Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
A Projection Operator for the Restoration of Divergence-Free Vector Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A nonlinear variational problem for image matching
SIAM Journal on Scientific Computing
Computing optical flow via variational techniques
SIAM Journal on Applied Mathematics
Reliable Estimation of Dense Optical Flow Fields with Large Displacements
International Journal of Computer Vision
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Using Prior Shapes in Geometric Active Contours in a Variational Framework
International Journal of Computer Vision
MAP MRF Joint Segmentation and Registration
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
A New Image Registration Technique with Free Boundary Constraints: Application to Mammography
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part IV
A Variational Approach to Multi-Modal Image Matching
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Knowledge-based Registration & Segmentation of the Left Ventricle: A Level Set Approach
WACV '02 Proceedings of the Sixth IEEE Workshop on Applications of Computer Vision
Segmentation of Myocardium Using Velocity Field Constrained Front Propagation
WACV '02 Proceedings of the Sixth IEEE Workshop on Applications of Computer Vision
Discrete multiscale vector field decomposition
ACM SIGGRAPH 2003 Papers
A Variational Framework for Joint Segmentation and Registration
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
TV Based Image Restoration with Local Constraints
Journal of Scientific Computing
Non-rigid registration using distance functions
Computer Vision and Image Understanding - Special issue on nonrigid image registration
Tracking Objects Using Density Matching and Shape Priors
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Variational Space-Time Motion Segmentation
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity
Journal of Mathematical Imaging and Vision
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
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
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
An Optimal Control Formulation of an Image Registration Problem
Journal of Mathematical Imaging and Vision
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Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well. We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach.