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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Orchard, J. (2005). Image deformation using velocity fields: An exact solution. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3656 LNCS, pp. 439–446). https://doi.org/10.1007/11559573_55
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