深度低秩的结构-纹理图像分割模型和算法研究

As an interdisciplinary study in computer science and mathematics, this project focuses on solving the segmentation problems of the images containing both structure details and texture details. This kind of images are called as the structure-and-texture image. We seek to propose new models as well as some efficient algorithms to these models in the frameworks of fuzzy region competition and image decomposition. The proposed segmentation methods will make good balance between the effectiveness of generating good segmentation results and the efficiency of obtaining these results. The main contributions of our work are listed as follows. Firstly, to overcome the drawbacks of classical fuzzy based image segmentation models in which the regions of images are hard to be estimated correctly, the nonconvex regularizer and the functional of the gradient in the so-called Sobolev space are introduced to preserve and to enhance the geometrical structures of the segmentation results, respectively. Secondly, to overcome the computational complexity of the high dimension texture descriptors, in this project the method of image structure- and-texture decomposition is coupled into the segmentation models. To further improve the segmentation results, the structure components of the images will be measured by a nonconvex regularizer, and the texture components will be measured by a deep low-rank measurement. Thirdly, the iterative reweighting method and the semi-quadratic minimization method are used to find the solutions of the nonconvex models. The existences of the solutions and the choices of the best weight functions will also be discussed. This project will break some new grounds in theories and provide some new models and algorithms for some applications of the structure-and- texture images. This project can also achieve the applications using the fuzzy and nonconvex optimization methods in image segmentation.

本项目属于计算机与数学的交叉研究项目。项目拟在区域竞争框架下，对结构和纹理并存的图像(结构-纹理图像)，采用模糊和图像分解的方法，建立新的图像分割模型和算法，目的是获取图像各个区域更清晰的边缘以及提高分割的效率。主要创新点：1.传统的模糊分割方法虽有利于估计图像区域，但不利于估计确定性边缘。本项目拟采用非凸正则项和Sobolev空间的梯度泛函保持和增强分割的边缘几何结构；2.将图像结构-纹理分解方法耦合到图像分割模型中，并对图像的结构成份和纹理块成份分别引入非凸保边约束和低秩的非凸逼近(深度低秩)约束，既能有效刻画图像纹理区域，又能显著提高分割效率；3.建立新的迭代重加权方法求解非凸分割模型，并结合半二次极小化方法来研究最优权的选取问题。本项目预期的成果将为结构-纹理图像的分割提供新的模型、快速有效的算法以及相应的理论支撑，有效实现模糊理论与非凸优化方法在计算机图像分割中的应用。

本项目对图像分割和显著性检测问题中不同区域的边缘几何结构信息的保持、图像纹理成分的刻画、快速算法的设计等进行了研究。提出一种基于非凸半范约束的低秩与稀疏耦合的图像分割模型、基于非局部各向异性扩散方程的显著性检测模型、基于非局部张量扩散的显著性检测模型、一种多特征融合的显著性流模型、基于图像结构-纹理分解的图像分割模型，以及一种基于本征图像分解的图像分割模型。上述模型中，我们采用矩阵的S1/2范数而不是核范数（即矩阵的S1范数）度量矩阵的低秩程度，以及采用L1/2范数而不是L1范数度量图像的稀疏程度。用Schatten-q拟范数来松弛低秩子空间聚类模型中的秩函数，并证明了Schatten-q正则最小化问题的最优解可以通过一个广义的矩阵软阈值收缩算子表示。将视觉显著性目标检测过程建模为一个非局部各项异性扩散方程的两个阶段，在第一阶段，利用边界先验进行了由边界到全图像的背景扩散，通过排序的方法选择了部分显著性值高的元素作为初始显著性种子。在第二阶段，从显著性种子出发将显著性值扩散到全图像域。在第二阶段的显著性迭代扩散过程中对显著性种子作了更新和优化，消除了错误种子的影响，从而有效抑制了背景。为了克服传统的显著性模型只考虑点与点之间的扩散强度而没有考虑到扩散方向的问题，引入非局部扩散张量，以在控制扩散强度的同时考虑扩散方向问题。在主方向上抑制扩散从而保证了背景和前景之间的差异性，在其他方向上加快扩散速度，从而保证相似部分作为一个整体高亮检测出来。将本征图像分解和图像卡通-纹理分解分别耦合到基于模糊区域竞争的图像分割模型中，并用总广义变差分别约束图像的阴影成分和卡通成分。经过数值验证，上述所提方法皆获得了比传统方法更好的图像分割和显著性检测效果。