Quasi-conformal neural network (QC-net) with applications to shape matching

M.Phil.Shape matching is an important research problem with a wide range of applications in various fields, such as computer graphics, computer visions and medical imaging. Shape matching is sometimes referred to as registration. Its goal is to find a meaningful one-to-one point-wise dense correspondences between two associated shapes or images. For instance, find a meaningful registration between two corresponding anatomical structures is a crucial process for the disease analysis in medical imaging. Shape matching is also important in computer graphics for the simulation of 3D animations. Existing algorithms for shape matching or registration often rely on some mathematical models based on some assumptions of the desired matching. Different regularisation terms have been recently proposed, aiming to constrain the registration map to lie in some certain mapping spaces, such as the space of diffeomorphisms. Most of these models cannot take data information into consideration effectively. The computation time can also be a challenge, especially when shapes or images are of very high resolution. Recently, deep learning has demonstrated great successes in imaging, which incorporates features from big data to significantly improve the accuracy. Motivated by this, in this thesis, our goal is to build a deep neural network based on quasi-conformal theories, called QC-Net, to obtain diffeomorphic registration maps between corresponding data. QC-Net incorporates data information from training data. As such, QC-net can output a meaningful registration map based on the known data structure learnt from the network. The loss function of the QC-Net is carefully designed using the Beltrami coefficient, so that a quasi -conformal and hence homeomorphic registration map. To the best of our knowledge, it is the first work to build a neural network with homeomorphic output. Once the network has been trained, the registration map can be obtained efficiently in real-time. Extensive numerical experiments have been carried out, which demonstrate its effectiveness to compute bijective landmark-matching registration with high accuracy. Our proposed QC-Net has also been successfully applied to various real applications, such as medical image registration and human face matching.图形配准在不同领域都是一项重要的研究问题。它具有广泛的应用范围。例如计算机图形学，计算机视觉以及医学影像。图形配准有时也被称为注册。它的目的是为两个图形或者图像找到一个稠密的点对点的对应关系。例如在医学影像领域，为解剖结构找到有意义的配准对疾病分析是一项非常重要的部分。图形配准在计算机图形学中的仿真与动画中也非常重要。现存的图形配准（注册）算法通常是基于对期望匹配的假设。为了将配准映射限制在特定的映射空间，许多不同的约束项被提出了。微分同胚映射是其中一个例子。在配准问题中，时间消耗通常也是一个难点问题。特别是在图像或者图形具有很高分辨率的时候。最近，深度学习在图像领域取得了巨大的成就。结合来自于巨大数据量中得到的特征信息，预测结果也可以得到巨大的准确性。受到深度学习的启发，在这篇论文中，我们将基于拟共形理论构建一个深度神经网络模型以期它能够为对应的数据产生用于配准的微分同胚。我们将这个模型称为拟共形网络(QC-net)。QC-Net会使用数据信息并基于网络学习到的内容为相应的对象输出一个有意义的配准映射。我们用Beltrami系数仔细设计了QC-net的损失函数，基于此我们可以得到一个拟共形映射，也就是一个微分同胚的配准映射。一旦网络被训练完成，配准映射就可以被实时地输出。我们会在文中给出一些数值实验去展示网络计算满足标记点匹配的双射配准映射的准确度。我们提出的QC-net在不同的实际应用中也取得了突出的效果。比如医学图像配准和人脸配准。Zhang, Han.Thesis M.Phil. Chinese University of Hong Kong 2020.Includes bibliographical references (leaves 86-94).Abstracts also in Chinese.Title from PDF title page (viewed on January 5, 2022)