A Reparameterisation Based Approach to Geodesic Constrained Solvers for Curve Matching

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...

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Vydáno v:International journal of computer vision Ročník 99; číslo 1; s. 103 - 121
Hlavní autoři: Cotter, Colin J., Clark, Allan, Peiró, Joaquim
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.08.2012
Springer
Springer Nature B.V
Témata:
Algorithms
Analysis
Applied sciences
Artificial Intelligence
Computer Imaging
Computer Science
Computer science; control theory; systems
Constraints
Correspondence
Deformation
Exact sciences and technology
Image Processing and Computer Vision
Matching
Mathematical analysis
Mathematical models
Mathematical optimization
Nonlinearity
Numerical analysis
Pattern Recognition
Pattern Recognition and Graphics
Pattern recognition. Digital image processing. Computational geometry
Principal components analysis
Registration
Studies
Topological manifolds
Velocity
Vision
Vision systems
Computational anatomy
Geodesic shooting
Curve registration
Diffeomorphism
Image registration
Equation of motion
Anatomy
Modeling
Particle method
Point estimation
Geodesic
Variational calculus
Hamiltonian mechanics
Mesh method
Hamiltonian
Numerical convergence
Numerical algorithm
ISSN:0920-5691, 1573-1405
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Shrnutí: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.
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ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-012-0520-0