Reaction-Diffusion filtering

Filtering a 3D CT Scanner of the head

Left image is a volume-rendered view of the inside of a patient head acquired with a CT scan.

Midlle image shows a slice of the dataset superimposed on the rendered view.

Right image is the same rendered view once the dataset has been filtered with the Beltrami flow.

Filtering a 3D Ultrasound of the heart with different reaction/diffusion weights

The Beltrami flow (Kimmel et al 1997, Sochen et al 1998) is one of the most effective denoising algorithms in image processing. For gray-level images, we show that the Beltrami flow equation can be arranged in a reaction-diffusion form, revealing the edge-enhancing properties of this flow. This also suggests the application of AOS method for faster convergence.

Links

• Fast Evolution of Image Manifolds and Application to Filtering and Segmentation in 3D Medical Images(article)
• The homepage of Joachim Weickert for articles on Anisotropic Filtering

math.lbl.gov/~deschamp