Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Motion of multiple junctions: a level set approach
Journal of Computational Physics
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Co-dimension 2 Geodesic Active Contours for MRA Segmentation
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
Segmentation and Measurement of the Cortex from 3D MR Images
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Segmentation of Bone in Clinical Knee MRI Using Texture-Based Geodesic Active Contours
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Using the Vector Distance Functions to Evolve Manifolds of Arbitrary Codimension
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Reconstructing open surfaces from unorganized data points
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
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Since the work by Osher and Sethian on level-sets algorithms for numerical shape evolutions, this technique has been used for a large number of applications in numerous fields. In medical imaging, this numerical technique has been successfully used for example in segmentation and cortex unfolding algorithms. The migration from a Lagrangian implementation to an Eulerian one via implicit representations or level-sets brought some of the main advantages of the technique, mainly, topology independence and stability. This migration means also that the evolution is parametrization free, and therefore we do not know exactly how each part of the shape is deforming, and the point-wise correspondence is lost. In this note we present a technique to numerically track regions on surfaces that are being deformed using the level-sets method. The basic idea is to represent the region of interest as the intersection of two implicit surfaces, and then track its deformation from the deformation of these surfaces. This technique then solves one of the main shortcomings of the very useful level-sets approach. Applications include lesion localization in medical images, region tracking in functional MRI visualization, and geometric surface mapping.