Abstract
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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Orchard, J. (2005). Image Deformation Using Velocity Fields: An Exact Solution. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2005. Lecture Notes in Computer Science, vol 3656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11559573_55
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DOI: https://doi.org/10.1007/11559573_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29069-8
Online ISBN: 978-3-540-31938-2
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