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.
|Journal||I E E E Transactions on Pattern Analysis and Machine Intelligence|
|Publication status||Published - 2017|
- Continuous piecewise-affine velocity fields
- Spatial transformations
Freifeld, O., Hauberg, S., Batmanghelich, K., & Fisher, J. W. (2017). Transformations Based on Continuous Piecewise-Affine Velocity Fields. I E E E Transactions on Pattern Analysis and Machine Intelligence, 39(12), 2496-2509. https://doi.org/10.1109/TPAMI.2016.2646685