Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Graphical Models and Image Processing
International Journal of Computer Vision
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Procedural annotation of uncertain information
Proceedings of the conference on Visualization '00
Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces: 730
Journal of Computational Physics
Preprocessing and Volume Rendering of 3D Ultrasonic Data
IEEE Computer Graphics and Applications
A Next Step: Visualizing Errors and Uncertainty
IEEE Computer Graphics and Applications
The Beltrami Flow over Implicit Manifolds
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Point-Based Probabilistic Surfaces to Show Surface Uncertainty
IEEE Transactions on Visualization and Computer Graphics
Visualizing Spatial Multivalue Data
IEEE Computer Graphics and Applications
Picturing data with uncertainty
SIGGRAPH '04 ACM SIGGRAPH 2004 Posters
A general framework for low level vision
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Forward-and-backward diffusion processes for adaptive image enhancement and denoising
IEEE Transactions on Image Processing
Journal of Biomedical Imaging
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Visualization of medical 3D data is a complex problem, since the raw data is often unsuitable for standard techniques like Direct Volume Rendering. Some kind of pre-treatment is necessary, usually segmentation of the structures of interest, which in turn is a difficult task. Most segmentation techniques yield a model without indicating any uncertainty. Visualization then can be misleading, especially if the original data is of poor contrast. We address this dilemma proposing a geometric approach based on distance on image manifolds and an alternative approach based on nonlinear diffusion. An effective algorithm solving Hamilton-Jacobi equations allows for computing a distance function for 2D and 3D manifolds at interactive rates. An efficient implementation of a semi-implicit operator splitting scheme accomplishes interactivity for the diffusion-based strategy. We establish a model which incorporates local information about its reliability and can be visualized with standard techniques. When interpreting the result of the segmentation in a diagnostic setting, this information is of utmost importance.