B样条滤波器建立表面轮廓中线的方法

根据离散B样条函数的Z域表达式，B样条空间中对信号的拟合和分解可以表示成FIR滤波器和IIR滤波器的滤波过程，再结合变分原则，构建了表面粗糙度测量中用于确定中线的B样条滤波器。将零相移滤波技术应用到B样条滤波器的实现中，得到了相应的差分方程。对一实际工件表面轮廓进行了实验，验证了该方法的可行性，该滤波器同样具有零相移的特性，与其它方法相比，其具有计算效率高的优点。     

广义B样条滤波器在表面形貌测量中的应用

摘 要：为了提取工件表面轮廓中线,给出一种基于三阶广义B样条函数的数字光滑滤波器。首先由线性方程微分方程推导出广义B样条函数。接着,利用广义B样条函数和变分公式结合推导出数字平滑滤波器,该数字平滑滤波器由一IIR滤波器和间接广义B样条变换组成。然后,给出了数字平滑滤波器的具体的递归算法,并且证明了该滤波器的通用特性。最后提取了一实际工件表面中线。实验结果表明：该滤波器具有比高斯滤波器更好的截止特性,该算法利用普通计算机提取11200点数据表面中线仅耗时0.002秒。该滤波器具有可调平滑性,零相移特性,克服了传统三阶样条插值的曲率低和振荡的缺陷,其递归滤波器的具体算法,算法简洁,效率高。     

对金刚石刀具刀尖圆弧波纹度评价的滤波分析

为准确评价超精密金刚石刀具刀尖圆弧波纹度,对金刚石刀具刀尖圆弧波纹度的评价进行了滤波分析。介绍了刀尖圆弧波纹度的评价方法,针对关键的滤波环节,分析了高斯滤波、高斯回归滤波、样条滤波和小波滤波的原理,根据实际采样数据设计模拟实验对比了上述4种滤波器的滤波特性。结果表明,对于不同轮廓中线但高频分量完全相同的轮廓,样条滤波器的滤波效果优于高斯滤波器,并通过实际应用对比了高斯滤波器和样条滤波器。实验结果表明:对具有不同轮廓中线但高频分量完全相同的模拟轮廓,分别采用高斯滤波器和样条滤波器,当截止波长分别取0.25mm和0.8mm时,高斯滤波器滤波结果的标准差分别为0.4366nm和9.6544nm,样条滤波器滤波结果的标准差分别为0.0271nm和1.1844nm,说明样条滤波器更适合于超精密金刚石刀具刀尖圆弧波纹度的评价。     

零相位滤波与最小二乘拟合下的聚焦形貌恢复

为提升形貌恢复精度,提出一种高精度的聚焦形貌恢复算法。该方法从序列图像的预处理以及深度值连续化处理角度入手,将零相位滤波与最小二乘拟合法相结合。自行设计了基于巴特沃斯低通的零相位滤波器用以聚焦评价函数曲线的滤波处理,在消除噪声干扰的同时,保持各空间数据点位置不变;根据聚焦评价函数曲线特性,利用基于高斯函数的最小二乘拟合峰值法获取窗口序列的聚焦位置,进一步提高了峰值定位精度;为得到更为连续化的被测物深度信息,采用三次B样条曲面对各个像素点的初始深度值进行插值。实验表明,方法兼具形貌恢复的平滑性及高精度性。     

基于高斯逼近的广义B样条平滑滤波快速算法

将添加了速度项s(xi)xi的平滑变分公式引入广义B样条滤波器,通过速度项αs(xi)αxi来增加数字滤波器传输特性对参数t1,t2的敏感性,推导出一个小尺度且能够快速逼近高斯滤波的平滑数字滤波器,并且讨论在不同截止角频率ωc下文中算法与标准高斯滤波器的逼近程度。最后对一个长度为19 000的实测轮廓数据进行滤波,实验结果表明:该滤波器一定程度上抑制了传统高斯滤波边界畸变的缺陷,且响应时间短,整个过程耗时1.6ms,仅为传统高斯滤波的1/40,为工程表面滤波提供了一种新方法。     

理想数字滤波器的谐波小波逼近模型与设计方法

分析谐波小波的频域特征和滤波特性,研究理想数字滤波器的谐波小波逼近模型与实现方法。利用谐波小波在频域具有良好的紧支特性和盒形特性,建立理想数字滤波器的小波逼近模型。通过谐波小波变换,实现逼近滤波器的带宽和中心频率的可调。该逼近滤波器的幅频特性已逼近理想数字滤波器的幅频特性,且具有零相移特性,并通过傅里叶变换实现其快速算法。通过算例和工程应用实例验证,该方法能有效地滤除噪声信号,具有算法简捷、快速等特点,能对实测信号进行实时滤波。     

