Finite Element Image Warping

Peter Kaufmann, Oliver Wang, Alexander Sorkine-Hornung, Olga Sorkine-Hornung, Aljoscha Smolic, Markus Gross

Finite Element Image Warping

Our unifying representation of image warping supports efficient adaptive meshing, high order basis functions, and more. (a) Original image, (b) automatic saliency map, (c) uniform scaling, (d) retargeting using existing methods (6767 degrees of freedom (DOF)), (e) retargeting using an adaptive mesh supported by our FEM framework (1325 DOF).


We introduce a single unifying framework for a wide range of content-aware image warping tasks using a finite element method (FEM). Existing approaches commonly define error terms over vertex finite differences and can be expressed as a special case of our general FEM model. In this work, we exploit the full generality of FEMs, gaining important advantages over prior methods. These advantages include arbitrary mesh connectivity allowing for adaptive meshing and efficient large-scale solutions, a well-defined continuous problem formulation that enables clear analysis of existing warping error functions and allows us to propose improved ones, and higher order basis functions that allow for smoother warps with fewer degrees of freedom. To support per-element basis functions of varying degree and complex mesh connectivity with hanging nodes, we also introduce a novel use of discontinuous Galerkin FEM. We demonstrate the utility of our method by showing examples in video retargeting and camera stabilization applications, and compare our results with previous state of the art methods.



We would like to thank Manuel Lang for helpful discussions and Feng Liu for providing a comparison to his stabilization method. Copyrights of the source videos belong to Mam- moth HD, Inc and ARS Film Production. Images were taken from the RetargetMe dataset. All copyrights belong to the respective owners.