电气自动化专业外文翻译(中英文对照翻译)-基于机器视觉数字图像放大应用于表面粗糙度的评估VIP

毕业设计（论文）外文翻译 Application of Digital Image Magnification for Surface Roughness Evaluation Using machine vision 基于机器视觉数字图像放大应用于表面 粗糙度 评估 ： ： 本 科 ： 电气与信息学院 ： 自动化 ： ： 讲 师 ： 2009 年 4 月 20 日 学生姓名 学历层次 所在系部 所学专业 指导教师 教师职称 完成时间 1 （ 本文档前部分为中文 ， 后部分为英文部分 ， 后部分英文部分为 PDF转化为 WORD版本 ， 不清晰之处 ， 可参考本人上传的英文 PDF版本原文 ， 可以免费下载英文 PDF版本 (下载地址 ： /p-34832907.html)， 以人格担保。可先下载英文 PDF版本后，再下载中文部分即本文档 ） 基于机器视觉数字图像放大 应用 于 表面粗糙度 的 评估 摘要： 在这本设计中，用机器视觉系统来捕捉图像，然后对加工 表面（平面、球面和其它形状）的 粗糙 度 进行量化处理， 并进行 回归分析。随后，原 始 图像 通过立方卷积插值技术和改进的线性边缘算法进行放大处理。 基于 表面图像 的特点，利用回归分析法对 Ga 参数进行评估，可以改善原始图像和放大图像的质量。最后，对放大参数 Ga和表面粗糙度之间的关系进 行了比较。 关键词 ： 立方卷积 ； 回归分析 ； 放大系数 ； 灰色平均水平 1. 导言 由于 工业自动化在制造业与 日益增的需求，机器视觉中起着重要作用的质量检验和过程监控。表面粗糙度检查是一项重要的质量控制过程，以确保制造部分符合指定的标准。这种检查通常是通过使用触控笔类文书 实现，其中相关的议案钻石核弹头的笔向粗糙度表面正在调查中。主要不 利的 始使用触控笔等测量 是它需要直接的身体接触，这限制了测量速度。此外，在该仪器读数的基础上数量有限的路线抽样，这可能并不代表真正的物体的表面。这种偏差可能会导致严重的错误在表面质量的 评估，尤其是当表面轮廓是定期的。由于这些缺点， 接触式文书，不适合用于高速自动检查。以前的研究人员使用的机器视觉技术为表面纹理评 估有涵盖数个计算参数，与笔轮廓测量平均粗糙度 面对同一表面。豪等人 . 1 利用统计参数，来自灰色一级强度直方图如范围和均值的分布和他们与相关的 RA 的价值确定，从笔的方法。名叫 al - Kindi 2 等人 2 实施了技术利用粗糙度参数的基础上双方间距之间的灰色水平高峰和数目的灰色水平高峰期每单位长度的扫描线，在 灰色水平形象，估计表面粗糙度。杜明仔等组队 3 ， 采用了两维傅立叶变换一个铸造表面，在双方的灰色水平的形象和二进制图像估计表面粗糙度的铸件（曲面绕 10 毫米）。杰森等人 4 第一次扫瞄散射模式从表面上看，模拟和数字电子产品的措施该光照强度事件对每个探测器，然后计算既反映和总事件的强度，这是当时的用于计算表面粗糙度（表面绕 20 毫米）。布拉德利等人 5应 用了光纤传感器的表面粗糙度测量。在他们的 工作变化，在表面图形变化的事件，并反射光线的表面上。 hisayoshi 佐藤等人 6 的工作是用扫描电子显微镜 估计表面粗糙度。他们表明，该剖面表面可以得到处理回分散的电子信号，这是在比例，表面上的倾向，沿电子束扫描，这意味着该剖面表面粗糙度可以得到结合强度的回到分散的电子信号。 bjuggern 等人 7 发展共综合红外散射执行的 RMS 粗糙度测量工程表面。长谷川等人 8 应用的分形特征的 ARMA 模型在方法模型加工表面概况。罗等人 9 测量表面粗糙度利用扫描探针显微技术，其中包括以上三维立体粗糙度参数表征表 面形貌。后捕捉的影像表面使用机器视觉系统制造各种过程，包括整形 、 铣 、 磨等。ramamoorthy 等人 1110 利用灰色水平强度直方图等，为建立新的光学参数粗糙度的评价。 ramamoorthy 等人 12 也用体积测定技术获得三维深度的分布等表面，并成功估计表面面积和体积的元件。大多数国 家的最先进的数字图像放大技术受到限制，他们不引入任何新的信息，以原始图像。这个缺乏资料，更确切地说没有高空间频率元件是负责为感知退化的放大图像，这是反映，在模糊的边缘。插值方法通常受聘于放大数字图像。一个最佳插值计划，即立方卷积开发的钥匙接近理想 sinc 功能截断它和这个非理想插值削减了一些高频率，这是目前在原来的形象领域带受限制的影响，对高分辨率图像。虽然三次样条法产生一个更好的高分辨率版本的形象，计算这是更为繁复相比，立方卷积。边缘模糊，更是严重与其他放大技术 13 。已经有若干试图在过去的改善，以达到形象放大。惠普 14 报道 有 办法在这方面，这是他们的专利。多数的这些方法的使用边缘信息在低分辨率对原始图像可插。 allebach 和黄 15 使用亚像素边缘估计技术，以产生高分辨率边缘图从低解析度影像，然后使用高解析度的边缘图， 3 以指导插值分辨率低的形象，到最后高使用的版本。詹森和 anastassiou 16 ，目前一办法分辨率增强基于一种新的边缘修改的作用者 。