表面形貌评定的B样条小波基准线的实现

随着科学技术的发展,对工件的表面精度提出了更高的要求。表面形貌特征在很大程度上影响了工件的技术性能和使用功能。近年来,国内外对表面形貌特征进行了大量的研究,制定了相关的标准。但是仍然存在一些不确定性和模糊性。文中针对高斯滤波器存在边界效应和对缺陷表面产生形变的不足,提出了一种B样条小波获取表面形貌功能评定基准线的方法。首先建立表面形貌的数学模型,采用小波分析的分解与重构原理,实现了表面形貌的数学模型的小波构建。最后根据小波变换的定义,用B样条函数构造出B样条小波函数,并将其应用于表面形貌的分析,从而实现了表面轮廓与基准线的分离。通过实例对比分析,该方法要优于高斯滤波获取基准线的方法。B样条小波分离法不仅消除了边界效应,而且消除了表面异常值高斯基准线的变形。     

一种新型稳健样条轮廓滤波器

在表面计量学中,通常利用轮廓滤波器提取轮廓中线作为表面评定的基准线。由于传统轮廓滤波器极易受到划痕和深谷等奇异信号影响而产生失真甚至错误的中线,为了增强其稳健性并保证评定精度,国际标准中给出了两种替代滤波器,即稳健型样条滤波器和高斯回归滤波器。然而,这两种滤波器的构造原理和实现算法迥异,其滤波特性差异较大,从而导致对同一表面具有不同的评定结果。为解决这一问题,提出将M估计权函数与样条滤波器相结合构造了一种新型稳健样条滤波器。该滤波器不但具有更强的抗差能力,其计算效率也远高于国际标准推荐的稳健滤波器。更重要的是,大量实验表明,其滤波特性与高斯回归滤波器接近,该滤波器的应用有助于表面评定标准的传递和测量结果比对。     

三角窗逼近法实现高斯滤波器

在中心极限定理和逼近理论的基础上,提出了一种用三角滤波器的级联来实现高斯滤波器的新方法.根据三角窗函数的对称性和三角滤波器的递归性,给出了高斯滤波器的实用逼近算法.实验表明,与传统的高斯滤波方法相比,新方法算法简单,计算效率高,且易于实现.     

样条滤波器算法的实现

在表面粗糙度测量中,样条滤波器比之前的2RC滤波器和高斯滤波器有更好的滤波效果,但是样条滤波器的截止波长λ,没有确定的定义,这使得样条滤波器的应用受到了限制.本文通过大量的计算,进行数据拟和得到了样条滤波器截止波长的拟合公式,通过该公式可以直接计算出p参数,它使得滤波器在截止波长处的传输特性为50%,而且其相关系数达到了1,非常接近实际的计算值.     

减小表面粗糙度测量高斯滤波幅度偏差

提出了一种减小表面粗糙度测量用的高斯滤波器幅度传输特性偏差的新方法。根据中心极限定理,可以构造出不同的高斯逼近滤波器。用多级一阶巴特沃思滤波器和多级移动平均滤波器分别去逼近高斯滤波器时,两者的幅度偏差方向相反、极值位置相近,所以这两种方法的线性组合可以大大减小偏差。用这两种不同逼近滤波器的并联方法构成的一个简单的线性组合滤波器,去逼近高斯滤波器的幅度传输特性,其幅度传输特性的最大偏差只有0．11％。这种新的逼近方法,算法简单、精度高,实现了表面测量高斯滤波处理的高精度和高效率的高度统一。     

三维表面测量中的高斯滤波快速算法

基于中心极限定理提出了一个高斯滤波器逼近模型,并利用冲激响应不变法设计了数字高斯滤波器.通过级联方法,该滤波器的幅度传输特性偏差可控制在(-0.28％～+1.14％)以内,扩展为二维高斯滤波器,其三维幅度传输特性偏差可控制在(-0.42％～+1.12％)以内.该滤波器采用递归实现算法,算法简便,易于实现.在递归算法的基...     

A universal spline filter for surface metrology

In this study, a novel fractional spline filter is proposed for surface metrology. The filter combines arbitrary order fractional spline function with variational principle, and is endowed with an adjustability of transition characteristic. If the order is high enough, the fractional spline filter can obtain more step-edge-like cut-off characteristic of the low-pass filter, and it can also realize the transmission characteristic of the Gaussian filter with high accuracy if the order equals to two. In addition, if the approximation parameter is set to zero, this filter will be simplified to a form of ordinary spline filter. Therefore, this fractional spline filter is called the universal spline filter. In order to reduce the computation time, the universal spline filter is calculated by a fast Fourier transform (FFT) algorithm. Furthermore, for practical use, an improved method prior to the FFT algorithm is proposed to suppress the end effect. Finally, the efficiency of the whole algorithm in comparison with the ordinary spline filter is demonstrated by the experiments, and it is also shown that the universal spline filter is able to alleviate the end effect significantly.     

