New PDE Based Models and Numerical Techniques in Level Set Surface Processing, Imaging Science and Materials Science

水平集表面处理、成像科学和材料科学中基于偏微分方程的新模型和数值技术

• 批准号: 0312222
• 负责人: Stanley Osher
• 金额: $ 78.67万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0312222&HistoricalAwards=false
• 关键词: New; PDE; Based; Models; Numerical

Stanley J. Osher and Luminita A. Vese The investigators together with junior faculty, postdoctoralfellows, and students develop novel and efficient computationaltechniques for partial differential equations of fourth orderarising in imaging science, including medical imaging, imageprocessing, computer vision, and graphics, as well as materialscience. They begin with analysis done on their previous TV modelby Yves Meyer. This gives a unique blend of nonlinear partialdifferential equation and functional analysis as well as new andvery useful models for image decomposition. This leads theinvestigators to the analysis of more general fourth orderequations used in imaging science, with geometric applicationsand interpretations, as well as new efficient computational andnumerical methods to approximate these and other related partialdifferential equations. Problems considered include imagedecomposition into cartoon plus texture, Wulff evolution ofshapes in crystal growth, image disocclusion by the Eulerelastica model, image restoration via geometry of level sets, aswell as reconstruction of surfaces from unorganized data points(such as LIDAR, LADAR, 3D cloud or geoscience data) in the formof patches belonging to the same unknown surface. This investigation dramatically advances thestate-of-the-art in material science (e.g., microchip design),image analysis, computer vision, and graphics. These fields areof great strategic value in the US information technologyindustry, in nanoscience, in homeland security, and in medicalimaging. The level set method and applications, developed by theinvestigators and collaborators, has impacted numerous areas oftechnology -- see, e.g., the Google website for close to 5,000hits on "Level Set Methods" with a spectacular range ofapplications from Hollywood graphics to underwater explosions tocontrol of passenger aircraft to developing new microchip designsand beyond. The investigators' new models reduce the burden oflaborious human operations for the processing of large-scale datasets, enhance the efficiency of domain scientists as well asordinary users, facilitate modeling and rendering tasks, andstreamline the pipeline of information and materials processing.

Stanley J. Osher和Luminita A. Vese 研究人员与初级教师，博士后研究员和学生一起为成像科学中的四阶偏微分方程开发新颖有效的计算技术，包括医学成像，图像处理，计算机视觉和图形学以及材料科学。 他们开始分析他们以前的电视模型由伊夫迈耶。 这给出了一个独特的混合非线性偏微分方程和功能分析以及新的和非常有用的模型图像分解。 这导致研究人员分析更一般的四阶方程用于成像科学，几何应用和解释，以及新的有效的计算和数值方法来近似这些和其他相关的偏微分方程。 所考虑的问题包括图像合成为卡通加纹理，Wulff演化的形状在晶体生长，图像的Eulerastica模型，图像恢复通过几何的水平集，以及重建的表面从无组织的数据点（如激光雷达，激光雷达，三维云或地球科学数据）的形式补丁属于同一个未知的表面。 这项研究极大地推进了材料科学的最新发展（例如，微芯片设计）、图像分析、计算机视觉和图形学。 这些领域在美国信息技术产业、纳米科学、国土安全和医学成像领域都具有重要的战略价值。 水平集方法和应用程序，由研究人员和合作者开发，已经影响了许多技术领域-见，例如，谷歌网站上的“水平集方法”的点击量接近5,000次，其应用范围非常广泛，从好莱坞的图形到水下爆炸，到客机的控制，再到开发新的微芯片设计等等。 研究人员的新模型减轻了处理大规模数据集的繁重人工操作的负担，提高了领域科学家和普通用户的效率，方便了建模和渲染任务，并简化了信息和材料处理的管道。