正交图像矩及其在精确定位与产品检测中的应用研究
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摘要
机器视觉技术是在图像处理及模式识别上发展起来的新兴技术。典型的机器视觉系统通过图像摄取装置获得目标图像,然后将信息传递给图像处理部分,实现模式识别、在线检测、目标跟踪等功能,并可驱动执行机构完成相关动作,具有非接触、高精度、高速等特点,是先进制造中的重要组成。
图像处理技术是机器视觉中的研究热点,直接影响到系统的性能,而图像矩是图像形状特征的表达方式,其描述了图像的区域特征。正交图像矩是图像矩中的一个重要分支,与非正交图像矩相比,具有多个显著的优点。
传统正交连续图像矩的计算需要进行坐标空间的重新映射和积分的近似化处理。在总结前人研究的基础上,提出了一种精确计算伪Zernike矩的方法。首先将伪Zernike矩转变为Fourier-Mellin矩的线性组合,然后利用若干个矩形、三角形和扇形区域的拼接来表征整个计算区域,接着通过三角函数的积分关系,提出了基于迭代关系求解上述形状区域矩积分的方法,降低计算复杂度。另外,介绍了基于递归的伪Zernike矩精确求解算法,以递归方法计算相邻矩,减少计算时间。
传统正交离散图像矩的求解不进行离散化和积分的近似化处理,一般通过迭代和对称关系进行求解。但是在大规模图像的高阶离散正交图像矩的求解中,迭代次数的增加将导致传递误差剧增。以Krawtchouk矩为研究对象,分析了Krawtchouk多项式在不同参数p下的对称关系,提出了一种Krawtchouk多项式双向递推的算法,最大迭代次数将缩减为原有次数的一半,从而提高Krawtchouk矩的计算精度。另外提出了分段双向迭代算法,可进一步减少迭代次数,降低计算过程中的传递误差。
径向正交图像矩是一类特殊的正交图像矩,其幅值与旋转角度无关,旋转不变量可直接获得。径向连续正交图像矩的计算过程需要离散化处理,此过程将产生离散误差。首先分析了笛卡尔坐标系与极坐标系的一一映射关系,然后基于径向连续正交图像矩的推导表达式,构建了极坐标系下具有正交性质的离散傅里叶表达式,从而构建了径向双离散傅里叶变换,最后利用正交的余弦变换替换傅里叶变换,避免复数运算,提高计算效率。
目标识别中图像特征量的选择是识别的关键因素。Zernike矩作为径向正交连续矩,直接反应了目标的区域特征,适合于复杂边界目标的描述。Zernike矩的裁剪半径直接影响到不变量的稳定性,提出了一种裁剪半径的计算方法。针对BP神经网络易陷入局部极值和初值敏感等问题,利用粒子群算法来优化神经网络的权值和阈值,混沌算子用于初始化神经网络的权值和阈值,并通过混沌机制使粒子群跳出早熟。
精确定位系统中图像处理的主要任务是求取图像中目标的位置。目标特征一般包括边缘特征和点特征两种,边缘特征的处理量较大,提出了基于点特征的匹配方法。首先利用自适应中值滤波器处理椒盐噪声,然后通过两级Zernike矩进行边缘的亚像素检测,接着采用曲率尺度空间的改进方法提取角点,最后由局部和全局匹配的方法完成目标的精确定位。
字符和缺陷是常见的产品检测项目。在字符识别中,选用Zernike矩和骨架特征作为特征量,采用两层串级的识别方法,可保证识别效果和识别效率；在缺陷检测中,利用平均灰度灰度矢量完成粗匹配,再通过正交Fourier-Mellin矩进行细匹配,可兼顾检测的准确性和快速性。
Machine vision technology is the emerging technology based on image processing and pattern recognition. The target image can be obtained through the image capturing device in a typical machine vision system, afterward the information is passed to the image processing section, then several functions such as Pattern recognition, online Inspection and target tracking can be achieved, the implementing agencies can be driven to complete the relevant action. It has the advantages of non-contact, high precision and rapidity, and is the important component of advanced manufacturing.
Image processing technology which has a direct impact on the machine vision system is research hotspot in the machine vision, and the image moments are the expression of the image shape feature, which describes the characteristics of the image area. Orthogonal image moments are an important branch of image moments, compared with non-orthogonal image moments, which have a number of significant advantages.
The calculation of traditional orthogonal continuous image moment needs the remapping of the coordinate space and the treatment of integral approximation. On the basis of previous research, the method of accurate calculation of the pseudo-Zernike moments is proposed. Firstly, pseudo-Zernike moments are converted into a linear combination of Fourier-Mellin moments, then the combination of a number of rectangles, triangles and fan-shaped region is used to express the entire computational domain, afterward, in order to reduce the computational complexity a recursive expression is deduced through the integral relationship of the trigonometric functions to solve the above-mentioned shape of the region's moment integral. In addition, the accureate computation of Pseudo Zernike moments based on the recursion is introduced, which uses the recursive relations to calculate the moments for the sake of reducing computation time.
