Discrete Optimization Methods for Computer Vision

计算机视觉的目标是开发自动处理视觉信息的系统。应用范围很广，从传统的工业检查和机器人导航，到视频会议和电影特效等新应用。******马尔可夫随机场（MRF）和条件随机场（CRF）是解决计算机视觉中遇到的具有挑战性的标记问题的流行概率模型。出现的模型需要计算密集的能量最小化。对于许多有趣的模型，精确最小化是一个np困难问题，只能找到一个近似解。因此，开发有效的最小化技术对于获得良好的解决方案至关重要。******我计划开发更有效的方法来最小化二进制非模能量，这是一个np困难的问题。二值能量对于图像分割、形状先验等问题都很有用。此外，任何多标签能量都可以转换为二元能量。因此二元非模能量构成了一类需要处理的重要能量。在我们之前的工作中，我们探索了基于信任域和辅助功能框架的两种方法。对于大多数应用，信任域比辅助函数方法效果更好，但辅助函数方法速度更快。我计划扩展辅助函数方法，使其同样快速但更准确。******我还计划为密集连接的crf开发有效的优化算法。密集连接的crf最近越来越受欢迎，特别是因为它们可以与最近非常成功的深度卷积神经网络（cnn）结合成一个系统。我计划开发统一的CNN和密集连接的CRF模型，使用高效的最小化方法，可以联合训练。******交互式分割是医学图像处理中的一种常用工具。由于数据的不确定性，甚至在医学专家之间也存在分歧，自动分割不太可能超过用户辅助分割的普及程度。然而，减少用户的工作量是很重要的。我计划开发分段工具，在大多数情况下需要最少的用户帮助，例如一次点击。******我打算继续研究形状先验分割。形状先验的结果是更准确的图像分割，因为它们排除了不可能的形状解决方案。在之前的工作中，我考虑了相当简单的一般形状先验，如凹凸性，对称性等。我将开发更具体于形状的形状先验。******提出的研究旨在产生新的优化工具，并推进优化工具对计算机视觉问题的适用性。这反过来又会导致计算机视觉领域中实际问题的性能提高

The goal of computer vision is to develop systems that automatically process visual information. The applications are numerous, ranging from the traditional ones such as industrial inspection and robot navigation, to the newer ones such as video conferencing, and special effects for the movie industry.******Markov Random Fields (MRF) and Conditional Random Fields (CRF) are popular probabilistic models for solving challenging labelling problems that are encountered in computer vision. Models that arise require computationally intensive energy minimisation. For many interesting models, the exact minimisation is an NP-hard problem, and only an approximate solution can be found. Thus developing efficient minimisation techniques is essential for obtaining a good solution. ******I plan to develop more effective methods for minimisation of binary non-submodular energies, which is an NP-hard problem. Binary energies are useful for a variety of problems such as image segmentation, shape priors, etc. Furthermore, any mutli-label energy can be converted to a binary energy. Thus binary non-submodular energies form an important class of energies to handle. In our previous work, we explored two approaches based on the trust region and the auxiliary function frameworks. For most applications, trust region works better than the auxiliary function approach, but auxiliary functions approach is faster. I plan to extend the auxiliary functions approach so that it is as fast but more accurate. ******I also plan to develop effective optimisation algorithms for densely connected CRFs. Densely connected CRFs are gaining popularity recently, especially since they can be combined with the recently hugely successful deep convolutional neural networks (CNNs) into one system. I plan to develop unified CNN and densely connected CRF models that use efficient minimisation methods and can be trained jointly. ******Interactive segmentation is a popular tool in medical image processing. Due to uncertainly in the data, and disagreement even among the medical specialists, automatic segmentation is unlikely to overtake user assisted segmentation in popularity. However, it is important to reduce user effort. I plan to develop segmentation tools that require a minimal user assistance in most cases, for example a single click.******I plan to continue research on segmentation with shape priors. Shape priors result in more accurate image segmentations since they rule out impossible shape solutions. In previous work I considered rather simple generic shape priors such as convexity, symmetry, etc. I will develop shape priors that are more shape-specific. ******The proposed research is intended to produce novel optimisation tools and to advance the applicability of optimisation tools for computer vision problems. This, in turn, will lead to an improved performance for the practical problems in computer vision field.**