摘要
本文介绍由变分优化模型导出的偏微分方程(PDEs)模型与几何曲率流驱动扩散在图像恢复方面的应用,以及多种非线性异质扩散模型,讨论了PDEs模型在图像分析与处理方面的优点。理论与实验结果表明,要恢复得到高质量的图像,PDEs模型的利用是极为必要的。文中还介绍了求解PDEs模型的数值方案。其中,曲率计算是一个关键问题,其结果直接参与自适应扩散的控制。详细总结了基于有限差分和水平集方法,求解藕合非线性异质扩散模型方程的数值方案。追求高质量图像、高精度计算方法、降低计算复杂性是本文处理方法不断进步的发展动力。
In this paper, the evolution of partial differential equations (PDEs) and curvature driven flows(CDFs) for image restoration in computer vision and pattern recognition has been introduced which usually originate from variation models. Together with PDEs and CDFs, several nonlinear anisotropic diffusion models have been developed for noisy removal and image enhancement, which are very influential in 2D or volume image processing. The advantages of PDEs models are discussed which convince one that PDEs' method is indispensable for high quality regardless of heavy computational load. Miscellaneous numerical schemes are employed to solve PDEs, such as finite, difference, multigrid method, and finite element method. Curvature calculation is the key action for every numerical scheme. A detail numerical scheme for the couple nonlinear anisotropic equations has been concluded mainly based on finite difference and level-set methods. High quality and precision with less computational load is everlasting pursuit.
出处
《数学进展》
CSCD
北大核心
2003年第3期285-294,共10页
Advances in Mathematics（China）
基金
中国科学院知识创新工程重大方向项目(KZXCX2-309)
国家自然科学基金(19471006)
