Combinatorial Optimization Methods for Computer Vision and Bio-medical Image Analysis

用于制造、医疗保健、安全和多媒体的自动计算机/机器人视觉仍在很大程度上 “正在进行的工作”和相对较少的方法在真实数据上产生一致可靠的结果。在立体视觉、运动分析、计算机辅助诊断(如MRI、CT)和其他应用中，高分辨率体积图像的大小要求计算机视觉算法具有非常高的效率。尽管在过去的10-20年里取得了显著的进展，但视觉界仍然在广泛地研究新的理论和数学概念，这些新的理论和数学概念可能会导致图像分割、形状表示、模型拟合、立体以及许多其他低层问题的计算可行的方法，这些问题构成了所有计算机视觉系统的基础。我的研究集中在用于低层视觉的实用的计算效率和数学上可靠的模型。这一主题为创造性的跨学科研究提供了一个令人兴奋的基础，将最优化、统计物理、信息论、学习、应用微分几何和其他数学科学联系在一起。大多数低层视觉问题可以用基于信息的方法(例如最小描述长度原则)、统计物理的概念(例如后验能量)或微分几何(最小曲面)来表示为优化问题。我的研究重点是低层视觉中的数学实体模型和相应的快速优化方法，这些方法要么计算它们的全局最小值，要么计算一些有保证质量的近似值。这类优化问题是对离散组合算法和连续变分技术的最新水平的挑战。首先，研究表明，视觉中的许多问题本质上是困难的(NP-Hard)，因此必须寻求有效的近似。其次，在解决视觉和医学成像中常见的海量3D或4D图像时，所提出的优化算法的计算效率和可扩展性至关重要。

Automatic computer/robot vision for manufacturing, health care, security, and multi-media is still largely "work in progress" and relatively few methods produce consistently reliable results on real data. Sheer size of high-resolution volumetric images in stereo-vision, motion analysis, computer-assisted diagnosis (e.g. MRI, CT), and other applications demands very high level of efficiency from computer vision algorithms. Despite significant progress in the last 10-20 years, the vision community is still widely researching new theories and mathematical concepts that could lead to computationally feasible methods for image segmentation, shape representation, model fitting, stereo, and many other low-level problems forming the base for all computer vision systems. My research concentrates on practical computationally-efficient and mathematically solid models for low-level vision. This topic offers an exciting ground for creative interdisciplinary research linking optimization, statistical physics, information theory, learning, applied differential geometry, and other mathematical sciences. Most low-level vision problems can be formulated as optimization problems using either information-based methodology (e.g. minimum description length principle), or concepts from statistical physics (e.g. posterior energy), or differential geometry (minimum surface). The focus of my proposed research are mathematically solid models in low-level vision and the corresponding fast optimization methods computing either their global minimum or some guaranteed-quality approximation. Such optimization problems are a challenge for the state of the art in discrete combinatorial algorithms and continuous variational techniques. Firstly, it was shown that many problems in vision are intrinsically difficult (NP-hard), thus effective approximations must be explored. Secondly, computational efficiency and scalability of the proposed optimization algorithms is crucial when a solution is sought on huge 3D or 4D image volumes common in vision and medical imaging.