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参数可调的通用半正交图像矩模型

何冰,崔江涛,肖斌,彭延国(西安电子科技大学;重庆邮电大学;西安电子科技大学计算机学院)

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;同时,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。主要从以下三个方面进行尝试研究:(1)尝试研究介于正交和非正交之间过渡区域,即半正交核函数的性能对图像的影响;建立适用于不同阶次的通用半正交矩理论模型;(2)尝试建立图像矩频域理论分析模型,通过调整各种不同矩基函数的带宽以及对应的截止频率,分析其对构造的低阶矩、中高阶矩以及高阶矩的影响,并进一步研究使用不同阶的矩(低阶、高阶)重构后图像的优劣。(3)打破传统正交矩的仅能全局描述图像的特性,尝试构造图像局部特征分析方法,建立图像ROI(感兴趣区域)特征提取的局部图像矩。(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,我们从频域的角度出发,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,其核心思想是将构造图像矩的核函数在频域的表示视为一种滤波器(如低通滤波),我们希望核函数对应的频带宽度(带宽)在图像低阶矩时较宽,同时截止频率尽可能衰减的较慢;而在图像高阶矩时对应的带宽较窄,同时截频尽可能衰减的较快。总之,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,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(以上这些图像矩其核函数均是由高阶多项式组成,计算的复杂度较高)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。为了推广三角函数在不同坐标空间可以构建相应的图像矩,增强其通用性;同时为了提高三角函数为核函数建立的矩的稳定性和图像重构的精确性,本文构建了一种半正交-三角函数矩,并通过理论分析和相关仿真实验进行了验证。(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(Zernike、伪Zernike、正交傅里叶-梅林矩及贝塞尔-傅里叶矩)相比在数值稳定性、图像重构、图像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。
关键词
A general semi-orthogonal moments with parameter-modulated

hebing,Cui Jiangtao,Xiao Bin,Peng yan guo(Xidian University)

Abstract
(Objective)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 tries 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 designing 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 frequency domain. By adjusting the bandwidth of basis functions and corresponding cut-off frequencies for various moments, we can analyze their effects on low-order moments, middle-order moments and high-order moments, and also further study the advantages and disadvantages of reconstructed images using different order moments (low-order and high-order). 3) To solve the traditional orthogonal moments which 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 ROI feature-extraction. (Method)Firstly, the kernel-functions of traditional orthogonal moments are modified appropriately and using the modified kernel-functions (basis functions) to replace the original kernel-functions in the traditional orthogonal moments, and only making it a special case for modified moments. The modified basis functions can effectively eliminate the numerical instability of image moments. Secondly, the low-order moments of an image can be quantitatively analyzed by using time-domain analysis method, but the high-frequency of an image (corresponding high-order moments) can not be described more reasonably. Therefore, from the perspective of frequency domain, we propose a time-frequency correspondence method to analyze and enhance the stability of different order moments. The main idea of this method is to treat the representation of the constructed image moments in frequency domain as a filter (such as low-pass filtering). We hope that the bandwidth corresponding to the kernel-functions will be wider when using low order moments, and the cut-off frequency will be attenuated as much as possible, while the bandwidth corresponding to the higher-order moments is narrower, and the cutoff frequency attenuates as fast as possible. In summary, various types of optimal-order moments can be established by adjusting the band-width of the modified kernel-function slightly. Finally, the semi-orthogonal trigonometric-function moments (SOTMs for?short) are implemented in this paper to investigate the properties of the general semi-orthogonal moments. Compared with the existing Zernike, pseudo-Zernike, orthogonal Fourier-Merlin moments and Bessel-Fourier moments (the above image moments are composed of higher order polynomials), the image moments with triangular functions as basis functions have faster computational speed and lower computational complexity in the field of image recognition due to their simple composition and the magnitude located in [-1,1]constantly. In order to generalize the triangular functions, which can construct corresponding image moments in different coordinates space, and also to improve the stability and the accuracy of image reconstruction, that using moments established by triangular functions as kernel-functions, a semi-orthogonal triangular function moments is proposed, which is verified by theoretical analysis and related simulation experiments. (Result) Theoretical analysis and a series of simulation experiments for correlated-images demonstrate that, the general semi-orthogonal moments outperfrom over the corresponding orthogonal moments(e.g., Zernike, pseudo-Zernike, orthogonal Fourier-Merlin moments and Bessel-Fourier moments) in terms of the numerical stability, image-reconstruction, image ROI feature detection, noise robustness testing and invariant recognition.
Keywords
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