Euler's Elastica and Curvature-Based Inpainting
Euler's Elastica and Curvature-Based Inpainting
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DOI：
10.1137/s0036139901390088
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Jianhong Shen;S. Kang;T. Chan
中科院分区：
文献类型：
--
作者：
Jianhong Shen;S. Kang;T. Chan
图像修复是一种特殊的图像修复问题，其中图像先验模型起着至关重要的作用。Euler’s elastica最初是由Mumford [algeaic Geometry and its Applications， Springer-Verlag, New York, 1994, pp. 491—506]作为曲线先验模型引入计算机视觉的。通过将弹性能量功能化，Masnou和Morel[第五届IEEE图像处理国际会议论文集，3 (1998),pp. 259—263]提出了一个基于弹性的变分图像绘制模型。目前的论文旨在促进其数学基础的发展，并研究其性质和与Bertalmio， Sapiro， Caselles和Ballester的早期工作的联系[SIGGRAPH 2000， ACM Press, New York， 2000]和Chan和Shen [J。视觉通讯。影像代表，12(2001)，第436—449页。提出了一种基于数值偏微分方程的计算方案，可以自动处理拓扑复杂的涂装域。
Image inpainting is a special image restoration problem for which image prior models play a crucial role. Euler's elastica was first introduced to computer vision by Mumford [Algebraic Geometry and its Applications, Springer-Verlag, New York, 1994, pp. 491--506] as a curve prior model. By functionalizing the elastica energy, Masnou and Morel [Proceedings of the 5th IEEE International Conference Image Processing, 3 (1998), pp. 259--263] proposed an elastica-based variational inpainting model. The current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of Bertalmio, Sapiro, Caselles, and Ballester [SIGGRAPH 2000, ACM Press, New York, 2000] and Chan and Shen [J. Visual Comm. Image Rep., 12 (2001), pp. 436--449]. A computational scheme based on numerical PDEs is presented, which allows the automatic handling of topologically complex inpainting domains.