Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
International Journal of Computer Vision
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
A PDE-based fast local level set method
Journal of Computational Physics
Computer Vision and Image Understanding
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
International Journal of Computer Vision
Multi-camera Scene Reconstruction via Graph Cuts
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Variational Problems and PDE's on Implicit Surfaces
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
How To Deal with Point Correspondences and Tangential Velocities in the Level Set Framework
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geodesic active regions and level set methods for motion estimation and tracking
Computer Vision and Image Understanding
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
Designing Spatially Coherent Minimizing Flows for Variational Problems Based on Active Contours
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Reconciling Landmarks and Level Sets
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 04
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Multi-view stereo beyond lambert
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
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
An analysis of variational alignment of curves in images
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
Analysis of Two-Dimensional Non-Rigid Shapes
International Journal of Computer Vision
Fast Musculoskeletal Registration Based on Shape Matching
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
New Possibilities with Sobolev Active Contours
International Journal of Computer Vision
Shape Metrics Based on Elastic Deformations
Journal of Mathematical Imaging and Vision
Narrow band region-based active contours and surfaces for 2D and 3D segmentation
Computer Vision and Image Understanding
A Local Normal-Based Region Term for Active Contours
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Geodesics in Shape Space via Variational Time Discretization
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Stabilization of parametric active contours using a tangential redistribution term
IEEE Transactions on Image Processing
Variational B-spline level-set: a linear filtering approach for fast deformable model evolution
IEEE Transactions on Image Processing
Joint Estimation of Shape and Reflectance using Multiple Images with Known Illumination Conditions
International Journal of Computer Vision
Active Contour Method with Separate Global Translation and Local Deformation
ICIRA '09 Proceedings of the 2nd International Conference on Intelligent Robotics and Applications
Journal of Mathematical Imaging and Vision
Converting level set gradients to shape gradients
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Adaptive smoothness based robust active contours
Image and Vision Computing
New Possibilities in Image Diffusion and Sharpening via High-Order Sobolev Gradient Flows
Journal of Mathematical Imaging and Vision
A Continuum Mechanical Approach to Geodesics in Shape Space
International Journal of Computer Vision
International Journal of Computer Vision
A fully implicit framework for Sobolev active contours and surfaces
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
Pattern Recognition Letters
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Sensitivity filtering from a continuum mechanics perspective
Structural and Multidisciplinary Optimization
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This paper tackles an important aspect of the variational problem underlying active contours: optimization by gradient flows. Classically, the definition of a gradient depends directly on the choice of an inner product structure. This consideration is largely absent from the active contours literature. Most authors, explicitely or implicitely, assume that the space of admissible deformations is ruled by the canonical L 2 inner product. The classical gradient flows reported in the literature are relative to this particular choice. Here, we investigate the relevance of using (i) other inner products, yielding other gradient descents, and (ii) other minimizing flows not deriving from any inner product. In particular, we show how to induce different degrees of spatial consistency into the minimizing flow, in order to decrease the probability of getting trapped into irrelevant local minima. We report numerical experiments indicating that the sensitivity of the active contours method to initial conditions, which seriously limits its applicability and efficiency, is alleviated by our application-specific spatially coherent minimizing flows. We show that the choice of the inner product can be seen as a prior on the deformation fields and we present an extension of the definition of the gradient toward more general priors.