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的最通用和最强大的工具之一是基于能量的方法。基本思想是将每一个可以想到的解决方案与成本或能量联系起来，使得低能量值对应于好的解决方案。不幸的是，大多数实际相关问题本质上都会导致非凸能量函数，因此全局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质量在很大程度上取决于初始化和算法的特定选择。在这个项目中，我们将开发依赖于高维空间中非凸能量凸化的全局方法，通过函数提升的方式来找到全局最优解。现有方法通过将范围离散化为标签来实现这种提升，最终限制了解决方案的准确性。相比之下，该项目将扩展最近的子标签精确提升方法的适用性，大大减少获得近似全局解决方案的额外成本，并允许在利用能量中的凸部分时逐渐考虑非凸部分。这允许开发能够随着问题的非凸性进行优雅扩展的求解器，并允许针对各种优化问题有效地计算接近全局最优的解决方案。