Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Journal of Mathematical Imaging and Vision - Special issue on mathematical imaging
A Boolean characterization of three-dimensional simple points
Pattern Recognition Letters
International Journal of Computer Vision
GRIN'01 No description on Graphics interface 2001
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Topology on Adaptive Octree Grids
Journal of Mathematical Imaging and Vision
Multi-label simple points definition for 3D images digital deformable model
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Fully deformable 3D digital partition model with topological control
Pattern Recognition Letters
A multiscale morphological approach to topology correction of cortical surfaces
Miar'06 Proceedings of the Third international conference on Medical Imaging and Augmented Reality
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We present a novel framework to exert topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automated topological changes. In some applications, where some a priori knowledge of the target topology is available, topological changes may not be desirable. This is typically the case in biomedical image segmentation, where the topology of the target shape is prescribed by anatomical knowledge. However, topologically constrained evolutions often generate topological barriers that lead to large geometric inconsistencies. We introduce a topologically controlled level set framework that greatly alleviates this problem. Unlike existing work, our method allows connected components to merge, split or vanish under some specific conditions that ensure that no topological defects are generated. We demonstrate the strength of our method on a wide range of numerical experiments and illustrate its performance on the segmentation of cortical surfaces and blood vessels.