图一小附近的 3 *3 约每像素在低解析度影像，首先是映射到一个最适合连续空间一步的优势。双向水平逼近作为一个地方的范本，即更高的分辨率抽样网格便可以叠加（如有争议值在地区的局部窗口重叠的是，以平均每场顺利错误） 。其结果是图像增加决议明显尖锐的优势。 biancardi等人 17 估计阶段和频率缺席波形缺席的频率从原来的低解析度图像，然后综合他们在高分辨率形象。这种技术，像一所 allebach 和黄，利用亚像素边缘估计从lowresolution 形象直接随后多项式插值的一 步。有限制，即使在被广泛接受机械笔的方法，如评价粗糙度，波纹度和形状误差。各种电器的过滤器，切断比率和放大期间使用的评价。在这方面的工作，企图做出数位放大，表面上形象。测试参数量化评估使用这种方法，比较研究已提交与机械笔参数与完整的分析。它已最后确定，这数字放大其次是定性评价的表面图像可得到很好的用于工程的表面，如形状，球磨和凹凸不平的地面填平。 2. 实验程序 实验进行了编写单位标本所做出的不同的加工过程，如磨削，铣削和塑造。表面具有不同纹理得到控制加工参数的这些进程。视觉系统构成一个 CCD 相机，图像处理软件， 一台电脑， 1 图像处理组和一个视频监控。图片的表面工件，以衡量人抓获相机和采集卡数字化形象和存储，帧在该缓冲区。数字化图像存储为一个数组的 512 *480 与 8 位像素亮度的决议。每个像素了一定的光照强度值。灰色尺度分析技术已通常用于处理和分析的形象。那个数字图像被转移到一个显示子系统。这里，图像数据被转换为标准电视格式并显示在电视监视器。 3. 放大的数字图像 放大数字图像基本上是一个问题亮度插值在输入图像，这也是低解析度影像。它开始与几何变换该输入像素，这是映射到一个新的立场，在输出的形象。一个几何变换是向量函数吨 映射像素（ X ， Y ）到一个新的立场。 r.库玛等人。 国际期刊机床与制造 45 （ 2005 ） 228-234 229（ x0 ， y0 ） 吨的定义是由它的两个组成方程： ），（ yxTx x ），（ yxTy y （ 1 ） 假设平面转型所给予的情商。 （ 1 ）取得的成就，和新的合作点坐标（ x0 ， y0 ） 获得。这一点不适合在一般离散栅格的输出形象，并收集转化点，使样本的输出图像 4 与非整数统筹。价值观对内 部网格有需要，每个像素值在输出图像栅格可以得到亮度插值一些周边的非整数的样本。亮度插值问题通常是表示在一个双重的方式确定的亮度原点在输入图像对应到点在输出的形象，倒卧于离散栅格。假设亮度值像素（ x0 ， y0 ） ，在输出图像需要加以计算，其中 x0 和 y0 就离散栅格（整数） 。该负责统筹的点（ X ， Y ）在原始图像可以得到反转平面转型的情况（ 1 ） ),(Ty)(x, -1 yx 一般来说，真正的统筹后，逆变换不符合输入图像离散栅格，所以亮度不知道。唯一提供的资料有关 原本连续的图像函数 f （ x ， y ）的是它的采样版本，一般事物点 g（ ldx ， kdy ） 。获得亮度的价值点（ X ， Y ）输入图像是重新取样。让的结果亮度插值予以标注由新生力量（ X ， Y ） ，其中 n 区别不同的插值方法。亮度可以表达的卷积方程： ),(),()yx,( ykyxlxhykxlgf nl k sn ( 2 ) 是所谓的插值内核，这是有不同的定义不同插值计划。它是指附近的该点即亮度理想。通常，只有一小点是用来，其中点下是零。因此，亮度插值是在效应 ；输入图像重新采样生成高分辨率版本的输入图像 .3 插值方法，这是使用相当广泛用于数字图像放大，是最接近的邻域插值，线性插值和双三次插值。在这文件，立方卷积算法，原本建议由钥匙，已受聘为实现数字化图像放大，这是被认为是最优计划（精度相比，它提供给计算负担） 。建议读者参考档号， 为详尽无遗的治疗，其概念和数学描述。 4. 改善图像放大 有各种可用的方法，以提高边缘后放大。有些是线性的优势轮廓 ，统计差分等再次线性边缘轮廓可以执行的离散卷积，锐化掩模和 Fourier 域滤波取决于性质形象。举例来说，边缘增强，为扫描图像是做了锐化掩模。在这种情况下的离散二维空间图像，离 散卷积是最常见的用。同时，运用优势轮廓，具有应该的高通形式，作为边缘是高频率的功能。那里有几个 3 *3 高通口供这样一项任务。这些口罩，拥有财产的总和，其要素是团结，以避免振幅的偏见，在处理图像。走出几个口罩一个，它已经用在这工作，是鉴于如下： 111191111H 5 5. 表面粗糙度估计 表面粗糙度参数用于整个在学习平均表面粗糙度（ RA ）的，因为它是最广泛使用的表面光洁度的参数，由研究人员和在业以及。它是算术平均数的绝对价值的高度，粗糙度的违规行为，从均值来衡量，这是在 Ra n/yR n1i ia 那里是彝族的高度，粗糙度的违规行为，从均值和 n 是多少采样数据。在这项研究中，一个特点，表面上的形象，被称为算术平均数的灰色水平遗传算法，是用来预测实际的表面粗糙度，工件。算术平均水平的灰色遗传算法可表示为遗传算法 nggggggGa mnm2m1 那里的 G1 ， G2， G3 Gn 。 