Journal article · Ahead of Print article
Transformations Based on Continuous Piecewise-Affine Velocity Fields
We propose novel finite-dimensional spaces of well-behaved transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), and supports convenient modeling choices such as smoothing priors and coarse-to-fine analysis.
Importantly, the proposed approach, partly due to its rapid likelihood evaluations and partly due to its other properties, facilitates tractable inference over rich transformation spaces, including using Markov-Chain Monte-Carlo methods. Its applications include, but are not limited to: monotonic regression (more generally, optimization over monotonic functions); modeling cumulative distribution functions or histograms; time-warping; image warping; image registration; real-time diffeomorphic image editing; data augmentation for image classifiers.
Our GPU-based code is publicly available.
Language: | English |
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Publisher: | IEEE |
Year: | 2017 |
Pages: | 2496-2509 |
ISSN: | 19393539 , 01628828 and 21609292 |
Types: | Journal article and Ahead of Print article |
DOI: | 10.1109/TPAMI.2016.2646685 |
ORCIDs: | Hauberg, Søren and 0000-0001-9816-9709 |
Continuous piecewise-affine velocity fields Diffeomorphisms Priors Spatial transformations Tessellations
Biomedical imaging Complexity theory Computational modeling Computer vision Distribution functions Histograms MCMC Spatial transformations, continuous piecewise-affine velocity fields, diffeomorphisms, tessellations, priors, MCMC Trajectory continuous piecewise-affine velocity fields diffeomorphisms priors tessellations