Linear and anisotropic diffusion in image processing

Linear and anisotropic diffusion in image processing: A study on implementation, parameters and segmentation

van Marlen, Patricia (TU Delft Electrical Engineering, Mathematics and Computer Science)

van Gijzen, Martin (mentor)
Vuik, Kees (graduation committee)
Remis, Rob (graduation committee)

Delft University of Technology

2018-04-12

The TU Delft and the LUMC are creating a low-field MRI scanner to use in third world countries. This type of MRI scanner has many advantages, but a downside is the amount of noise in the obtained images. A way to reduce noise is diffusion filtering. This thesis discusses the theory of some linear and nonlinear diffusion filtering methods and tests them on several test problems. The methods range from the basic linear method, the heat equation, to the more advanced Perona-Malik method. The results indeed show that the Perona-Malik method generates better results, sometimes when combined with a Gaussian kernel to decrease its ill-posedness.
Two numerical methods have been compared for these anisotropic diffusion filtering methods: the Forward Time, Central Space method and the Additive Operator Splitting method. The advantage of the AOS method is the unconditional stability for al positive time step sizes, while FTCS implementation is only stable for time steps smaller than 0.25. The results for the AOS method were also slightly better than for the FTCS method and almost never lead to instability. The FTCS method showed instability more often.
The parameter choice is of significant importance for the outcome. Several options for determining the gradient threshold parameter K, time step size and stopping time S have been investigated. A new estimation for the time step size and stopping time S have been proposed and compared. The results are images with good visual quality for both introduced methods. Also, an adaptive time step has been tested to overcome the instability for unstable methods and this seems to be succesful.
Lastly, region growing segmentation has been applied to images obtained with the proposed stopping time S. Segmentation is an additional way to investigate the quality of these outcomes. For most test problems the partitioning resembles the partitioning of the original image.
However, choosing certain parameters stays a challenge and can be of interest for further examination. It also remains a goal to investigate the discussed methods on data obtained with the actual TUD/LUMC MRI scanner.

anisotropic
diffusion
filtering
Imaging

http://resolver.tudelft.nl/uuid:05d331d1-72ef-4c65-9c92-2a5c132ad7eb

Student theses

master thesis

© 2018 Patricia van Marlen