CAREER: Analysis and Modeling for Image Processing Problems

这位研究人员将与他的学生和合作者一起，解决图像处理和计算机视觉中的重要分析和计算问题，这些问题也出现在其他各种领域，如计算机图形学、人口动力学和材料科学。该研究计划的一个重要分析部分将侧重于更好地理解在不适定扩散方程中观察到的粗化现象，这些粗化现象在图像处理(在图像分割模型中出现)、颗粒流(它们描述颗粒材料中剪切带的形成)和种群动力学(它们对某些类型的细菌的聚集进行建模)等不同领域中遇到。研究计划的第二部分将开发新的数值算法，用于有效计算几何运动下的多相运动，几何运动是包含体积和表面张力项的能量的最陡峭下降。这些界面运动不仅在基本的图像处理和图像分割等视觉过程中经常遇到，而且在材料科学中也经常遇到，在材料科学中它们可以描述多晶材料中的晶界运动。在这个方向上将使用一些数值思想，包括水平集方法和它的一些新的替代方法。这些算法将在具有高度科学意义的大规模计算中进行测试，例如使用许多颗粒对材料中的颗粒生长进行三维模拟。此外，研究人员还将继续他的研究计划，将成功的图像处理模型扩展到计算机图形学中的表面处理。受该研究计划的结果影响的图像处理和计算机视觉任务包括图像去噪和分割，这是当从图像或视频中自动提取有用信息时需要的基本初步操作。图像去噪的目的是去除图像中的伪影和噪声，以便更可靠地执行后续操作。分割的目标是识别图像中被不同对象占据的部分。这些程序起主要作用的实际应用的例子包括医学成像、人脸识别以及目标识别和跟踪。从本研究计划的分析部分获得的见解将阐明为这些视觉任务开发的一些最受欢迎但不完全理解的技术的性质，从而允许更有效地使用这些技术。将作为该项目的一个主要部分开发的新计算方法将能够有效和准确地解决在这些计算机视觉应用中遇到的数值问题，从而减少从图像和视频中提取知识所需的计算机时间。这项研究计划的目标是计算机视觉中的数值问题，这些问题与材料科学中的一些核心问题中的数值问题有许多相似之处。这种联系将使新的计算方法有可能应用于材料中晶界运动的大规模模拟；这种计算能力是非常可取的，在预测材料的性能和可靠性方面将是无价的。

The investigator, together with his students and collaborators, will tackle important analytical and computational problems from image processing and computer vision that arise also in a variety of other fields, such as computer graphics, population dynamics, and materials science. A significant analytical component of the research program will focus on better understanding the coarsening phenomena observed in ill-posed diffusion equations that are encountered in such disparate fields as image processing (where they appear in models of image segmentation), granular flow (where they describe the formation of shear bands in granular materials), and population dynamics (where they model aggregation of certain types of bacteria). A second component of the research program will develop novel numerical algorithms for efficient computation of the motion of multiple phases under geometric motions arising as steepest descent for energies that contain bulk and surface tension terms. These interfacial motions are frequently encountered not only in fundamental image processing and vision procedures such as image segmentation, but also in materials science where they can describe grain boundary motion in polycrystalline materials. A number of numerical ideas will be utilized in this direction, including the level set method and some novel alternatives to it. The algorithms will be tested on large scale computations of high scientific interest, such as three dimensional simulations of grain growth in materials, using many grains. In addition, the investigator will continue his research program in extending successful image processing models to the context of surface processing in computer graphics.The image processing and computer vision tasks that will be impacted by results from this research program include image denoising and segmentation, which are fundamental preliminary operations that are needed whenever useful information is to be extracted from images or video automatically. The goal of image denoising is to remove artifacts and noise from images so that subsequent operations can be performed more reliably. The goal of segmentation is to identify parts of an image occupied by distinct objects. Examples of practical applications where these procedures play a primary role include medical imaging, face recognition, and target identification and tracking. Insights gained from the analytical component of this research program will elucidate the nature of some of the most popular but incompletely understood techniques developed for these vision tasks, and consequently allow more effective use of these techniques. The new computational methods that will be developed as a major part of the project will allow efficient and accurate solution of the numerical problems encountered in these computer vision applications, and thus reduce the computer time needed for knowledge extraction from images and video. The numerical issues from computer vision that will be targeted by this research program have a lot in common with numerical issues seen in some central problems in materials science. This connection will in particular make it possible to apply the new computational methods to large scale simulations of the motion of grain boundaries in materials; this computational capability is highly desirable and would be invaluable in predicting the performance and reliability of materials.