Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
IEEE Computer Graphics and Applications
Cortical Surface Reconstruction Using a Topology Preserving Geometric Deformable Model
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
Model-Based Object Recognition - A Survey of Recent Research
Model-Based Object Recognition - A Survey of Recent Research
An energy-driven approach to linkage unfolding
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Information-Theoretic Active Polygons for Unsupervised Texture Segmentation
International Journal of Computer Vision
A topology-preserving level set method for shape optimization
Journal of Computational Physics
Active Polyhedron: Surface Evolution Theory Applied to Deformable Meshes
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
More-Than-Topology-Preserving Flows for Active Contours and Polygons
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Proceedings of the twenty-second annual symposium on Computational geometry
Visualization and Measurement of the Cortical Surface
Journal of Cognitive Neuroscience
Active Contours Under Topology Control--Genus Preserving Level Sets
International Journal of Computer Vision
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
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We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface with respect to a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. The third is a method that dramatically improves the computational speed of the 3D topology preservation approach by creating a tree structure of the 3D surface and using a recursion technique. Experiments results show that the proposed approach can successfully unfold highly convoluted surfaces such as the cortex while preserving their topology during the evolution.