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。基本思想是将每一种可能的解决方案与成本或能源联系起来，使低能源值对应于好的解决方案。遗憾的是，大多数与实际相关的问题都不可避免地导致能量函数的非凸性，从而使得全局极小值的计算变得非常困难。因此，经典局部极小化方法的解质量在很大程度上依赖于算法的初始化和特定的选择。在这个项目中，我们将开发全局方法，这些方法依赖于高维空间中非凸能量的凸化，通过泛函提升来寻找全局最优解。现有的方法通过将范围离散为标签来实现这一提升，最终限制了解的准确性。相反，这个项目将扩展最近的子标签精确提升方法的适用性，这些方法极大地降低了获得近似整体解的额外成本，并允许在利用能量中的凸部分的同时逐渐考虑非凸性。这允许开发随问题的非凸性而优雅地扩展的求解器，并允许在广泛的优化问题上高效地计算接近全局最优解。