Author: Liu, Chaoyu
Title: New frameworks for image segmentation methods involving variational models and neural networks
Advisors: Qiao, Zhonghua (AMA)
Degree: Ph.D.
Year: 2023
Subject: Image processing -- Digital techniques
Neural networks (Computer science)
Hong Kong Polytechnic University -- Dissertations
Department: Department of Applied Mathematics
Pages: xiii, 84 pages : color illustrations
Language: English
Abstract: This thesis proposes several efficient methods to improve the performance of variational models and neural networks for image segmentation. Among them, an initialization method and three models with efficient minimization methods are proposed to tackle initialization and noise issues in traditional mathematical methods. Additionally, a new framework based on inverse evolution layers (IELs) is proposed to incorporate mathematical properties into neural networks.
The proposed initialization method is referred to as the Inhomogeneous Graph Laplacian Ini­tialization Method (IGLIM), which can provide much more reliable initial values for variational models than existing methods. One of the new variational models is proposed by integrating the Allen-Cahn term with a local binary fitting energy term to segment images with intensity inhomogeneity and noise. To solve the Allen-Cahn equation derived from the variational model, we adopt the Exponential Time Differencing (ETD) method for temporal discretization and the Central Finite Difference method for spatial discretization. In addition, we also proved the energy stability of proposed numerical schemes for our Allen-Cahn local binary fitting (ACLBF) model. Limited by the LBF term, ACLBF model is only applicable to binary segmentation. For multiphase segmentation, we incorporate the Allen-Cahn term into Chan-Vese model and propose the Allen-Cahn Chan-Vese model to settle the multi-phase image segmentation. The minimization process is similar to the ACLBF model, and the discrete maximum bound principle and energy stability are also proved for the proposed numerical schemes. Another variational model for multiphase segmentation is proposed based on a local variance force (LVF) term and a more efficient minimization algorithm called ICTM-LVF. With the LVF, the proposed model is also effective in segmenting images with noise. The ICTM-LVF is then designed to solve this model efficiently. This well-targeted minimization algorithm, developed from the Itera­tive Convolution-Thresholding Method (ICTM), enjoys energy-decaying property under some conditions and has much more efficient performance in segmentation.
For neural networks, a novel approach to incorporating PDE-based mathematical models into neural networks is proposed by designing novel regularization layers derived from the inverse processes of the evolution equations in mathematical models. These regularization layers can achieve specific regularization purposes and enable the neural networks to have corresponding properties of the mathematical models. The construction and implementation of these inverse evolution layers (IELs) are simple and can be easily designed on various physical evolutions and neural networks. Additionally, the design process can provide these layers with intuitive and mathematical interpretability. To demonstrate the effectiveness, efficiency, and simplicity of this approach, the heat-diffusion IELs are designed as an example to endow semantic segmentation models with smoothness. Furthermore, it is theoretically proven that the derived layers can be regarded as regularizers for a certain type of loss, and it is also proved that the outputs trained with heat-diffusion IELs will be closer to clean labels under some reasonable assumptions. The experimental results indicate that the IGLIM, two proposed variational models, and IELs can effectively and efficiently solve the initialization problem and noise issue in image segmentation.
Rights: All rights reserved
Access: open access

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