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Transformations Based on Continuous Piecewise-Affine Velocity Fields.

Authors
  • Freifeld, Oren
  • Hauberg, Soren
  • Batmanghelich, Kayhan
  • Fisher, Jonn W
Type
Published Article
Journal
IEEE transactions on pattern analysis and machine intelligence
Publication Date
Dec 01, 2017
Volume
39
Issue
12
Pages
2496–2509
Identifiers
DOI: 10.1109/TPAMI.2016.2646685
PMID: 28092517
Source
Medline
License
Unknown

Abstract

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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