The calculation of traditional discrete orthogonal image moments don't require the treatment of discretization and integral approximation, and is usually solved by iteration and symmetry relations. However, the increase of the number of iterations will result in dramatic increase of transmission error in solving large-scale image of the high order discrete orthogonal image moments. Considering Krawtchouk moments as the object of study, the symmetry relations of Krawtchouk Polynomials in different parameter P are analyzed, and a novel bi-recursive algorithm is proposed to calculate Krawtchouk polynomial in which the maximum number of iterations will be reduced to the original number of general. The new algorithm can improve the accuracy of the calculation of the Krawtchouk moment. In addition, the calculation of subparagraph can be taken account into this algorithm, which further reduces the number of iterations and the impact of the transmission error.
The radial orthogonal image moments which have the characteristics of the radial moments are a special class of orthogonal image moments, and the amplitude of these moments has nothing to do with the angle of rotation, and therefore the rotation invariant can be directly obtained. The calculation of radial continuous orthogonal image moments requires the treatment of discretization, which causes the discretization error. The radial Bi-discrete Fourier transform is presented on the basis of the derivation formula of the radial continuous orthogonal moments. First the mapping relationship of the Cartesian coordinates and polar coordinates is studied, and then a polar coordinate system with orthogonal discrete Fourier expression is built, finally the orthogonal cosine transform is used to replace the Fourier transform in order to avoid complex operations and improve computational efficiency.
The choice of image feature is the key factors in target recognition. Zernike moments as the radial orthogonal continuous moments have a direct response of the regional characteristics of the target, and are suitable for the description of the complex boundary goal. The cutting radius of Zernike moments directly affects the stability of the invariants, and the method of calculating a cutting radius is proposed. Because BP neural networks is easy to fall into local extreme value and is sensitive to initial value, particle swarm algorithm is used to optimize the weights and thresholds of neural networks, and chaos operator is utilized to initialize weights and thresholds of neural network, then particle swarm takes advantage of the chaos mechanism avoiding precocity.
The main task of image processing of dynamic accurate location systems is to strike the image of the target location. The target characteristics generally include edge features and point features, in which edge features need a larger handling capacity compared with point features. A point feature-based matching method is introduced. Firstly, adaptive median filter is used to deal with salt and pepper noise, and then two-level Zernike moments is utilized for the edge of the sub-pixel detection, followed by the modified method of the curvature scale space is applied to extract corner points, and finally the positioning of the target is completed through the local and global match.
Character and defect are the common projects of product inspection. Zernike moments and skeleton features are chosen as features in the character recognition, and a two-tier cascade identification method is used to ensure the recognition performance and identify efficiency. Firstly, the mean gray level grayscale vector is used to complete the rough match, and finally orthogonal Fourier-Mellin moments are utilized for fine matching. This new method can take into account the accuracy and rapidity of dectection.
图像处理技术是机器视觉中的研究热点,直接影响到系统的性能,而图像矩是图像形状特征的表达方式,其描述了图像的区域特征。正交图像矩是图像矩中的一个重要分支,与非正交图像矩相比,具有多个显著的优点。
传统正交连续图像矩的计算需要进行坐标空间的重新映射和积分的近似化处理。在总结前人研究的基础上,提出了一种精确计算伪Zernike矩的方法。首先将伪Zernike矩转变为Fourier-Mellin矩的线性组合,然后利用若干个矩形、三角形和扇形区域的拼接来表征整个计算区域,接着通过三角函数的积分关系,提出了基于迭代关系求解上述形状区域矩积分的方法,降低计算复杂度。另外,介绍了基于递归的伪Zernike矩精确求解算法,以递归方法计算相邻矩,减少计算时间。
传统正交离散图像矩的求解不进行离散化和积分的近似化处理,一般通过迭代和对称关系进行求解。但是在大规模图像的高阶离散正交图像矩的求解中,迭代次数的增加将导致传递误差剧增。以Krawtchouk矩为研究对象,分析了Krawtchouk多项式在不同参数p下的对称关系,提出了一种Krawtchouk多项式双向递推的算法,最大迭代次数将缩减为原有次数的一半,从而提高Krawtchouk矩的计算精度。另外提出了分段双向迭代算法,可进一步减少迭代次数,降低计算过程中的传递误差。
径向正交图像矩是一类特殊的正交图像矩,其幅值与旋转角度无关,旋转不变量可直接获得。径向连续正交图像矩的计算过程需要离散化处理,此过程将产生离散误差。首先分析了笛卡尔坐标系与极坐标系的一一映射关系,然后基于径向连续正交图像矩的推导表达式,构建了极坐标系下具有正交性质的离散傅里叶表达式,从而构建了径向双离散傅里叶变换,最后利用正交的余弦变换替换傅里叶变换,避免复数运算,提高计算效率。
目标识别中图像特征量的选择是识别的关键因素。Zernike矩作为径向正交连续矩,直接反应了目标的区域特征,适合于复杂边界目标的描述。Zernike矩的裁剪半径直接影响到不变量的稳定性,提出了一种裁剪半径的计算方法。针对BP神经网络易陷入局部极值和初值敏感等问题,利用粒子群算法来优化神经网络的权值和阈值,混沌算子用于初始化神经网络的权值和阈值,并通过混沌机制使粒子群跳出早熟。
精确定位系统中图像处理的主要任务是求取图像中目标的位置。目标特征一般包括边缘特征和点特征两种,边缘特征的处理量较大,提出了基于点特征的匹配方法。首先利用自适应中值滤波器处理椒盐噪声,然后通过两级Zernike矩进行边缘的亚像素检测,接着采用曲率尺度空间的改进方法提取角点,最后由局部和全局匹配的方法完成目标的精确定位。
字符和缺陷是常见的产品检测项目。在字符识别中,选用Zernike矩和骨架特征作为特征量,采用两层串级的识别方法,可保证识别效果和识别效率；在缺陷检测中,利用平均灰度灰度矢量完成粗匹配,再通过正交Fourier-Mellin矩进行细匹配,可兼顾检测的准确性和快速性。
Machine vision technology is the emerging technology based on image processing and pattern recognition. The target image can be obtained through the image capturing device in a typical machine vision system, afterward the information is passed to the image processing section, then several functions such as Pattern recognition, online Inspection and target tracking can be achieved, the implementing agencies can be driven to complete the relevant action. It has the advantages of non-contact, high precision and rapidity, and is the important component of advanced manufacturing.
