Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
International Journal of Computer Vision
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Shape Priors for Level Set Representations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
Level Set Evolution without Re-Initialization: A New Variational Formulation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Conformal Metrics and True "Gradient Flows" for Curves
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Generalized Gradients: Priors on Minimization Flows
International Journal of Computer Vision
International Journal of Computer Vision
Nonparametric shape priors for active contour-based image segmentation
Signal Processing
Cooperative Object Segmentation and Behavior Inference in Image Sequences
International Journal of Computer Vision
Towards recognition-based variational segmentation using shape priors and dynamic labeling
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
A geometric formulation of gradient descent for variational problems with moving surfaces
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
IEEE Transactions on Image Processing
Image segmentation with one shape prior - A template-based formulation
Image and Vision Computing
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The level set representation of shapes is useful for shape evolution and is widely used for the minimization of energies with respect to shapes. Many algorithms consider energies depending explicitly on the signed distance function (SDF) associated with a shape, and differentiate these energies with respect to the SDF directly in order to make the level set representation evolve. This framework is known as the "variational level set method". We show that this gradient computation is actually mathematically incorrect, and can lead to undesirable performance in practice. Instead, we derive the expression of the gradient with respect to the shape, and show that it can be easily computed from the gradient of the energy with respect to the SDF. We discuss some problematic gradients from the literature, show how they can easily be fixed, and provide experimental comparisons illustrating the improvement.