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Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes. This enables simple and efficient implementation, but in turn, restricts the representation capability of the deformation, often leading to unsatisfactory warping results. We present a novel, flexible polygonal finite element (poly-FEM) method for content-aware image warping. Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image. This allows highly adaptive meshes and smoother warping with fewer degrees of freedom, thus significantly extending the flexibility and capability of the warping representation. Benefiting from the continuous formulation of image deformation, our poly-FEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations. We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-of-the-art methods.


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Polygonal finite element-based content-aware image warping

Show Author's information Juan Cao1,2( )Xiaoyi Zhang1,2Jiannan Huang1,2Yongjie Jessica Zhang3
School of Mathematical Sciences, Xiamen University, Xiamen361005, China
Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen 361005, China
Department of Mechanical Engineering, CarnegieMellon University, Pittsburgh, PA 15213, USA

Abstract

Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes. This enables simple and efficient implementation, but in turn, restricts the representation capability of the deformation, often leading to unsatisfactory warping results. We present a novel, flexible polygonal finite element (poly-FEM) method for content-aware image warping. Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image. This allows highly adaptive meshes and smoother warping with fewer degrees of freedom, thus significantly extending the flexibility and capability of the warping representation. Benefiting from the continuous formulation of image deformation, our poly-FEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations. We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-of-the-art methods.

Keywords:

image warping, finite element method (FEM), polygonal element, mesh generation
Received: 09 February 2022 Accepted: 08 March 2022 Published: 03 January 2023 Issue date: June 2023
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Publication history

Received: 09 February 2022
Accepted: 08 March 2022
Published: 03 January 2023
Issue date: June 2023

Copyright

© The Author(s) 2022.

Acknowledgements

We would like to thank the reviewers for their valuable comments. The research of Juan Cao was supported by the National Natural Science Foundation of China(Nos. 61872308, 61972327, and 62272402), and the XiamenYouth Innovation Funds (No. 3502Z20206029). YongjieJessica Zhang was supported in part by NSF CMMI-1953323 and a Honda grant.

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