Functional Lifting 2.0: Efficient Convexifications for Imaging and Vision

功能性提升 2.0：用于成像和视觉的高效凸化

• 批准号: 394737018
• 负责人: Professor Dr. Daniel Cremers
• 金额: --
• 依托单位: Lehrstuhl für Informatik IX: Bildverarbeitung und Künstliche Intelligenz
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/394737018?language=en
• 关键词: Functional; Lifting; 2.0; Efficient; Convexifications

One of the most versatile and powerful tools for solving computer vision and image processing problems is the class of energy-based methods. The basic idea is to associate with every conceivable solution a cost - or energy - in such a way that low energy values correspond to good solutions. Unfortunately, most practically relevant problems inherently lead to non-convex energy functions, so that the computation of global minimizers becomes very challenging. Consequently, the solution quality in classical local minimization methods heavily depends on the initialization and the particular choice of algorithm. In this project, we will develop global methods that rely on a convexification of non-convex energies in high-dimensional spaces by means of functional lifting in order to find globally optimal solutions. Existing approaches implemented this lifting by discretizing the range into labels, ultimately limiting the solution accuracy. In contrast, this project will extend the applicability of recent sublabel-accurate lifting methods that greatly reduce the extra cost of obtaining an approximate global solution and allow to gradually take into account the non-convexities while exploiting convex parts in the energy. This allows to develop solvers that scale gracefully with the non-convexity of the problem, and allow to efficiently compute close-to-globally optimal solutions on a wide range of optimization problems.

解决计算机视觉和图像处理问题最通用，最强大的工具之一是基于能量的方法。基本思想是将每个可能的解决方案与成本或能量 - 低能值相对应的成本或能量联系在一起。不幸的是，大多数实际上相关的问题固有地导致了非凸能函数，因此全球最小化器的计算变得非常具有挑战性。因此，经典局部最小化方法中的解决方案质量在很大程度上取决于算法的初始化和特定选择。在这个项目中，我们将通过功能提升来开发依赖于高维空间中非凸能能量的凸化的全局方法，以找到全球最佳的解决方案。现有方法通过将范围离散到标签中，最终限制了解决方案的准确性，从而实现了这种提升。相比之下，该项目将扩大最近的Sublabel精确提升方法的适用性，这些方法大大降低了获得近似全球解决方案的额外成本，并允许逐渐考虑到非凸度的同时利用能量中的凸零件。这允许开发解决问题的求解器，以优雅地扩展问题，并允许在广泛的优化问题上有效计算几乎全球最佳解决方案。