指引是灰度级的价值观表面图像沿一条线和通用汽车公司是指的灰色价值观这可以定为通用汽车 nggggn21m ）（ 灰色的平均水平 （ GA ）的已计算所有表面后的形象，表面上被俘虏。这些遗传算法的价值观已校准与各自的核证登记机关价值观来衡量使用触控笔。回归方程，已制定的每一项加工工艺的基础上的数据在表 1-3。 表 1. 加工参数用于磨削和表面粗糙度值 转速（转每秒） 切削深度（微米） 光学参数 Ga 触控笔参数 Ra 他们分别如下： （一）削磨： Ga0 0 3 3 2 2.00 0 0 4 4.0)109.1(52.0R 5a （二）削铣： 6 0 . 1 9 8 5 G a0 . 4 1 50 . 0 0 6 9 4-0 . 0 0 0 397.0Ra （三）塑造 GaRa 3 2 8.061.544.110 6 8 3.01 8 2.7 6. 放大和表面粗糙度 较早前的研究工作进行对粗糙度评价的表面上使用，机器视觉的参与相关光谱等表面粗糙度价值观和这些已表明后续电力法行为。简介这种表面显示的要小题大做这意味着，当被放大，增加详情粗糙度的出现和出现类似的原始配置文件。在这方面的文件，企图已做出关联灰色的平均水平（ GA ）的价值观得到了从图像与各自的表面粗糙度和研究的行为，这种相关性在不同程度的图像放大为三个加工业务。因此，图像工件抓获机器视觉被放大的因素， 2 ， 5 ， 10 和 20 使用放 大技术中提到的第 3 条和改善线性的优势图像轮廓算法 18 。 表 2 加工参数用于磨削和表面粗糙度值 转速（每分钟）深度（毫米每分钟）削减深度（毫米）光学参数 Ga 触控笔参数 Ra 表 3 加工参数用于磨削和表面粗糙度值 转速（每分钟）深度（毫米每分钟）削减深度（毫米）光学参数 Ga 触控笔参数 Ra 7 特征的形象，根据研究，遗传算法，提取和 GA 之间有关联和表面粗糙度在 Ra 的基础上，建立数据表在 46（三维加工工艺） 的基础上的价值观相关系数，以便获得，图像已制订之间的放大系数和 相关系数从数据和显示在图 . 1， 3 个加工进程。 7. 结果与讨论 结果与讨论的基础上，立方卷积算法，数字图像加工工件已放大为加工参数用于磨削和表面粗糙度值转速（ rpm ）切削深度（ DOC ）的（毫米）遗传算法。 表 4 变异的遗传算法不同的放大系数 表 5 变异的遗传算法不同的放大系数 表 6 变异的遗传算法不同的放大系数 8 广泛的放大指数从 2*至 20*走的步骤，适合今后的任务确定表面粗糙度，以评估成效改善计划，一旦适用于他们。立方卷积仍然是其中一个最好的方法，对于放大数字图像而言，维护边缘的细节时，相比于 其他方法，模糊的边缘已发现大幅削减。它是一个巨大的优势，因为边缘影响图像参数果断，有效保存的优势是必要的为所有的图像处理应用，包括表面粗糙度的决心。计算简单所提供的立方卷积方法不能放弃为稍好的结果，所给予的三次样条法。基本上的准确性插值技术提供图像放大取决于其收敛比率。立方卷积提供了一个为 O （ H3 的）收敛速度而三次样条有一个四阶收敛速度，即澳（蛋白 H4 ） 。这意味着消除或改动的条件插值核，以达到更高的收敛速度，而这反过来又需要较高计算的努力获得插值系数。因此，是一个贸易小康之间的准确性，所提供的 插值技术和效率的条款计算的努力， 图 .1 放大系数变化的相关系数与放大系数的 三个加工过程 此外，这是实施很容易由现代数字化计算机和图像处理器。虽然目前的算法是最优选择，它不能防止感知退化的优势 。 9 图 .2 A 100* 100 图像（最上层）的一个地面 其 2 *放大（中）和放大和改进的图像 一些模糊的痕迹可以看出，在每一个放大图像。计算表面粗糙度参数确切地说，这是必须要为了最大限度地恢复锐利的边缘。基于线性边缘图像算法，放大图像一直受到边缘增强他们中的一些显示在无结果。第 10 2 和第 3 随原来，以及放大和 改善。 图 . 3A 100 * 100 图像（最上层）一球磨表面。 其 2*放大（中）和放大和改进的图像 法产生的图像大大增强敏锐性和详细性。退化和模糊的边缘，伴随着放大，已被删除相当大的程度上。作为结果表明，这种方法 11 最好的工程在案件夏普和罚款边缘，例如地面可清楚地看到，运用这一算法，作为指数放大倍率的增加，该算法的有效性录得跌幅，这是对预期的线路。回归方程发展了，最大误差 2 ，平均误差为 0.7 ，在案件磨削，最大误差的 6.34 ，平均误差为 1.2 案件的铣削和最大误差为 8.2 ，平均误 差为 3.72 ，在案件的形成。这种趋势可以解释，从事实，即大的变化在当地的表面的特点，球磨面形成，比较到地面 事物略多不准确的相关性之间的遗传算法和 RA 。最后，在图 .1 ，有一增加的相关系数与放大指数和增量，这是更加明显，在案件地面元件相比，球磨和形。如前所述，由于当地大的变化表面粗糙度，在案件球磨和形表面，放大算法变得越来越无效与放大指数。这反过来又意味着放大图像球磨，形成表面无法预测实际或 真正 的表面特性一个很小的区域的形象（这是受放大率），相比放大的形象，地面工件，由于大和不规则表面特征的变 化，使其难以放大算法插补亮度的价值，一个像素从它的相邻像素正确。