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。其应用范围非常广泛，从传统的工业检测和机器人导航到较新的视频会议和电影行业的特效。 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签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，精确的最小化是一个NP难问题，只能找到一个近似的解决方案。因此，开发有效的最小化技术是必不可少的，以获得一个好的解决方案。 我计划开发更有效的方法来最小化二进制非次模能量，这是一个NP难问题。二进制能量是有用的各种问题，如图像分割，形状先验等，此外，任何多标签的能量可以转换为二进制能量。 因此，二元非次模能量形成了一类重要的能量来处理。在我们以前的工作中，我们探索了两种方法的基础上的信赖域和辅助功能的框架。对于大多数应用，信赖域比辅助函数方法更好，但辅助函数方法更快。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。最近，密集连接的CRF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，这些模型使用有效的最小化方法，并且可以联合训练。 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，自动分割不太可能在普及程度上超过用户辅助分割。但是，重要的是减少用户的工作量。我计划开发在大多数情况下需要最少用户帮助的细分工具，例如单击。 我计划继续研究形状先验分割。形状先验导致更准确的图像分割，因为它们排除了不可能的形状解决方案。在以前的工作中，我考虑了相当简单的通用形状先验，如凸性，对称性等，我将开发形状先验更具体。 拟议的研究旨在产生新的优化工具，并提高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的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.