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Title: Transformations based on continuous piecewise-affine velocity fields

Here, 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.
ORCiD logo [1] ;  [2] ;  [1] ;  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  2. DTU Compute, Kongens Lyngby (Denmark)
Publication Date:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Additional Journal Information:
Journal Volume: 39; Journal Issue: 12; Journal ID: ISSN 0162-8828
Research Org:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)
Contributing Orgs:
• O. Freifeld, K. Batmanghelich, and J.W. Fisher III are with the Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Tech-nology, Cambridge MA 02319, USA. E- mail: {freifeld, kayhan, Fisher} • S. Hauberg is with the Section for Cognitive Systems, DTU Compute, Kongens Lyngby, Denmark 2800. E- mail:
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; trajectory; computational modeling; distribution functions; histograms; computer vision; biomedical imaging; complexity theory
OSTI Identifier: