Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image processing: flows under min/max curvature and mean curvature
Graphical Models and Image Processing
International Journal of Computer Vision
Invariant geometric evolutions of surfaces and volumetric smoothing
SIAM Journal on Applied Mathematics
Volume-preserving mean curvature flow as a limit of a nonlocal Ginzburg-Landau equation
SIAM Journal on Mathematical Analysis
Regularization of ill-posed problems via the level set approach
SIAM Journal on Applied Mathematics
Co-dimension 2 Geodesic Active Contours for MRA Segmentation
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
Front Propagation and Level-Set Approach for Geodesic Active Stereovision
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
A PDE-Based Level-Set Approach for Detection and Tracking of Moving Objects
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Journal of Cognitive Neuroscience
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
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Level set methods provide a robust way to implement geometric flows, but they suffer from two problems which are relevant when using smoothing flows to unfold the cortex: the lack of point-correspondence between scales and the inability to implement tangential velocities. In this paper, we suggest to solve these problems by driving the nodes of a mesh with an ordinary Differential equation. We state that this approach does not suffer from the known problems of Lagrangian methods since all geometrical properties are computed on the fixed (Eulerian) grid. Additionally, tangential velocities can be given to the nodes, allowing the mesh to follow general evolution equations, which could be crucial to achieving the final goal of minimizing local metric distortions. To experiment with this approach, we derive area and volume preserving mean curvature flows and use them to unfold surfaces extracted from MRI data of the human brain.