Efficient and robust computational methods for biomedical image analysis, NATO Project Reference : PST.CLG.979123

RESEARCH PLAN The research group will design and study original numerical schemes for solving nonlinear degenerate parabolic partial differential equations (PDEs) arising in image analysis. Their efficient and robust implementation on modern computer architecture and application to problems of image analysis in biomedical engineering and medical imaging will also be an object of the study. We will mainly deal with important problems of nonlinear image filtering and robust image segmentation for 2D, 3D images, 2D+time and 3D+time image sequences given in rectangular, cylindrical and other nontrivial geometries related to recent acquizition devices and techniques. The numerical schemes will be studied regarding stability and efficiency of computations as well as regarding the convergence to the weak solutions of the corresponding PDEs. The discretized mathematical models will be based on generalizations of the nonlinear image selective smoothing equation of the Perona-Malik type and on the morphologically invariant geometrical equations of mean curvature flow type. The image sequences will be processed and segmented using space and time coherence of moving structures. The robust semi-implicit time-scale discretizations, variational spatial discretizations and fast and robust linear algebra solvers will be used in order to achieve fast and stable solutions. Since image processing operations add further dimension to the problem (the so called scale space), in case of 3D+time image sequences we have to solve 5 dimensional problems which is a chalenge for high scale and parallel computing approaches.