Image processing technology which has a direct impact on the machine vision system is research hotspot in the machine vision, and the image moments are the expression of the image shape feature, which describes the characteristics of the image area. Orthogonal image moments are an important branch of image moments, compared with non-orthogonal image moments, which have a number of significant advantages.
The calculation of traditional orthogonal continuous image moment needs the remapping of the coordinate space and the treatment of integral approximation. On the basis of previous research, the method of accurate calculation of the pseudo-Zernike moments is proposed. Firstly, pseudo-Zernike moments are converted into a linear combination of Fourier-Mellin moments, then the combination of a number of rectangles, triangles and fan-shaped region is used to express the entire computational domain, afterward, in order to reduce the computational complexity a recursive expression is deduced through the integral relationship of the trigonometric functions to solve the above-mentioned shape of the region's moment integral. In addition, the accureate computation of Pseudo Zernike moments based on the recursion is introduced, which uses the recursive relations to calculate the moments for the sake of reducing computation time.
The calculation of traditional discrete orthogonal image moments don't require the treatment of discretization and integral approximation, and is usually solved by iteration and symmetry relations. However, the increase of the number of iterations will result in dramatic increase of transmission error in solving large-scale image of the high order discrete orthogonal image moments. Considering Krawtchouk moments as the object of study, the symmetry relations of Krawtchouk Polynomials in different parameter P are analyzed, and a novel bi-recursive algorithm is proposed to calculate Krawtchouk polynomial in which the maximum number of iterations will be reduced to the original number of general. The new algorithm can improve the accuracy of the calculation of the Krawtchouk moment. In addition, the calculation of subparagraph can be taken account into this algorithm, which further reduces the number of iterations and the impact of the transmission error.
The radial orthogonal image moments which have the characteristics of the radial moments are a special class of orthogonal image moments, and the amplitude of these moments has nothing to do with the angle of rotation, and therefore the rotation invariant can be directly obtained. The calculation of radial continuous orthogonal image moments requires the treatment of discretization, which causes the discretization error. The radial Bi-discrete Fourier transform is presented on the basis of the derivation formula of the radial continuous orthogonal moments. First the mapping relationship of the Cartesian coordinates and polar coordinates is studied, and then a polar coordinate system with orthogonal discrete Fourier expression is built, finally the orthogonal cosine transform is used to replace the Fourier transform in order to avoid complex operations and improve computational efficiency.
The choice of image feature is the key factors in target recognition. Zernike moments as the radial orthogonal continuous moments have a direct response of the regional characteristics of the target, and are suitable for the description of the complex boundary goal. The cutting radius of Zernike moments directly affects the stability of the invariants, and the method of calculating a cutting radius is proposed. Because BP neural networks is easy to fall into local extreme value and is sensitive to initial value, particle swarm algorithm is used to optimize the weights and thresholds of neural networks, and chaos operator is utilized to initialize weights and thresholds of neural network, then particle swarm takes advantage of the chaos mechanism avoiding precocity.
The main task of image processing of dynamic accurate location systems is to strike the image of the target location. The target characteristics generally include edge features and point features, in which edge features need a larger handling capacity compared with point features. A point feature-based matching method is introduced. Firstly, adaptive median filter is used to deal with salt and pepper noise, and then two-level Zernike moments is utilized for the edge of the sub-pixel detection, followed by the modified method of the curvature scale space is applied to extract corner points, and finally the positioning of the target is completed through the local and global match.
Character and defect are the common projects of product inspection. Zernike moments and skeleton features are chosen as features in the character recognition, and a two-tier cascade identification method is used to ensure the recognition performance and identify efficiency. Firstly, the mean gray level grayscale vector is used to complete the rough match, and finally orthogonal Fourier-Mellin moments are utilized for fine matching. This new method can take into account the accuracy and rapidity of dectection.
引文
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