Surgical Planning Laboratory - Brigham & Women's Hospital - Boston, Massachusetts USA - a teaching affiliate of Harvard Medical School

Surgical Planning Laboratory

The Publication Database hosted by SPL

All Publications | Upload | Advanced Search | Gallery View | Download Statistics | Help | Import | Log in

Transformations Based on Continuous Piecewise-Affine Velocity Fields

Institution:
1Department of Computer Science, Ben-Gurion University, Be'er Sheva, Israel.
2Section for Cognitive Systems, DTU Compute, Kongens Lyngby, Denmark.
3Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA.
Publisher:
IEEE Computer Society
Publication Date:
Dec-2017
Journal:
IEEE Trans Pattern Anal Mach Intell
Volume Number:
39
Issue Number:
12
Pages:
2496-509
Citation:
IEEE Trans Pattern Anal Mach Intell. 2017 Dec;39(12):2496-509
PubMed ID:
28092517
PMCID:
PMC5889303
Keywords:
Spatial transformations, continuous piecewise-affine velocity fields, diffeomorphisms, tessellations, priors, MCMC
Appears in Collections:
NA-MIC
Sponsors:
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Freifeld O., Hauberg S., Batmanghelich K., Fisher J.W. Transformations Based on Continuous Piecewise-Affine Velocity Fields. IEEE Trans Pattern Anal Mach Intell. 2017 Dec;39(12):2496-509 PMID: 28092517. PMCID: PMC5889303.
Downloaded: 297 times. [view map]
Paper: Download, View online
Export citation:
Google Scholar: link

We propose novel finite-dimensional spaces of well-behaved 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.

Additional Material
1 File (93.614kB)
Freifeld-IEEE Trans Pattern Anal Mach Intell2017-fig4.jpg (93.614kB)