Comments on the paper 'A novel 3D wavelet-based filter for visualizing features in noisy biological data', by Moss et al.

Moss et al. (2005) describe, in a recent paper, a filter that they use to detect lines. We noticed that the wavelet on which this filter is based is a difference of uniform filters. This filter is an approximation to the second‐derivative operator, which is commonly implemented as the Laplace of Gaussian (or Marr–Hildreth) operator. We have compared Moss' filter with (1) the Laplace of Gaussian operator, (2) an approximation of the Laplace of Gaussian using uniform filters and (3) a few common noise reduction filters. The Laplace‐like operators detect lines by suppressing image features both larger and smaller than the filter size. The noise reduction filters only suppress image features smaller than the filter size. By estimating the signal‐to‐noise ratio and mean square difference of the filtered results, we found that the filter proposed by Moss et al. does not outperform the Laplace of Gaussian operator. We also found that for images with extreme noise content, line detection filters perform better than the noise reduction filters when trying to enhance line structures. In less extreme cases of noise, the standard noise reduction filters perform significantly better than both the Laplace of Gaussian and Moss' filter.     

High-order spline filter: Design and application to surface metrology

The differences between the transmission characteristics of the standard cubic spline filter and the Gaussian filter lead to different evaluation results even for the same profile. There is indeed an adverse impact on the comparison of measurement results and the applications of the related international standards. A novel high-order spline filter is proposed to resolve this practical problem of approximating the Gaussian filtering characteristic. The design of the new filter is based on an improved variational approach by adding the high order derivative terms to the bending energy part whose structural parameters are determined by the aid of the universal Taylor series, so as to realize the convergence to the function of the Gaussian filter. In addition, a cascade algorithm in terms of the low-order filters is also developed in order to ensure stable performance of the high-order filter. Its effectiveness and application were verified by the experiments.     

新一代GPS区域滤波技术在表面结构计量中的应用研究

基于GPS区域标准滤波技术,深入研究了区域滤波技术中的高斯滤波技术在三维表面结构计量中的应用;进行了区域高斯滤波技术的规范应用研究;并以实例阐述了其在工程实际中的优越性及可行性.该区域滤波技术不仅能实现表面特征信息的分离与提取,而其为表面结构的精确计量提供了一条可行之路,为新一代GPS标准的贯彻实施提供了一定的技术支撑.     

结合引导滤波和卷积稀疏表示的红外与可见光图像融合

为了解决红外与可见光图像融合时信息容易相互干扰、影响融合质量的问题,将引导滤波、高斯低通滤波与非下采样方向滤波器组相结合,提出一种新的图像融合方法。利用引导滤波和高斯低通滤波,将源图像分解为低频近似部分、强边缘部分和高频细节部分,并将高频细节部分进行非下采样方向滤波,进一步得到高频方向细节部分;对低频近似部分应用基于局部区域能量的融合规则,对强边缘部分提出一种基于卷积稀疏表示的融合规则,对高频方向细节部分提出改进的脉冲耦合神经网络的融合规则,得到相应的融合部分,并通过逆变换得到最终的融合图像。对多组红外与可见光图像的实验结果表明,算法得到的融合结果的主观视觉效果和客观评价指标均优于传统的图像融合方法,其客观评价指标中的标准差、信息熵、互信息、平均梯度和空间频率相比融合效果较好的基于离散小波变换和稀疏表示的融合方法平均提高20.28%、2.24%、47.41%、5.34%、8.02%。     

Digital smoothing of the Langmuir probe I-V characteristic

Electrostatic probes or Langmuir probes are the most common diagnostic tools in plasma discharges. The second derivative of the Langmuir probe I-V characteristic is proportional to the electron energy distribution function. Determining the second derivative accurately requires some method of noise suppression. We compare the Savitzky-Golay filter, the Gaussian filter, and polynomial fitting to the Blackman filter for digitally smoothing simulated and measured I-V characteristics. We find that the Blackman filter achieves the most smoothing with minimal distortion for noisy data.     

TRANSFER-FUNCTION APPROXIMATIONS OF THE RAINFLOW FILTER

The rainflow filter is a non-linear filter which can be used to eliminate small-amplitude oscillations in a signal. In this paper, two approaches for investigation of the filter by means of an approximating transfer function are presented. The estimates are obtained from rainflow-filtered spectral simulations. One method is based on clipped Gaussian processes, the other uses a spline interpolation in the filtered time series. Examples are given for processes with different types of spectral densities. A certain reduction of small-amplitude cycles is obtained by use of the transfer function, but the threshold effect, characteristic for the rainflow filter, is missed.