This is an introduction of fuzzy set theory, fuzzy logic and their applications in image processing. I will closely follow the book by Gonzalez and Woods and try to explain what are fuzzy set and fuzzy logic, and the procedures we can take to use fuzzy techniques for image processing. After introducing the basic concepts and algorithms of fuzzy sets, I will give two examples of using fuzzy techniques for image enhancement and edge detection.

In this paper, we present a novel framework to simulate and visualize blood flow at high levels of detail through the aortic valve. We generate a 4D reconstruction of the aortic root using contrast-enhanced CT imagery, and attach it to a model of the left ventricle segmented from the Visible Human Project dataset. This full R-R animated model is then used as solid boundary conditions in a highly-accurate FDM Navier-Stokes fluid solver. We perform this simulation on both healthy and diseased aortic hearts, and then build visualizations of the velocity and vorticity fields produced by the simulator. In our quantitative analysis of the flow, we find significantly elevated vorticities in the diseased valve simulation. These results produce a view of the flow fields clearer than previous imaging techniques can provide.