图像分割是图像处理中的一个基本问题, 是基于图像模式识别和图像理解的基础.图像分割已广泛应用于目标检测、医学诊断、对象追踪、智能交通等领域. 选择性分割和全局分割是两种常用的图像分割方法. 前者是将感兴趣的区域或目标从背景中分离出来, 后者是将所有前景目标从背景中分离出来. 近年来, 研究人员提出了大量的图像分割模型和算法. 其中, 基于变分模型的图像分割方法由于具有良好的数学理论基础受到广泛关注. 本文重点设计了选择性图像分割和全局图像分割的变分模型, 具体成果如下: 
       1）提出一个新的变分图像平滑模型和一个活动轮廓模型来进行选择性图像分割. 该方法包括两个阶段. 第一阶段是预处理步骤, 目的是平滑给定的图像, 从而减少噪声或杂乱背景对分割的影响. 第二阶段是对预处理后的图像进行选择性分割. 具体来说, 在第一阶段, 提出了一个保边的加权变分平滑模型, 该模型能较好地保留图像边缘, 滤除噪声和小尺度细节. 在第二阶段, 设计了一个改进的活动轮廓模型来实现选择性分割. 模型使用全局稀疏梯度场来刻画图像边缘, 因为它比传统的梯度算子对噪声具有更强的鲁棒性. 此外, 使用一组标记点来构造初始轮廓, 可以获得更有效和更准确地分割. 在真实医学图像上的大量实验表明, 所提出的平滑模型可以极大地促进第二阶段的处理, 并且无论在视觉评价还是定量评价方面, 所提方法的分割效果都显著优于相关方法. 
       2）提出了一个基于阈值的选择性分割方法. 为了方便阈值选择, 提出了一个新的图像平滑模型. 平滑模型由正则项和保真项组成, 其中正则项是基于一个训练好的即插即用去噪神经网络, 保真项引入依赖于目标区域内一组标记点的权重. 该平滑模型能在保护目标区域的同时, 有效地平滑其它区域. 大量的实验表明, 新的平滑模型有利于阈值选择和阈值分割, 得到的分割结果无论在视觉上还是定量评价上都明显优于相关的选择性分割方法. 
       3）提出了一个基于边缘和区域信息的全局分割方法, 该方法能有效分割噪声强、强度不均匀的图像. 首先使用一个现有的去噪器对原始图像进行预处理获得一幅平滑图像, 以避免噪声和弱边缘对后期边缘检测的影响. 然后对预处理后的平滑图像给出一个全局分割活动轮廓模型. 该模型包含三个保真项: 一个基于边缘的保真项和两个基于区域的保真项. 基于边缘的保真项是一个依赖平滑图像梯度的边缘停止函数, 驱使活动轮廓在目标的边界停止演化. 基于全局区域的保真项旨在最小化平滑图像与局部拟合图像之间的差异，而基于局部区域的保真项则考虑图像的点拟合. 为了保证水平集函数的光滑化, 采用高斯滤波对水平集函数进行正则化. 实验结果表明, 该模型对噪声和强度不均匀有很强的鲁棒性; 与相关的分割模型相比, 所提模型的分割精度有显著优势.  

    Image segmentation is a fundamental problem in image processing, and is the foundation of image based pattern recognition and image understanding. Image segmentation has been widely used in target detection, medical diagnosis, object tracking, intelligent transportation and other fields. Selective segmentation and global segmentation are two popular image segmentation tasks. The former one aims to separate the target regions or objects of interest from the background, while the later one aims to separate all objects from the background. In recent years, a large number of models and algorithms have been proposed. Among them, the variational models have been widely attended because of good mathematical explanation. In this thesis, we focus on designing variational models for selective image segmentation and global image segmentation. The specific achievements are as follows.
    1) A new variational image smoothing model and an active contour model are proposed for selective image segmentation. The proposed method consists of two stages. The first stage is a preprocessing step, which aims to smooth the given image, thus reducing influence of noise, or cluttered background on the segmentation. The second stage performs selective segmentation on the preprocessed image. For the first stage, a weighted variational smoothing model is proposed, which can preserve the edge of the image well and filter out noise and small scale details. For the second stage, a modified active contour model is designed to achieve selective segmentation. In the proposed active contour model, the global sparse gradient field is used to depict image edges, because it is more robust to noise than the traditional gradient operator. In addition, we use a set of marker points to construct the initial contour, which leads to more effective and accurate segmentation. Extensive experiments on real medical images show that, the proposed smoothing model can greatly facilitate the second stage, and the segmentation performance of the proposed method is significantly superior to relevant methods in terms of either visual assessment or quantitative evaluation. 
    2) A thresholding based selective segmentation method is proposed. To facilitate threshold selection, we propose a new image smoothing model. The smoothing model consists of a regularization term and a fidelity term, where the regularization term is based on a trained plug and play denoising neural network, and the fidelity term introduces weights dependent on a set of marker points in the target region. The smoothing model can effectively smooth out other regions while protecting the  target region. Extended experiments show that the new smoothing model effectively facilitate the threshold selection and the threshold segmentation, and the obtained segmentation results are significantly superior to that obtained by relevant selective segmentation methods in both visual and quantitative evaluation.
    3) Based on edge and region information, we present a global segmentation method, which can effectively segment images with strong noise and intensity inhomogeneity. First, an existing denoiser is applied to the original image to obtain a smooth image, hoping to reduce the influence of the noise and weak edges on the later edge detection. Then, an active contour model is given for global segmentation of the smoothed image. The model consists of three fidelity terms: one edge based and two region based. The edge based fidelity term is an edge stop function depending on the gradients of the smoothed image, forcing the active contour stop evolving at the boundary of the target. The global region-based fidelity term aims to minimized the discrepancy between the smoothed image and its local fitting image, while local region-based fidelity term considers pointwise image fitting. In order to ensure the smoothness of the level set function, Gaussian filter is used to regularize the level set function. Extended experiments show that the model has good robustness to noise and intensity inhomogeneity. Compared with relevant segmentation models, the proposed model also has significant advantages in segmentation accuracy.

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