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 language | English |
|---|---|
| Publication date | 2015 |
| Number of pages | 9 |
| Publication status | Published - 2015 |
| Event | 15th International Conference on Computer Vision - Santiago, Chile Duration: 11 Dec 2015 → 18 Dec 2015 Conference number: 15 http://pamitc.org/iccv15/ |
Conference
| Conference | 15th International Conference on Computer Vision |
|---|---|
| Number | 15 |
| Country/Territory | Chile |
| City | Santiago |
| Period | 11/12/2015 → 18/12/2015 |
| Internet address |
Bibliographical note
© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, includingreprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.