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.
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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 Xiamen Youth Innovation Funds (No. 3502Z20206029). Yongjie Jessica Zhang was supported in part by NSF CMMI-1953323 and a Honda grant.
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Juan Cao is an associate professor in the School of Mathematical Sciences, Xiamen University, China. She received her Ph.D. degree in applied mathematics from Zhejiang University, China, in 2009. Her research interests include computer aided geometric design, and computer graphics.
Xiaoyi Zhang received her B.S. degree from Soochow University in 2018, and M.S. degree from Xiamen University in 2021. She is currently an engineer in Vivo. Her research interests include computer graphics and image processing.
Jiannan Huang received his B.S. degree from Ningxia University in 2015, and M.S. degree from Xiamen University in 2018. He is currently an engineer in Xiamen Road and Bridge Information Engineering Co. Ltd. His research interests include computer aided geometric design and computer graphics.
Yongjie Jessica Zhang is the George Tallman Ladd and Florence Barrett Ladd Professor of Mechanical Engineering at Carnegie Mellon University with a courtesy appointment in the Department of Biomedical Engineering. She received her B.Eng. degree in automotive engineering and M.Eng. degree in engineering mechanics from Tsinghua University, China, and M.Eng. degree in aerospace engineering and engineering mechanics and Ph.D. degree in computational engineering and sciences from the Oden Institute, the University of Texas at Austin. Her research interests include image processing, computational geometry, mesh generation, finite element methods, isogeometric analysis, data-driven simulation, and their applications in computational biomedicine, materials science, and engineering.
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Cao, J., Zhang, X., Huang, J. et al. Polygonal finite element-based content-aware image warping. Comp. Visual Media 9, 367–383 (2023). https://doi.org/10.1007/s41095-022-0283-7
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DOI: https://doi.org/10.1007/s41095-022-0283-7