【作者】 李黎；

【导师】 付波；

【作者基本信息】 湖北工业大学 ， 控制理论与控制工程， 2011， 硕士

【摘要】 图像的矩函数和其不变性的定义起始于上世纪的60年代。自1961年Hu首次提出矩的不变性理论以来,矩和矩函数已经被广泛应用于图像处理和模式识别的各个领域。几何矩是最早出现的矩,它构造简单,计算方便。不足之处是在处理一些复杂的图像时,变换不是很方便,且随着阶数的增加,出现计算不稳和不易集中分析的现象。正交矩的显著特点就是可以描述图像的独立特征,具有最小的信息冗余度;由于其取值范围有一定的要求,常在计算前对定义域归一化。图像处理的计算方法通常是数值计算,采用离散求和的方式来逼近真实积分运算。而上述给出的几种矩函数都采用了连续积分的形式。Zernike矩由于具有旋转不变性,低噪声灵敏度,正交性和最小的信息冗余度,在图像工程领域得到广泛的应用。然而,由于Zernike矩的基函数为连续函数,在离散化的过程中无法避免造成很大的离散误差。为了解决这个问题,Mukundan等提出了离散正交Tchebichef矩。随后,又提出了定义在极坐标上的径向Tchebichef矩,解决了离散正交矩定义在笛卡尔坐标系下不易获得旋转不变量的问题。但是Mukundan方法通过整数点采样,在半径较小时采样点数过多,而半径较大时采样点数不足,同时在处理大图像时效率比较低。本文先对大小为N×N的图像作方圆变换,然后在单位圆平面上作离散向量基,径向以N/2点的离散径向Tchebichef多项式为正交基,周向以4+8i点的离散Fourier为正交基,这样构成一类新的离散径向Tchebichef矩。实验结果分析,在处理大图像时本文所提方法比Mukundan方法好,同时消除了Mukundan方法在重构图像时出现的雪花点等现象。为了进一步提高图像重构效果,本文提出采用分段迭代法来减小多项式迭代时的误差累积,经过实验验证可以得到更好的图像重构效果。更多还原

【Abstract】 The definition of the moment function and invariance of the image began from the 60’s in last century. The moment and its function have been widely used in image processing and pattern recognition in various fields since Hu firstly put up with the moment’s invariant theory in 1961.Geometric moment is the earliest moment, simple and convenient. But the Inadequacy thing is when in dealing with some complex image, the transformation is not very convenient. And with the order increasing, the phenomenon of instability in calculation and not easy to concentrate on analysis will appear.A distinctive feature of orthogonal moments is to describe the independent characteristics of the image, with minimum redundancy of information. because of its value range have certain requirements , the domain often be normalized before calculation.Current computational method of Image processing is numerical calculation, in a way of the discrete summation to approach the real integral operation. While the several given moment functions are all using a continuous integration form.Because Zernike moments have features like rotational invariance, low noise sensitivity, orthogonality and the minimum redundancy of information, they are widely applied in image engineering field.However, since the basis functions of the Zernike moments are continuous functions, large discretization error is unavoidably caused during the process of discretization.To solve this problem, discrete orthogonal Tchebichef moments are proposed by Mukundan, etc. then another radial Tchebichef moments which are defined in polar coordinates are proposed. Solve the discrete orthogonal moments defined in the Cartesian coordinate system is not easy to obtain rotation invariant problem. Mukundan’s method adopted integer-point sampling which has defects of too many sampling points when the radius is small while the number of points are insurfficent when the radius is large and the efficiency of processing image is low.A square-to-circular image transformation is introduced to the image and make discrete vetor base which discrete radial Tchebichef polynomial orthgonal to discrete Fourier in circumferential direction constructing a kind of new discrete radial Tchebichef moments. The experimental results show that the suggested method is better than Mukundan’s method when processing large image and eliminates snowflake in the process of image reconstruction. In order to enhance the effect of the image reconstruction,in this paper the section iterative method is proposed to reduce the error accumulation. Experimental results show that we can get better image reconstruction results.更多还原