而在案件磨削，制服表面纹理，有助于放大计划预测（通过插值，因为这样的性质是算法）价值观，这是明显接近实际。它也有人指出，图 .1 跟随权力的法律。 8. 结论 目前的工作清楚地表明，机器视觉的做法，可以用来评估表面粗糙度的加工表面，并在评价良好的线性关系 RA 和遗传算法是观察一个高层次的准确性。立方卷积插值方法被证明是最佳的选择，放大数字图象和随后的形象可以改善所做的线性优势图像算法。计算遗传算法，光学粗糙度值，从这些放大和改善图像有更好的相关性（即高相关 系数）与平均表面粗糙度（ RA ）的测量为组件使用加工操作成型，铣和磨削，显示其成效在测量中的应用表面粗糙度使用的机器视觉系统。它可以也可以推断，这个计划的光学表面粗糙度估计似乎更有前景的加工业务 ， 产生一个统一的和定期的表面纹理（如作为磨削） 。 参考 文献 1 F. Luk, V. Hyunh, W. North, 机器视觉系统测量表面粗糙度 ,物理期刊（英） ,科学仪器 22 （ 1989 年） 977-980 . 2 G.A. Al-kindi, R.M. Baul, K.F. Gill,应 用机器视觉在自动检查工程表面 ,国际杂志制作工艺的研究二（ 1992 ） 241-253 . 3 D.-M. Tsai, C.-F. Tseng,铸件表面粗糙度分类 ,模式识别 32 （ 1999 ） 389-405 . 4 D.G. Jason, J.M. Rourke, A.C. Bell,交流电钟高速表面粗糙度测量 ,ASME 第 34 条第（ 106 ） （ 1984 ） 34-39 . 5 C. Bradley, J. Bohlmann, S. Kurada,光纤传感器的表面粗糙度测量 ,杂志制造科学 12 与工程 120 （ 1998 ） 359-367 . 6 H. Sato, M.O. Hori, 表面粗糙度测量扫描电子显微镜， Cirp 史册 31 期（ 1982 年） 457-462 . 7 M. Bjuggren, L. Krummenacher, L. Mattsson, 非接触面粗糙度测量工程表面的总集成红外散射 ,精密工程 20 （ 1997 ） 33-45 . 8 M. Hasewaga, K. Okuda, J.C. Liu, M. Nunobiki,一种新方法建模加工表 面轮廓的程序 ,研究所机械工程 240 （ 1996 ） 177-182 . 9 K. Carneiro, C.P. Jensen, J.F. Jorgensen, J. Garnoes, 粗糙度参数表面的原子力显微镜 ,史册 cirp44 （ 1995 ） 517-522 . 10 B. Ramamoorthy, V. Radhakrishnan,统计办法表面纹理的分类 ,国际期刊 ,磨损 167（ 1993 年） 155-161 . 11 M. Kiran, B. Ramamoorthy, V. Radhakrishnan,评价表面粗糙度的视觉系统 ,国际期刊机床与制造 38 （ 1998 ） 685-690 . 12 A. Kartik, S. Chandra, B. Ramamoorthy, S. Das,三维工具磨损的测量和利用可视化立体成像 ,国际期刊的机床和制造 37 （ 1997 ） 1573 年至 1581 年 . 13 R.G. Keys,立方卷积插值数字图像加工，交易 IEEE ASSP （ 29 （ 6 ） （ 1981 ） 11531160. 14 J. Allebach, P.W. Wong,边缘定向插值 ,学校电气与计算机工程系 ,普渡大学 ,西lajayette ,47907-1285. 15 J. Allebach, P.W. Wong,边缘定向插值程序 ,icip 96,第二卷 .三 , lausnne ,社区会堂 ,1996 年 . 707-710 页 . 16 K. Jensen, D. Anastassiou,亚像素边缘的本地化和插值的静止图像 ,图像处理 4（ 1995 年） 285-295 . 17 A. Biancardi, L. Cinque, L. Lombardi 改善形象放大 ,模式识别 35 （ 2002 ） 677-687 . 18 A. Majumdar, B. Bhushan,角色分形几何在粗糙度表征和接触力学的表面上的应用 ,ASME 杂志摩擦学 112 （ 1990 ） 205-216 . 