图像Retinex问题的方法及应用

兰州大学机构库 >数学与统计学院

	图像Retinex问题的方法及应用
Alternative Title	The Methods for Image Retinex Problem and Applications
	杨雪
Subtype	博士
Thesis Advisor	黄玉梅
	2020-05-17
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	理学博士
Degree Discipline	计算数学
Keyword	Retinex理论 Retinex问题反射图像光照图像变分方法线性互补问题模系迭代方法高动态范围图像交替迭代法秩最小化矩阵填充图像配准
Abstract	Retinex理论解释了人类视觉感知物体色彩的原理. 该理论表明尽管从物体到达人眼的可见光是物体反射率和光照值的乘积, 但人类视觉系统感知到的物体色彩只和物体固有的反射率有关, 与光照条件无关. 因而在不同光照条件下, 人眼感知到的物体色彩是不变的. 然而, 相机等图像设备记录到的物体图像像素值是由物体反射率和光照值的乘积决定的, 因而在不同光照条件下得到的物体图像的色彩是不同的. Retinex问题的目标是要利用在一定光照条件下拍摄到的物体的图像, 构造有效方法获取尽可能反映物体真实色彩的物体反射率所对应的反射图像以及光照值对应的光照图像. Retinex问题在图像增强、阴影去除、遥感图像校正和目标选择与跟踪等很多图像领域有着广泛的应用. 本论文主要研究了解决Retinex问题的方法及其在高动态范围图像合成中的应用. 自Retinex理论提出以来, Retinex问题得到了广泛的研究, 并构造了很多有效的方法, 比如随机路径方法、递归方法、中心环绕方法、偏微分方程方法和变分方法等. 变分方法是近年来提出的求解Retinex问题的一种重要方法. 本论文中, 假设反射图像和光照图像是空间光滑的, 我们构造了求解Retinex问题的一个变分模型, 该模型包含反射率值和光照值需要满足的物理约束条件. 我们证明了该变分模型等价于一个矩阵为对称正定矩阵的线性互补问题, 并采用不精确模系迭代方法求解了此线性互补问题. 在不精确模系迭代方法的每步迭代中, 需要求解一个大型稀疏线性方程组, 由于该方程组的系数矩阵结构的特殊性, 其解是通过求解只有其一半大小的线性方程组得到的. 同时, 我们证明了用不精确模系迭代方法求解所得到的线性互补问题时的收敛性. 数值实验表明, 所提出的方法可以快速求解线性互补问题, 得到反射图像. 当用模系迭代方法求解矩阵为对称半正定矩阵的线性互补问题时, 通过分析极小范数问题的解与线性互补问题的解之间的关系, 以及矩阵为对称半正定矩阵的线性互补问题的解的性质, 给出了用模系迭代方法求解矩阵为对称半正定矩阵的线性互补问题的收敛性分析. 我们也证明了不精确模系迭代方法的收敛性. 利用模系迭代方法, 我们求解了一个由Retinex问题变分模型转化得到的矩阵为对称半正定矩阵的线性互补问题. 数值实验结果表明计算结果和理论分析是一致的, 并且得到了Retinex问题的高质量解. 考虑了高动态范围图像合成问题, 给出了一个基于Retinex方法的高动态范围图像合成模型及求解方法. 在拍摄场景时, 由于硬件的限制, 相机所获得的图像中场景的亮度范围要比场景真实的亮度范围小很多. 高动态范围图像是可以显示场景更大范围的亮度和细节的图像. 获得高动态范围图像的主要方法是利用多幅不同曝光的图像, 合成能够反映所拍摄场景真实色彩的高动态范围图像. 高动态范围图像中的亮度和Retinex理论中从图像分离出来的光照紧密相关. 在本论文中, 我们利用反射图像和光照图像各自的性质和多幅不同曝光图像的光照图像构成的光照矩阵的低秩性, 构造了矩阵秩最小化的高动态范围图像合成模型, 并设计了交替迭代法求解该模型. 在数值实验中, 考虑了静态场景和有运动物体的场景的高动态范围图像合成问题. 实验结果表明所提方法能较好的去除图像中的噪声, 保存图像的细节, 并有效的解决高动态范围图像合成中的配准问题, 去除高动态范围图像合成中产生的鬼影.
Other Abstract	Retinex theory explains how the human visual system perceives colors of objects. This theory manifests that even though the amount of visible light of an object reaching the eyes is the product of reflectance and illumination, the colors of the object that human vision perceives depend only on the intrinsic reflectance of the object while are unrelated to the illumination amount on the object. Therefore, human visual system can identify the same colors of a given object under varying illumination conditions. However,the image intensity of an object recorded by image acquisition equipmentssuch ascameras is determined by the product ofreflectance and illumination, so the object's colors in the recorded imagevary with varied illuminations. By using the image obtained under a certain illumination, the purpose of the retinex problem is to find efficient methods to recoverthe reflectance that can reveal the true colors of the object, orthe illumination. Applications of the retinex problem exist in broad imaging areas such as image enhancement, shadow removal, remote sensing image correction, and target selection and tracking. In this paper, we mainly studythe methods for retinex problem and its applications in high dynamic range image synthesis. Since the retinex theory was proposed, retinex problem has been widely studied, and many effectivemethods for the retinex problem have been proposed in the literature, these methods include the random path methods, the recursive methods, the center-surround methods, the partial differential equation methods and the variational methods. The variational methods are an important kind of methods developed in recent years. In this paper, by assuming spatial smoothness priors onboth reflectance andillumination, we propose