Mathematical Sciences: Diffusion flows propagating with curature-dependent speed with applications to image processing

数学科学：以与结构相关的速度传播的扩散流及其在图像处理中的应用

• 批准号: 9405808
• 负责人: Vladimir Oliker
• 金额: $ 3.7万
• 依托单位: Emory University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9405808&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Diffusion; flows; propagating

9405808 Oliker A continuing investigation of nonlinear diffusion flows propagating with speed depending on mean, Gauss, and other curvature functions is proposed. Such diffusion processes play a critical role in models of phase transitions, flame propagation, material wearing, signal and image processing, and others. Questions of existence, uniqueness, onset of singularities, and asymptotic properties will be studied. Efficient and robust algorithms for computing diffusion flows will be developed and tested. The results will be applied to improve existing and develop new computational algorithms and codes for image and signal processing. It is anticipated that the developed image processing codes will have a variety of important applications in communications, medicine, target identification, and Global Change studies, especially for denoising images distorted by atmospheric turbulence.

9405808 OLIKER提出了根据平均值，高斯和其他曲率函数对非线性扩散流动的持续研究。 这种扩散过程在相变，火焰传播，材料磨损，信号和图像处理等模型中起关键作用。 将研究存在的问题，独特性，奇异性发作和渐近特性。 将开发和测试用于计算扩散流的高效且健壮的算法。 结果将应用于改善现有的并开发新的计算算法以及用于图像和信号处理的代码。 可以预料，开发的图像处理代码将在通信，医学，目标识别和全球变化研究中具有多种重要应用，尤其是在使大气湍流扭曲的图像变形时。