13 International Journal of Machine Tools & Manufacture 45 (2005) 228-234 /locate/ijmactool Application of digital image magnification for surface roughness evaluation using machine vision Rajneesh Kumar, P. Kulashekar, B. Dhanasekar, B. Ramamoorthy* Department of Mechanical Engineering, Manufacturing Engineering Section, Indian Institute of Technology Madras, Chennai 600 036, India Received 25 November 2003； accepted 15 July 2004 Available online 11 September 2004 Abstract In this work, a machine vision system has been utilized to capture the images and then the quantification of the surface roughness of machined surfaces (ground, milled and shaped) is done by the application of regression analysis. Subsequently, original images have been magnified using Cubic Convolution interpolation technique and improved (edge enhancement) through Linear Edge Crispening algorithm. Based on the surface image features, a parameter called G a has been estimated using regression analysis, for the original images and for the magnified quality improved images. Finally, a comparison has been carried to establish correlation between magnification index, G a and surface roughness. q 2004 Elsevier Ltd. All rights reserved. Keywords: Cubic convolution； Regression analysis； Magnification factor； Grey level average 1. Introduction With growing demand of industrial automation in manufacturing, machine vision plays an important role in quality inspection and process monitoring. Surface rough- ness inspection is one of the essential quality control processes that are carried out to ensure that manufactured parts conform to specified standards. This kind of inspection is normally done through the use of stylus type instruments, which correlate the motion of a diamond-tipped stylus to the roughness of the surface under investigation. The major disadvantage of using a stylus instrument for such measurements is that it requires direct physical contact, which limits the measuring speed. In addition, the instru- ment readings are based on a limited number of line samplings, which may not represent the real characteristics of the surface. This kind of deviation may cause serious errors in the surface quality assessment especially when the surface profile is periodic. Because of these drawbacks, contact type instruments are not suitable for high-speed * Corresponding author. Tel.: C91-44-445-8538； fax: C91-44-235- 0509. E-mail address: ramooiitm.ac.in (B. Ramamoorthy). 