Level sets on non-planar manifolds for ridge detection on isosurfaces

Sovira Tan; Jianhua Yao; Michael M. Ward M.D.; Lawrence Yao M.D.; Ronald M. Summers M.D.

doi:10.1117/12.708217

5 March 2007 Level sets on non-planar manifolds for ridge detection on isosurfaces

Sovira Tan, Jianhua Yao, Michael M. Ward M.D., Lawrence Yao M.D., Ronald M. Summers M.D.

Proceedings Volume 6512, Medical Imaging 2007: Image Processing; 651230 (2007) https://doi.org/10.1117/12.708217
Event: Medical Imaging, 2007, San Diego, CA, United States

Abstract

We describe an algorithm for evolving a level set on a non-planar manifold like the isosurface of a 3D object. The surface is represented by a triangular mesh and the feature that guides our level set via a speed function is its curvature. We overcome the difficulty of computing the gradient and curvature of the level set distance function on a non-planar, non-Cartesian mesh by performing the calculations locally in neighborhoods small enough to be considered planar. Moreover we use a least squares estimation of derivatives to replace finite differences and achieve better accuracy. The algorithm was motivated by our need to detect the ridge lines of vertebral bodies. The advantage of using level sets is that they are capable of producing a continuous ridge line despite noise and gaps in the ridge. We tested our algorithm on 40 vertebral bodies (80 ridge lines). 76 ridge lines showed no noticeable mistakes. The same set of parameters was used. For the remaining 4, we had to change the parameters of the speed function sigmoid to correct small under- or over-segmenting. To further test our algorithm we designed a synthetic surface with large curvature and to which we added noise and a ridge. The level set was able to evolve on the surface and stop at the ridge. Tests on synthetic cylinders with a ground truth ridge and to which we added noise indicate that the level set has good accuracy.

Citation Download Citation

Sovira Tan, Jianhua Yao, Michael M. Ward M.D., Lawrence Yao M.D., and Ronald M. Summers M.D. "Level sets on non-planar manifolds for ridge detection on isosurfaces", Proc. SPIE 6512, Medical Imaging 2007: Image Processing, 651230 (5 March 2007); https://doi.org/10.1117/12.708217

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