Variational numerical methods in image processing and analysis

Karol Mikula

Department of Mathematics, Slovak University of Technology, Bratislava, Slovakia
Gość Stefan Banach Centre of Excellence

 

In many applications computers analyse images or image sequences, quality of which can be poor, e.g., they are contaminated by noise and/or boundaries of image objects are partly missing (e.g. in medical imaging, or ilusory contours extraction).
We show how nonlinear partial differential equations can be used to denoise and segment such images, complete the missing boundaries, etc. We will discuss dicretizations by the variational methods of the geometrical image selective smoothing and segmentation equations (weighted mean curvature flow and Perona-Malik problem). We describe mainly finite/complementary volume methods for solving related strongly nonlinear and degenerate diffusion equations and prove their stability properties and convergence to weak solutions, respectively.
The extension of the methods to adaptive scheme strategies improving computational efficiency will be also discussed. The computational results in echocardiography and subjective contours extraction will be discussed.
 
 

5.04.2002