Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiresolution elastic matching
Computer Vision, Graphics, and Image Processing
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
Landmark matching via large deformation diffeomorphisms
IEEE Transactions on Image Processing
| Hi-index | 0.00 |
In image deformation, one of the challenges is to produce a deformation that preserves image topology. Such deformations are called “homeomorphic”. One method of producing homeomorphic deformations is to move the pixels according to a continuous velocity field defined over the image. The pixels flow along solution curves. Finding the pixel trajectories requires solving a system of differential equations (DEs). Until now, the only known way to accomplish this is to solve the system approximately using numerical time-stepping schemes. However, inaccuracies in the numerical solution can still result in non-homeomorphic deformations. This paper introduces a method of solving the system of DEs exactly over a triangular partition of the image. The results show that the exact method produces homeomorphic deformations in scenarios where the numerical methods fail.