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
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Generalized Gradients: Priors on Minimization Flows
International Journal of Computer Vision
International Journal of Computer Vision
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Coarse-to-Fine Segmentation and Tracking Using Sobolev Active Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Global Solutions of Variational Models with Convex Regularization
SIAM Journal on Imaging Sciences
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A Variational Method for Geometric Regularization of Vascular Segmentation in Medical Images
IEEE Transactions on Image Processing
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We present a convenient framework for Sobolev active contours and surfaces, which uses an implicit representation on purpose, in contrast to related approaches which use an implicit representation only for the computation of Sobolev gradients. Another difference to related approaches is that we use a Sobolev type inner product, which has a better geometric interpretation, such as the ones proposed for Sobolev active contours. Since the computation of Sobolev gradients for surface evolutions requires the solution of partial differential equations on surfaces, we derive a numerical scheme which allows the user to obtain approximative Sobolev gradients even in linear complexity, if desired. Finally, we perform several experiments to demonstrate that the resulting curve and surface evolutions enjoy the same regularity properties as the original Sobolev active contours and show the whole potential of our method by tracking the left ventricular cavity acquired with 4D MRI.