RI: Medium: Collaborative Research: Graph Cut Algorithms for Domain-specific Higher Order Priors

最优化是一种表达和解决各种成像问题的强大范例。现代优化方法在涉及像素对之间相互作用的问题上取得了相当大的成功。这带来了重要的进展，但许多成像问题显然需要对高阶相互作用进行显式建模。这个项目正在通过拥有图形算法和计算机视觉专业知识的研究人员之间的密切合作来应对这一挑战。该项目专注于两个核心应用：磁共振图像重建和自然图像的边界检测。除了它们本身的兴趣之外，这些应用还与其他重要的成像问题密切相关，如fMRI失真校正、超分辨率、血管成像和道路检测。从计算的角度来看，具有高阶相互作用的优化问题本质上是困难的。对于具有特定性质的问题，可以降低计算复杂度。通过识别许多重要成像问题的共同性质，有可能设计出广泛适用的强大的优化方法。该项目汇集了计算机视觉和算法领域的研究人员。这种合作带来了计算机视觉和成像社区广泛感兴趣的新算法。这些算法有可能改变几类重要问题的解决方式。所有正在开发的算法都正在接受仔细的评估，它们的实现在Web存储库中广泛提供。在布朗、康奈尔和罗格斯大学举办的讲习班和小型课程促进了这些想法的传播。

Optimization is a powerful paradigm for expressing and solving a variety of imaging problems. Modern optimization methods have had considerable success on problems that involve interactions between pairs of pixels. This has lead to important advances, but many imaging problems clearly require explicit modeling of higher-order interactions. This project is addressing this challenge through a close collaboration between researchers with expertise in graph algorithms and computer vision. The project is focused on two core applications: MRI image reconstruction and boundary detection in natural images. Besides their innate interest, these applications are closely related to other important imaging problems such as fMRI distortion correction, super-resolution, angiography and road detection. Optimization problems with high-order interactions are inherently difficult from a computational point of view. The computational complexity can be reduced for problems with specific properties. By identifying common properties in many important imaging problems it is possible to design powerful optimization methods that are broadly applicable. The project is bringing together researchers in computer vision and algorithms. The collaboration is leading to new algorithms that are of broad interest to the computer vision and imaging communities. These algorithms have the potential to transform the way that several important classes of problems are solved. All of the algorithms being developed are being carefully evaluated, with their implementations made widely available on a web repository. Dissemination of the ideas is facilitated by workshops and mini-courses being organized at Brown, Cornell and Rutgers.