Transformations Based on Continuous Piecewise-Affine Velocity Fields
Freifeld O, Haubert S, Fisher J III, Batmanghelich N, Transformations Based on Continuous Piecewise-Affine Velocity Fields. IEEE Trans Pattern Anal Mach Intell. 2017 Dec;39(12):2496-2509. Epub 2017 Jan 1. PubMed PMID: 28092517. doi: 10.1109/TPAMI.2016.2646685.
We propose novel finite-dimensional spaces of well-behaved Rn ! Rn 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.