基于迭代法的图像矩的计算误差分析与算法优化

发布时间：2018-03-27 18:36

本文选题：图像矩　切入点：迭代法　出处：《湖北工业大学》2017年硕士论文

【摘要】：图像矩是用来抽取图像特征的一种算法。自上世纪60年代图像矩被提出以来,立刻引起各国学者的关注与研究,并被广泛应用于目标识别、模式识别和图像处理等领域中。与其它图像特征相比,图像矩特征在上述领域的应用中具有无与伦比的优势,可以说,目前找不到任何一种图像特征能在效率和稳定性上与其相比。然而,与其他特征提取算法一样,图像矩算法一样存在着计算精度的问题。在利用矩函数提取和处理图像时会伴随有计算误差,这些计算误差在运算过程中会逐渐放大,导致图像矩算法不收敛,最终损害图像矩运算的精度,造成模式识别困难与图像重构失真。目前只有少量的研究者对该问题进行过研究,尚无研究者系统地、定性地研究过图像矩误差的问题。笔者在查阅了国内外的相关资料后发现:没有任何判断图像矩收敛性的准则被提出。在这种情况下,笔者打算系统地研究一下图像矩算法的误差产生与传递机理,尝试找出一些评判图像矩收敛性的准则与判据,并在此基础上对传统的图像矩算法作出一些优化与改进,以抑制其计算过程中的误差。本文所做的主要研究工作有以下:(1)以迭代法的图像矩为对象,介绍了图像矩误差的产生根源与种类,研究了图像矩运算中误差的传递过程,阐释了误差对算法精度和算法收敛性所造成的影响,为后两步的研究打下了基础。(2)将迭代法图像矩中的误差传递式转换为二阶离散误差系统来研究,通过判断该误差系统的稳定性从而判断算法的收敛性。在判断误差系统的稳定性时,笔者采用了李亚普洛夫方法,范数度量方法和奇异值分解法三种方法,并根据这三种方法提出了几个判断常规图像矩算法收敛性的判据。最后通对几种图像矩进行误差分析与图像重构实验,验证了上述判据与准则的可行性。(3)提出了两种优化算法抑制传递误差的方法,着重介绍了第二种方法-参数优化方法,该方法通过修正不稳定图像矩迭代式的参数将不收敛的算法转化为收敛的算法,从而有效地抑制了传递误差。最后利用此优化过的方法对图像进行了重构和误差分析实验,结果验证了该优化方法的可行性。
[Abstract]:Image moment is an algorithm used to extract image features. Since the image moment was proposed in 1960s, it has attracted the attention and research of scholars all over the world, and has been widely used in target recognition. In the fields of pattern recognition and image processing, compared with other image features, image moment features have unparalleled advantages in the application of these fields. At present, no image features can be compared with them in terms of efficiency and stability. However, as with other feature extraction algorithms, Image moment algorithm has the same problem of calculation accuracy. When using moment function to extract and process images, there will be calculation errors, which will be magnified gradually in the course of operation, resulting in the image moment algorithm does not converge. Finally, the accuracy of image moment operation is damaged, which results in the difficulty of pattern recognition and distortion of image reconstruction. At present, only a small number of researchers have studied this problem, and no researchers have systematically studied this problem. The problem of image moment error has been studied qualitatively. After consulting the relevant data at home and abroad, the author finds that there is no criterion to judge the convergence of image moment. In this case, The author intends to systematically study the error generation and transfer mechanism of the image moment algorithm, try to find out some criteria and criteria to judge the convergence of image moment, and on this basis, make some optimization and improvement to the traditional image moment algorithm. In order to restrain the error in the calculation process, the main research work in this paper is as follows: (1) taking the image moment of the iterative method as the object, the origin and type of the error of the image moment are introduced, and the transmission process of the error in the calculation of the image moment is studied. The effect of error on the accuracy and convergence of the algorithm is explained, which lays a foundation for the study of the latter two steps. The error transfer formula in the iterative image moments is converted into a second order discrete error system. By judging the stability of the error system, the convergence of the algorithm is judged. In judging the stability of the error system, the author adopts three methods, namely, the Lyapunov method, the norm metric method and the singular value decomposition method. According to these three methods, several criteria for judging the convergence of conventional image moment algorithm are proposed. Finally, error analysis and image reconstruction experiments are carried out on several image moments. The feasibility of the above criteria and criteria is verified. (3) two optimization algorithms are proposed to suppress the transfer error, and the second method, the parameter optimization method, is introduced emphatically. The method converts the unconvergent algorithm into a convergent algorithm by modifying the parameters of the iterative formula of the unstable image moment, thus effectively suppressing the transfer error. Finally, the image reconstruction and error analysis experiments are carried out by using the optimized method. The results show that the optimization method is feasible.
【学位授予单位】：湖北工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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