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Transformations Based on Continuous Piecewise-Affine Velocity Fields

1Department of Computer Science, Ben-Gurion University, Be'er Sheva, Israel.
2Section for Cognitive Systems, DTU Compute, Kongens Lyngby, Denmark.
3Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA.
IEEE Computer Society
Publication Date:
IEEE Trans Pattern Anal Mach Intell
Volume Number:
Issue Number:
IEEE Trans Pattern Anal Mach Intell. 2017 Dec;39(12):2496-509
PubMed ID:
Spatial transformations, continuous piecewise-affine velocity fields, diffeomorphisms, tessellations, priors, MCMC
Appears in Collections:
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Freifeld O., Hauberg S., Batmanghelich K., Fisher J.W. Transformations Based on Continuous Piecewise-Affine Velocity Fields. IEEE Trans Pattern Anal Mach Intell. 2017 Dec;39(12):2496-509 PMID: 28092517. PMCID: PMC5889303.
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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.

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