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
A fast level set method for propagating interfaces
Journal of Computational Physics
Object-centered surface reconstruction: combining multi-image stereo and shading
International Journal of Computer Vision
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
A parametric deformable model to fit unstructured 3D data
Computer Vision and Image Understanding
Computer Vision and Image Understanding
Shape and Nonrigid Motion Estimation Through Physics-Based Synthesis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
GRIN'01 No description on Graphics interface 2001
Geodesic active regions and level set methods for motion estimation and tracking
Computer Vision and Image Understanding
Segmentation of medical images under topological constraints
Segmentation of medical images under topological constraints
Multi-View Stereo Reconstruction and Scene Flow Estimation with a Global Image-Based Matching Score
International Journal of Computer Vision
Multi-view stereo beyond lambert
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
A Moving Grid Framework for Geometric Deformable Models
International Journal of Computer Vision
A Statistical Overlap Prior for Variational Image Segmentation
International Journal of Computer Vision
3D Topology Preserving Flows for Viewpoint-Based Cortical Unfolding
International Journal of Computer 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
Technical Section: Interactive free-form level-set surface-editing operators
Computers and Graphics
Topology noise removal for curve and surface evolution
MCV'10 Proceedings of the 2010 international MICCAI conference on Medical computer vision: recognition techniques and applications in medical imaging
Fully deformable 3D digital partition model with topological control
Pattern Recognition Letters
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms
Journal of Mathematical Imaging and Vision
A multiple object geometric deformable model for image segmentation
Computer Vision and Image Understanding
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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 the genus of the initial active contour (i.e. its number of handles) is preserved. 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.