|Efficient Diffeomorphisms and Their Applications|
We propose novel finite-dimensional spaces of well-behaved Rn → Rn transformations. These transformations 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 such as 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, facilitate tractable inference over rich transformation spaces, including using methods based on Markov-Chain Monte-Carlo (MCMC). 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. Other applications include data augmentation for image classifiers. Finally, we provide a GPU-accelerated code.
People Involved: Oren Freifeld, Soren Hauberg, Kayhan Batmanghelich, John W. Fisher III
[ ICCV '15 paper ] [ ICCV '15 BibTex ] [ ICCV '15 Supplemental Material ] [ Preprint extending our ICCV '15 paper ] [ Preprint's supplemental material ] [ ICCV '15 Code 1: uses GPU; requires an NVIDIA card; written in Python+CUDA ] [ ICCV '15 Code 2: CPU-only; partial implementation; written in Julia ] [ ICCV '15 Video 1: Conditional warp ] [ ICCV '15 Video 2: spotlight ] [ AISTATS '16 paper ] [ AISTATS '16 Video ] [ AISTATS '16 code: Coming soon ] [ AISTATS '16 Datasets (AlignMNIST and AlignMNIST500) ] An example: An example with boundary conditions: An example with boundary conditions and volume preservation: An example for landmark-based inference: