参数可调的通用半正交图像矩模型  

General semi-orthogonal moments with parameter modulation

作　　者：何冰 崔江涛[1] 肖斌[3] 彭延国[1] He Bing;Cui Jiangtao;Xiao Bin;Peng Yanguo(School of Computer Science and Technology,Xidian University,Xi'an 710071,China;School of Mathematics and Physics,Weinan Normal University Weinan 714000,China;School of Computer Science and Technology,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]西安电子科技大学计算机科学与技术学院,西安710071 [2]渭南师范学院数理学院,渭南714000 [3]重庆邮电大学计算机科学与技术学院,重庆400065

出　　处：《中国图象图形学报》2019年第10期1711-1727,共17页Journal of Image and Graphics

基　　金：国家自然科学基金项目(61572092,61702403);陕西省自然科学基金项目(2018GY-054);渭南市科技局基础研究项目(2017JCYJ-2-6,ZDYF-JCYJ-17-zsg)~~

摘　　要：目的为了提高以正交多项式为核函数构造的高阶矩数值的稳定性,增强低阶矩抗噪和滤波的能力,将仅具有全局描述能力的常规正交矩推广到可以局部化提取图像特征的矩模型,从频率特性分析的角度定义一种参数可调的通用半正交矩模型。方法首先,对传统正交矩的核函数进行合理的修正,以修正后的核函数(也称基函数)替代传统正交矩中的原核函数,使其成为修改后的特例之一。经过修正后的基函数可以有效消除图像矩数值不稳定现象。其次,采用时域的分析方法能够对图像的低阶矩作定量的分析,但无法对图像的高频部分(对应的高阶矩)作更合理的表述。因此提出一种时-频对应的方法来分析和增强不同阶矩的稳定性,通过对修正后核函数的频带宽度微调可以建立性能更优的不同阶矩。最后,利用构建的半正交-三角函数矩研究和分析了通用半正交矩模型的特点及性质。结果将三角函数为核函数的图像矩与现有的Zernike、伪Zernike、正交傅里叶-梅林矩及贝塞尔-傅里叶矩相比,由于核函数组成简单,且其值域恒定在[-1,1]区间,因此在图像识别领域具有更快的计算速度和更高的稳定性。结论理论分析和一系列相关图像的仿真实验表明,与传统的正交矩相比,在数值稳定性、图像重构、图像感兴趣区域(ROI)特征检测、噪声鲁棒性测试及不变性识别方面,通用的半正交矩性能及效果更优。Objective This study aims to improve the numerical stability of high-order moments and the ability of anti-noise and filtering for low-order moments, which are defined with orthogonal polynomial kernel-functions. A general semi-orthogonal moments with parameter-modulated is defined from frequency-response analysis, which is a generalization of the traditional orthogonal moments. This paper mainly attempts to study from the following three aspects: 1) we take on the challenge of studying the influence of the performance of semi-orthogonal kernel-functions onto an image between orthogonal and non-orthogonal moments and design a general semi-orthogonal moment theory model for different orders;2) we take on the challenge of trying to establish a theoretical analysis model of image moments in the frequency domain;by adjusting the bandwidth of the basis functions and the corresponding cut-off frequencies for various moments, we can analyze their effects on low-order moments, middle-order moments, and high-order moments and further study the advantages and disadvantages of reconstructed images by using different order moments(low-order and high-order);3) to solve the traditional orthogonal moments that can only describe the characteristics of the image globally, we take on the challenge of constructing image local feature analysis method and establishing the local image moments of region of interest(ROI) feature extraction. Method The kernel functions of the traditional orthogonal moments are modified appropriately by using the modified kernel-functions(basis functions) to replace the original kernel-functions in the traditional orthogonal moments, making it a special case for modified moments. The modified basis functions can effectively eliminate the numerical instability of image moments. The low-order moments of an image can be quantitatively analyzed by time-domain analysis method, but the high-frequency of an image(corresponding high-order moments) cannot be described reasonably. Therefore, from the perspective of

关 键 词：半正交 正交矩 图像重构 数值稳定性 不变性识别 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]