a variational modelwith the physical constraints imposed on reflectance values and illuminations. We show that the proposed model is equivalent to a linear complementarity problem with symmetric positive definite matrix, and an inexact modulus iteration method is applied to solve it. A large sparse linear system of equations arises in the inexact modulus iteration method. By utilizing the special structure of the coefficient matrix, the solution of the linear system is obtained by solving a smaller linear system of only half of the unknowns. The convergence of the inexact modulus iteration method for solving the linear complementarity problem for the proposed model is also demonstrated. The experiments showthatthe proposed method is very fast. The linear complementarity problems with symmetric positive semidefinite matrix is solved by the modulus iteration method andthe convergenceis demonstrated by analyzing the relations between the solutions of the norm minimization problem and the solutions of the linear complementarity problem, and the properties of the solutions of the linear complementarity problem with symmetric positive semidefinite matrix. The convergence of the inexact modulus iteration method for solving the linear complementarity problem with symmetric positive semidefinite matrix is also demonstrated. We apply the modulus iteration method to solve the linear complementarity problem with symmetric positive semidefinite matrix resulted from a model for retinex problem. Experiments numerically show the effectiveness of the proposed method for retinex problem and the convergence of the modulus iteration method for solving the linear complementarity problem with symmetric positive semidefinite matrix. We also consider the high dynamic range image synthesis problem.A retinex-based high dynamic range image synthesis model and its solving methods are presented. When we photograph a scene, the recorded imagescan not represent the whole brightness levels of the scene due to the limited capacity of thehardwareof cameras. The images that can represent much greater range of brightness levels and preservemore details of the scene than those recorded images are called high dynamic range images.The generalapproach is to capture multiple images of the scene with different exposures and combine them to generate a high dynamic rangeimage that can reveal the true colorsof the scene. The brightness of the high dynamic range image is closely related to the illuminationsseparated from the recordedimagesin retinex theory. In this paper, we propose a retinex-based high dynamic range image synthesis model based on the properties of the reflectance and illumination, and the low rank property of the illumination matrix composed by illuminations separated from multiple images taken with different exposures,and an alternating iterative method is designed to solve the proposed model. The high dynamic range image synthesis problemsof static scenes and scenes with moving objects are considered in the experiment. The results show that the proposed method can remove the noises in images effectively, preserve the details of images, and produce the state-of-the-art performance in image alignment and removing the ghost artifacts.
Pages	89
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/463348
Collection	数学与统计学院
Affiliation	数学与统计学院
First Author Affilication	School of Mathematics and Statistics
Recommended Citation GB/T 7714	杨雪. 图像Retinex问题的方法及应用[D]. 兰州. 兰州大学,2020.

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