3D Segmentation Using Level Set Methods

Heriot-Watt University, Edinburgh, Scotland Zsolt Husz Mokhled Al-TarawnehÍzzet Canarslan University of Newcastle upon Tyne, England Istanbul Technical University, Turkey Péter HorváthSebahattin Topal University of Szeged, Hungary Middle East Technical University, Ankara, Turkey

Input: Medical and/or other images Operation: Compute gradient image. Define a transform, for example polar, a cost function, for example circumference and gradient. Minimize path in transformed data by cost minimization. Alternative, use a snake for example using Greedy algorithm. The object is to find an algorithm to link the points identified on a gradient map to give continuous enclosing contours. Think out extension to 3d Output: Contour (with image) 3D Segmentation Using Level Set Methods

Initialization Gradient Visualisation / Post-processing Narrow Band Reinitialisation Level Set

Browse between images Initialize a sphere Initialize a region in a slice Replicate or clear region Starting process End program

Active Contours Problems: Initialization Topological changes 3D implementation [Kass, Witkin, Terzopoulos ’88]

Level-Set methods Embed the contour to a higher dimension space level set function: . [Osher and Sethian ‘88]

Level set extension to 3D The contour moves in a 3D space (  3 ) Energy minimization: Gradient Descent Method local optimization 

Visualisation Interface between algorithms: 3D matrix volume 3D volume matrix Conversion to VRML → flexibility Two approaches: triangular mesh marching cubes Examples:

Conclusions Pros – noise prone – 3D segmentation is natural – isolated components are permitted Cons –LS is parameterised –LS slower than 3D snakes –processing resources (CPU, memory) Future work –automatic parameter adjustment –multi-scale processing –combined intensity and edge based segmentation

References [1] S. Osher and J. A. Sethian, “Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations”, J. Comp. Phys., vol. 79, pp.12–49, 1988 [2] M. Kass, A. Witkin, and D. Terzopoulos. Snakes, “Active Contour Models”, International Journal of Computer Vision 1(4), pp.321–331, 1988 [3] T. Chan and L. Vese, “An Active Contour Model without Edges” in SCALE-SPACE ’99: Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision, pp. 141– 151, Springer-Verlag, 1999 [4] C. Xu and J. L. Prince, “Snakes, Shapes, Gradient Vector Flow”, IEEE Transactions on Image Processing, Vol. 7, no. 3, pp , 1998

Thank you for your attention Questions?