Highly-Expressive Spaces of Well-Behaved Transformations: Keeping It Simple

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

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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 ex-act 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.
Original languageEnglish
Publication date2015
Number of pages9
Publication statusPublished - 2015
Event15th International Conference on Computer Vision - Santiago, Chile
Duration: 11 Dec 201518 Dec 2015
Conference number: 15
http://pamitc.org/iccv15/

Conference

Conference15th International Conference on Computer Vision
Number15
CountryChile
CitySantiago
Period11/12/201518/12/2015
Internet address

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Cite this

Freifeld, O., Hauberg, S., Batmanghelich, K., & Fisher, J. W. (2015). Highly-Expressive Spaces of Well-Behaved Transformations: Keeping It Simple. Paper presented at 15th International Conference on Computer Vision, Santiago, Chile.