SIAM Journal on Scientific and Statistical Computing
A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
Iterative point matching for registration of free-form curves and surfaces
International Journal of Computer Vision
Rigid, affine and locally affine registration of free-form surfaces
International Journal of Computer Vision
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part IV
3D Statistical Shape Models Using Direct Optimisation of Description Length
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
The Trimmed Iterative Closest Point Algorithm
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 3 - Volume 3
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
Statistical variability in nonlinear spaces: application to shape analysis and dt-mri
Statistical variability in nonlinear spaces: application to shape analysis and dt-mri
2D-Shape Analysis Using Conformal Mapping
International Journal of Computer Vision
Python for Scientific Computing
Computing in Science and Engineering
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Large Deformation Diffeomorphic Metric Curve Mapping
International Journal of Computer Vision
Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal Datasets
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Shape Analysis of Elastic Curves in Euclidean Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parameterization-invariant shape statistics and probabilistic classification of anatomical surfaces
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Estimation of smooth growth trajectories with controlled acceleration from time series shape data
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
SIAM Journal on Imaging Sciences
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation
International Journal of Computer Vision
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We present a numerical algorithm for a new matching approach for parameterisation independent diffeomorphic registration of curves in the plane, targeted at robust registration between curves that require large deformations. This condition is particularly useful for the geodesic constrained approach in which the matching functional is minimised subject to the constraint that the evolving diffeomorphism satisfies the Hamiltonian equations of motion; this means that each iteration of the nonlinear optimisation algorithm produces a geodesic (up to numerical discretisation). We ensure that the computed solutions correspond to geodesics in the shape space by enforcing the horizontality condition (conjugate momentum is normal to the curve). Explicitly introducing and solving for a reparameterisation variable allows the use of a point-to-point matching condition. The equations are discretised using the variational particle-mesh method. We provide comprehensive numerical convergence tests and benchmark the algorithm in the context of large deformations, to show that it is a viable, efficient and accurate method for obtaining geodesics between curves.