed in detail. Computational results in processing of 3D echo-cardiographic sequences obtained by rotational acquisition technique and by real-time 3D echo volumetrics acquisition technique are presented. Quantitative error estimation is also provided.