Transformations based on continuous piecewise-affine velocity fields

Freifeld, Oren; Hauberg, Soren; Batmanghelich, Kayhan; Fisher, III, John W.

doi:10.1109/TPAMI.2016.2646685

Title: Transformations based on continuous piecewise-affine velocity fields

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Abstract

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.

Authors:

^[1]; Hauberg, Soren ^[2]; Batmanghelich, Kayhan ^[1]; Fisher, III, John W. ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
DTU Compute, Kongens Lyngby (Denmark)

Publication Date:: Wed Jan 11 00:00:00 EST 2017

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 Org.:: • 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}@csail.mit.edu • S. Hauberg is with the Section for Cognitive Systems, DTU Compute, Kongens Lyngby, Denmark 2800. E- mail: sohau@dtu.dk

OSTI Identifier:: 1367523

Grant/Contract Number:: NA0002534

Resource Type:: 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

Publisher:: IEEE

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; trajectory; computational modeling; distribution functions; histograms; computer vision; biomedical imaging; complexity theory

Citation Formats


                    Freifeld, Oren, Hauberg, Soren, Batmanghelich, Kayhan, and Fisher, III, John W. Transformations based on continuous piecewise-affine velocity fields.  United States: N. p., 2017. 
Web.  doi:10.1109/TPAMI.2016.2646685.

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                    Freifeld, Oren, Hauberg, Soren, Batmanghelich, Kayhan, & Fisher, III, John W. Transformations based on continuous piecewise-affine velocity fields.  United States.  https://doi.org/10.1109/TPAMI.2016.2646685

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                    Freifeld, Oren, Hauberg, Soren, Batmanghelich, Kayhan, and Fisher, III, John W. Wed .  
"Transformations based on continuous piecewise-affine velocity fields".  United States.  https://doi.org/10.1109/TPAMI.2016.2646685.  https://www.osti.gov/servlets/purl/1367523.

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@article{osti_1367523,

  title        = {Transformations based on continuous piecewise-affine velocity fields},

  author       = {Freifeld, Oren and Hauberg, Soren and Batmanghelich, Kayhan and Fisher, III, John W.},

  abstractNote = {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.},

  doi          = {10.1109/TPAMI.2016.2646685},

  journal      = {IEEE Transactions on Pattern Analysis and Machine Intelligence},

  number       = 12,

  volume       = 39,

  place        = {United States},

  year         = {Wed Jan 11 00:00:00 EST 2017},

  month        = {Wed Jan 11 00:00:00 EST 2017}

}

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