Applications of PDEs and Optimization in Medical Image and Surface Processing

Professor Bin Dong
Department of Mathematics
UC San Diego


Variational, level set and PDE based methods and their applications in digital image processing have been well developed and studied for the past twenty years. These methods were soon applied to medical image processing problems. However, the study for biological shapes, e.g. surfaces of brains or other human organs, are still in its early stage. The bulk of this talk explores some applications of variational, level set and PDE based methods in biological shape processing and analysis.

There will be three topics in this talk. The first one is on 3D brain aneurysm capturing using level set based method, which is inspired by the technique of illusory contours in image analysis. The second one is on multiscale representations(MSR) of 3D shapes, which is wavelet flavored but level set and PDE based. The third one is on Bregman iteration as a fast solver for L1-minimizations and its application to image processing problems in DNA sequencing.