RUI: Variational and PDE based methods for image processing

RUI：基于变分和偏微分方程的图像处理方法

• 批准号: 0505729
• 负责人: Stacey Levine
• 金额: $ 13.99万
• 依托单位: Duquesne University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505729&HistoricalAwards=false
• 关键词: RUI; Variational; PDE; based; methods

This project will develop, analyze, and apply new models for solving three fundamental problems in image processing: (1) edge-preserving noise removal; (2) image decomposition into objects plus textures; (3) recovery of lost information through image interpolation (or 'image inpainting'). The main feature of this new class of models is their ability to isolate and detect in natural scenes target objects that are obstructed by noise, textures, or other occluding objects, without generating erroneous or misleading features in the process. The identification and/or development of false object boundaries has long been a challenge for edge-preserving image processing models; this project seeks to find a universal approach for solving this problem. These new models are based on variational methods and partial differential equations. The investigator will establish their mathematical validity, determine properties of their solutions, develop efficient and accurate numerical schemes for their implementation, and directly apply these models to solve critical problems in the sciences and engineering.Through existing collaborations with researchers in medical imaging, materials science, geology, pharmaceuticals, and optical character recognition, the investigator and undergraduate students will use these new models to solve key issues in science and technology. These problems include removing noise while isolating key medical features in highly degraded magnetic resonance images, identifying and analyzing the grain structure of nanoscale materials for optimizing high technology metals, and identifying land cover regions that are at high risk for hazards such as wildfires or flooding in remotely sensed images where the boundaries of these regions are obstructed by textures such as roads or topography. Currently, the only reliable methods for treating each of these problems depend on hand-drawn object boundaries. This is prohibitively time consuming on large data sets, so automating the boundary detection process will greatly enhance the state of the art. False object detection can be devastating in any one of these applications, so existing automated methods cannot be directly applied. This project seeks to find theoretically sound approaches that avoid this drawback while removing obstructions and accurately identifying target objects.

该项目将开发，分析和应用新模型来解决图像处理中的三个基本问题：（1）删除边缘的降噪； （2）将图像分解为对象加上纹理； （3）通过图像插值（或“图像插入”）恢复丢失的信息。 这类新型模型的主要特征是它们在自然场景中隔离和检测的能力，这些对象被噪声，纹理或其他遮挡物体阻塞，而无需在此过程中产生错误或误导性特征。 长期以来，对偏边的图像处理模型的识别和/或开发错误对象边界一直是一个挑战。该项目旨在找到解决此问题的通用方法。 这些新模型基于变异方法和部分微分方程。 研究者将建立其数学有效性，确定其解决方案的特性，为实施而开发有效，准确的数值方案，并直接应用这些模型来解决科学和工程中的关键问题。通过与医学成像，材料科学，地理学，药物科学，药品和光学性质认识的研究人员和研究人员的研究人员在研究中与研究人员和研究的新模型相关的研究人员，将这些模型用于这些新模型，并将这些模型用于这些新模型。 这些问题包括在高度降级的磁共振图像中隔离关键的医疗特征时消除噪音，识别和分析纳米级材料的谷物结构，以优化高科技金属，并识别出对野火的高风险或诸如野火或洪水的高风险的土地覆盖区域，例如这些区域被纹理或纹理界面的界限所阻碍的图像，例如纹理或构图。 当前，治疗这些问题的唯一可靠方法取决于手绘对象边界。 这在大型数据集上非常耗时，因此自动化边界检测过程将极大地增强技术状态。 错误的对象检测可能在这些应用程序中的任何一个中都是毁灭性的，因此无法直接应用现有的自动化方法。 该项目试图找到理论上合理的方法，以避免这种缺点，同时消除障碍物并准确识别目标对象。