Combinatorial Optimization for Computer Vision and Biomedical Image Analysis

自动计算机/机器人视觉用于制造、医疗保健、安全和多媒体是一个非常活跃的研究领域，但真实的数据性能在质量、速度或两者方面仍远未达到完美。由于各种数字媒体和计算资源的可用性激增，潜在应用程序的数量显着增加，但数据的大小和复杂性也随之增加。尽管在过去的10-15年中取得了重大进展，但计算机视觉和生物医学图像分析社区正在寻找新的算法和数学模型，即使是分割，重建，检测等基本问题。算法的鲁棒性、计算效率和可扩展性是至关重要的因素。在具有高维特征的大真实的数据背景下，高阶正则化约束的有效优化方法仍然是一个挑战。** 我的计算机视觉和生物医学图像分析方法主要基于离散模型和组合优化方法。我过去的研究证明了许多强大的组合算法（例如，图切割，a-扩展，设施定位等）。或离散近似方法（例如，基于边界优化、信赖域），在视觉和生物医学成像中的广泛问题中，为数学上合理的高阶图形模型计算全局最优或可证明的良好解。这些优化方法为N-D图像分割、多相机立体、纹理合成、运动分析、目标检测/识别和薄结构估计等难题带来了突破性的结果。** 有很多理由继续研究正则化的离散算法，这是我的长期目标。替代的连续方法只需要GPU实现来生成与离散方法相当的运行时间。它们也不稳定或可重复，这解释了缺乏公开可用的代码-与组合算法（从我的小组网站上每天有20-30次下载）相反。其他替代方法缺乏几何调整，使得不可能整合原则性结构/拓扑约束。我计划在未来五年内研究的问题涉及高阶先验的有效优化，结构化部分有序标记，基于曲率的血管提取，高维特征空间聚类的正则化约束，以及将原则性的快速多对象分割技术与基于核SVM和神经网络的对象分类机器学习方法相结合。

Automatic computer/robot vision for manufacturing, health care, security, and multi-media is a very active area of research, but real data performance is still far from perfect in quality, speed, or both. Due to explosion in availability of ever diverse digital media and computational resources, the number of potential applications grew significantly, but so did the size and complexities of the data. Despite significant progress in the last 10-15 years, the computer vision and biomedical image analysis communities are looking for new algorithms and mathematical models even for basic problems like segmentation, reconstruction, detection. Robustness, computational efficiency, and scalability of algorithms are crucial factors. Efficient optimization methods for high-order regularization constraints in the context large real data with high-dimensional features remain a challenge. ******My approach to computer vision and biomedical image analysis is largely based on discrete models and combinatorial optimization methods. My past research demonstrated many powerful combinatorial algorithms (e.g. graph cut, a-expansion, facility location, etc.) or discrete approximation methods (e.g. based on bound optimization, trust region) computing either globally optimal or provably good solutions for mathematically justified high-order graphical models in a wide range of problems in vision and biomedical imaging. These optimization methods lead to breakthrough results for difficult problems like N-D image segmentation, multi-camera stereo, texture synthesis, motion analysis, object detection/recognition, and thin-structure estimation. ******There are many reasons to continue research in discrete algorithms for regularization, which is my long term goal. Alternative continuous approaches require GPU implementations only to generate running times comparable to discrete methods. They are also not as stable or repeatable explaining lack of publicly available code - in contrast to combinatorial algorithms (with 20-30 daily downloads from my group's web site). Other alternative methodologies lack geometric justification making it impossible to integrate principled structural/topological constraints. The problems I plan to work on in the next five years are related to efficient optimization for high-order priors, structured partially-ordered labeling, curvature-based vessel extraction, regularization constraints for clustering in high-dimensional feature spaces, and integration of principled fast multi-object segmentation techniques with machine learning methodologies for object classification based on kernel SVM and neural networks.