TY - GEN
T1 - Highly-expressive spaces of well-behaved transformations
T2 - 15th IEEE International Conference on Computer Vision, ICCV 2015
AU - Freifeld, Oren
AU - Hauberg, Soren
AU - Batmanghelich, Kayhan
AU - Fisher, John W.
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/17
Y1 - 2015/2/17
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84973902150&partnerID=8YFLogxK
U2 - 10.1109/ICCV.2015.333
DO - 10.1109/ICCV.2015.333
M3 - Conference contribution
AN - SCOPUS:84973902150
T3 - Proceedings of the IEEE International Conference on Computer Vision
SP - 2911
EP - 2919
BT - 2015 International Conference on Computer Vision, ICCV 2015
PB - Institute of Electrical and Electronics Engineers
Y2 - 11 December 2015 through 18 December 2015
ER -