Discrete optimization methods and their applications in computer vision

简单地说，计算机视觉就是教计算机看，也就是感知场景中出现了哪些物体，它们位于哪里，它们在哪里移动。自动处理视觉信息的能力导致了几乎无限数量的应用，从传统的应用，如工业检查、安全和监控、机器人导航，到较新的应用，如视频会议、虚拟旅行和电影业的特殊效果。每年都在开发新的应用程序。一种基于优化的计算机视觉方法特别有前途，并已被证明在适用于不同视觉领域方面相当成功。近年来，在立体匹配、图像分割、图像恢复、多视角重建等计算机视觉基本任务方面取得了巨大的进步，这在很大程度上要归功于有效的优化技术的发展。应该指出的是，最近的进展是由于优化算法本身，因为它们被应用到的大多数目标函数已经在计算机视觉中使用了很长时间，但是没有好的方法来优化它们，因此性能平平。我之前的大部分研究都致力于开发高效的优化算法，专门为计算机视觉问题设计的。与此同时，我对优化方法在特定计算机视觉任务中的应用非常感兴趣。我发现理论方法和实际应用之间存在着协同效应。正是在试图解决实际应用程序的过程中，人们发现了有趣的新优化问题。反过来，解决新的优化问题会导致实际应用程序性能的提高。我提出了两个研究努力，一个是针对基于优化技术的理论问题，另一个方向是优化技术的实际应用。这两个方向的研究是紧密交织在一起的。

Computer vision, simply stated, is about teaching computers to see, that is to perceive which objects are present in a scene, where they are located, and where they are moving. The ability to atomatically process visual information leads to a virtually unlimited number of applications, ranging from the traditional ones such as industrial inspection, security and surveillance, robot navigation, to the newer ones such as video conferencing, virtual travel, and special effects for the movie industry. New applications are being developed each year.An optimisation based approach to computer vision is particularly promising and has already proved quite successful in applicability across different vision domains. There has been a tremendous progress in recent years in such fundamental computer vision tasks as stereo correspondence, image segmentation, image restoration, multi-view reconstruction, in large part due to the development of effective optimisation techniques. It should be noted that the recent progress is due to the optimisation algorithms themselves, since most of the objective functions they are being applied to have been used in computer vision for a long time but without good means to optimise them, and, therefore, with mediocre performance. A large portion of my previous research has been devoted to developing efficient optimisation algorithms, designed specifically for computer vision problems. At the same time, I am very interested in applications of optimisation methods to specific computer vision tasks. I find that there is a synergy between the theoretical methods and practical applications. It is from trying to solve a practical application that one finds interesting new optimisation problems. In turn, solving a new optimisation problem leads to an improved  performance on a practical application. I propose two research efforts, one directed at the theoretical issues in optimisation based techniques, and the other direction is towards practical applications of optimisation techniques.  The research in these two directions is closely intertwined.