A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Curvature Based Image Registration
Journal of Mathematical Imaging and Vision
A Level-Set Based Approach to Image Registration
MMBIA '00 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis
On the Incorporation of shape priors into geometric active contours
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
A Variational Framework for Joint Segmentation and Registration
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
Optimal registration of deformed images
Optimal registration of deformed images
Linear and Non-linear Geometric Object Matching with Implicit Representation
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Linear and Non-linear Geometric Object Matching with Implicit Representation
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
A topology-preserving level set method for shape optimization
Journal of Computational Physics
Coupled PDEs for Non-Rigid Registration and Segmentation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Image Registration with Guaranteed Displacement Regularity
International Journal of Computer Vision
Multiscale Joint Segmentation and Registration of Image Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mumford–Shah based registration: a comparison of a level set and a phase field approach
Computing and Visualization in Science
Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Combined Segmentation and Registration Framework with a Nonlinear Elasticity Smoother
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
SIAM Journal on Imaging Sciences
Simultaneous registration and segmentation of anatomical structures from brain MRI
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Global Regularizing Flows With Topology Preservation for Active Contours and Polygons
IEEE Transactions on Image Processing
Self-Repelling Snakes for Topology-Preserving Segmentation Models
IEEE Transactions on Image Processing
Journal of Scientific Computing
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In this paper, we present a new non-parametric combined segmentation and registration method. The shapes to be registered are implicitly modeled with level set functions and the problem is cast as an optimization one, combining a matching criterion based on the active contours without edges for segmentation (Chan and Vese, 2001) [8] and a nonlinear-elasticity-based smoother on the displacement vector field. This modeling is twofold: first, registration is jointly performed with segmentation since guided by the segmentation process; it means that the algorithm produces both a smooth mapping between the two shapes and the segmentation of the object contained in the reference image. Secondly, the use of a nonlinear-elasticity-type regularizer allows large deformations to occur, which makes the model comparable in this point with the viscous fluid registration method. In the theoretical minimization problem we introduce, the shapes to be matched are viewed as Ciarlet-Geymonat materials. We prove the existence of minimizers of the introduced functional and derive an approximated problem based on the Saint Venant-Kirchhoff stored energy for the numerical implementation and solved by an augmented Lagrangian technique. Several applications are proposed to demonstrate the potential of this method to both segmentation of one single image and to registration between two images.