【作者】 谢可夫；

【导师】 罗安；

【作者基本信息】 中南大学 ， 控制理论与控制工程， 2007， 博士

【摘要】 量子衍生方法研究如何借鉴和利用量子理论的基本概念、原理和公理化数学体系来建立在当前计算机上实现的、用于解决某些具体问题的新方法或改进方法。量子衍生图像处理方法是量子衍生方法在图像处理领域的拓展，它为该领域的理论研究和技术实现提供了一种新的观念和思路。本文将量子理论作为一种基于量子力学基本假设集的公理化数学体系，应用该体系的数学原理创建和描述了所提出的各种图像处理方法。具体内容包括：应用量子态叠加和测量原理，改造传统的数学形态学。本文提出并构造用于形态运算的一种新的结构元素，即叠加态结构元素，并构造了基于叠加态结构元素的坍缩形态学运算。在坍缩形态学运算中，叠加态结构元素可随移动位置的改变调整其大小和形状，这种调整通过一个测量算子对叠加态结构元素的测量来实现。本文提出了一种根据图像局部特征生成测量算子的方法，在此基础上建立了图像的自适应形态滤波和自适应形态学边缘检测方法。计算机仿真结果表明，这种自适应形态滤波比传统的形态滤波有更强的噪声滤除能力，成功地解决了传统的形态滤波算法中结构元素的选择问题；自适应形态学边缘检测方法可以不需要预滤波，直接地从受噪声污染的图像中检测出图像的边缘信息，避免了传统处理方式中预滤波对图像边缘的破坏。提出了一种自适应图像中值滤波方法。在这种自适应中值滤波算法中，模板可根据移动位置之邻域的灰度分布生成。在具体实现时，首先将该邻域内各像素灰度分别转化为量子比特并施加量子门操作，再对变换和操作后的像素进行随机观测使其坍缩生成中值运算模板。由于这种模板与图像的局部特征相适应，因此这种自适应中值滤波方法有更好的滤波效果。本文给出了这种自适应中值滤波方法的数学描述和它的计算机仿真实现。仿真结果表明，这种自适应中值滤波能在更好地保留图像细节同时有效地滤除噪声，而且对噪声的强度不敏感。利用量子理论公理体系创建新的图像边缘检测方法。本文提出可用量子叠加态来表示图像像素之间的关联，由此像素灰度的变化便表现为量子态的纠缠，因此可用线性厄米算符在量子叠加态中的平均值来判断图像的边缘。理论和计算机仿真实验均证明，这种新的边缘检测方法具有视觉补偿功能，能在图像的高或低灰度区域有效地检测出微弱灰度变化引起的边缘效应。因此该方法更符合机器视觉的要求。在一定的条件下，该方法能退化到基于梯度的边缘检测方法，并且其合理性可由概率理论予以解释。提出了一种图像智能滤波方法并仿真实现。针对基于模板的非线性图像滤波算法的模板优化问题，本文提出了一种智能图像滤波机制。该机制由学习优化和滤波两个过程构成。通过对样本图像集的学习生成优化模板，再用所得到优化模板对待处理的图像进行非线性滤波。学习优化过程利用量子衍生遗传算法实现，模板被编码成量子染色体，通过随机观测使量子染色体种群坍缩生成候选解集，并利用量子旋转门实现种群的更新。一个智能中值-开-闭滤波仿真实例验证了所提出的智能滤波机制的可行性。更多还原

【Abstract】 The quantum-inspired method is a new method or improvement onthe method available now which is created by borrowing fundamentalconception and interesting principles from quantum theory for solvingsome practical problem. The quantum-inspired method for imageprocessing is an extension of quantum-inspired method to imageprocessing field. It provides a new idea for the theory research andtechnological realization in image processing field.In this dissertation, quantum throry is reguarded as an anxiomssyetem based the fundamental postulates of quantum mechanics andapplied to created and describe those quantum-inspired methods forimage processing proposed here. The concrete work of the dissertation issummarized as follows.An improvement on mathematics morphology is made here byapplying of the principles about superposition and measurement ofquantum state. A new structure element similar to a superposition ofstates in quantum mechanics, nemaed quantum superposition structureelement, short for QSE, is proposed and constrcted and a newmorphological operation mechanism based QSE, called collapsingmorphological operation is defined. The shape of QSE in collapsingmorphological operation can be varied with its moving location in imagethrough a measurement to QSE by an operator. A method used forproducing the operator used for measuring according to local feature ofimage is proposed and the methods use for self-adapted filtering and edgedetecting of image based collapsing morphological operation are createdfrom this. The result obtained in the computer simulation of thisself-adapted filtering show that this filtering method has more powerfulcapability to filter noise in image than customary morpgologyfilter.Therefore, the problem of how to select a suitable structure elementin morphology operation can be solved. The result obtained in thecomputer simulation of this edge detecting method show that this methodcan detect directly edge of image corrupted by noise without pre-filtering.Therefore, the damaging of edge in pre-filtering can be avoied. A self-adaped median filtering is also proposed in thisdissertation.The mask used for median operation is produced according todistribution of gray scale of pixels in the neighborhood of its movinglocation in image. In order to realize this, each gray scale of all pixels inthe neighborhood is transformed into quantum bit and is operatedsuccessively by quantum gate. Then, a random observation of the pixelsis carried to make them collapsing to produce a mask adapted for themoving location. This improved median filtering is a self-adaptedfiltering because of mask varied with local feature of image in its movinglocation. Therefore,the result obtained by applying this median filter isbetter than that obtained by conventional median filter. The principle ofthis median filterin is described in mathematics formulation and itsrealization simulated in computer is made here. The result obtained in thesimulation show that this method can not only efficiently filter the noisein image and reserve the detail of image fairly good, but also is notsensitive to the intensity of noise in image.Another important content in this dissertation is how to applyingquantum throry as an anxioms syetem to creat new edge detecting methodof image. In this new method created here, the relation between twopixels is described by means of the superposition of two quantum bitcorresponding to their gray scales. Quantum entanglement is used fordescribing the change of gray scale of the pixels and the average of linearhermitian operator in the superposition of two quantum bit is used forjudging the edge of image. A function of this new edge detecting methodto compensate visual sense of human is proved theoretically and isverified in computer simulation. This method agrees with the demand ofmachine’s visual sense because the edge resulting from a very litterchange in gray scale in the region of image with higher or lower gray canbe detected. The fact that the method can be degenerated that methodbased gradient operation on some condition is given, and also theauxiliary proof about rationality of this method by means of probabilitytheory is given too here.To solve the problem about mask optimizing in no-linear imagefiltering based on mask operation, a scheme with artificial intelligence for image filtering is also proposed here. This scheme consists of twoprocedures, namely study-optimization procedure and filtering procedure.An optimized mask can be obtained in the study-optimization procedurethrough learning from a set of image samples prepared and then ano-linear filtering for the image needed to processing is carried out by themask obtained in filtering procedure. This study-optimization procedureis realized by means of quantum-inspired genetic algorithm. In therealization, the masks are described by chromosomes coded in quantumbit and a random observation of these chromosomes are taken to makethem collapsing to produce a set of probable solution for the masks, andthe population consisted of these chromosomes is updated by applyingquantum rotation gate operator. The result obtained in the computersimulation to a median-opening-closing filter of this scheme shows thatthis algorithm proposed here is practicable.更多还原