Highly-expressive spaces of well-behaved transformations: Keeping it simple

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations

Abstract

We propose novel finite-dimensional spaces of Rn ? Rn transformations, n ? {1, 2, 3}, derived from (continuously-defined) parametric stationary velocity fields. Particularly, we obtain these transformations, which are diffeomorphisms, by fast and highly-accurate integration of continuous piecewise-affine velocity fields, we also provide an exact solution for n = 1. The simple-yet-highly-expressive proposed representation handles optional constraints (e.g., volume preservation) easily and supports convenient modeling choices and rapid likelihood evaluations (facilitating tractable inference over latent transformations). Its applications include, but are not limited to: unconstrained optimization over monotonic functions, modeling cumulative distribution functions or histograms, time warping, image registration, landmark-based warping, real-time diffeomorphic image editing. Our code is available at https://github.com/freifeld/cpabDiffeo.

Original languageEnglish
Title of host publication2015 International Conference on Computer Vision, ICCV 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2911-2919
Number of pages9
ISBN (Electronic)9781467383912
DOIs
StatePublished - 17 Feb 2015
Externally publishedYes
Event15th IEEE International Conference on Computer Vision, ICCV 2015 - Santiago, Chile
Duration: 11 Dec 201518 Dec 2015

Publication series

NameProceedings of the IEEE International Conference on Computer Vision
Volume2015 International Conference on Computer Vision, ICCV 2015
ISSN (Print)1550-5499

Conference

Conference15th IEEE International Conference on Computer Vision, ICCV 2015
Country/TerritoryChile
CitySantiago
Period11/12/1518/12/15

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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