深度低秩的结构-纹理图像分割模型和算法研究

项目名称： 深度低秩的结构-纹理图像分割模型和算法研究

项目编号： No.61472257

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 计算机科学学科

项目作者： 徐晨

作者单位： 深圳大学

项目金额： 85万元

中文摘要： 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。

中文关键词： 图像分割；图像分解；变分；偏微分方程；低秩表示

英文摘要： 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.

英文关键词： image segmentation;image decomposition;variational calculus;partical differential equation;low-rank representation