0890-6955/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.07.001 automated inspection. Previous researchers using machine vision techniques for surface texture assessment have covered several calculated parameters, with stylus profil- ometer measurements of average roughness (area) per- formed on the same surface. Luk et al. 1 utilized statistical parameters, derived from the grey level intensity histogram such as the range and the mean value of the distribution and correlated them with the R a value determined from the stylus method. Al-Kindi et al. 2 implemented a technique utilizing a roughness parameter based on both the spacing between grey level peaks and the number of grey level peaks per unit length of a scanned line in the grey level image to estimate the surface roughness. Du-Ming Tsai et al. 3 employed a two-dimensional Fourier transform of a cast surface in both the grey level image and binary image to estimate the surface roughness of castings (for surfaces with R aO10 mm). Jason et al. 4 first scan the scattering pattern from the surface, the analog and digital electronics measure the light intensity incident on each detector, then compute both the reected and total incident intensity which are then used to compute the surface roughness (for surfaces with R aO20 mm). Bradley et al. 5 employed a fiber optics sensor for surface roughness measurement. In their work, changes in the surface topography are manifested as phase 14 R. Kumar et al. / International Journal of Machine Tools & Manufacture 45 (2005) 228 -234 changes of the incident and reected light on the surface. Hisayoshi Sato et al. 6 worked on the estimation of surface roughness using a scanning electron microscope. They showed that the profile of a surface could be obtained by processing back scattered electron signals which are in proportion to the surface inclination along the electron beam scanning, which meant that the profile of the surface roughness can be derived by integrating the intensity of the back scattered electron signal. Bjuggern et al. 7 developed a total integrated infrared scatterometer to perform the rms roughness measurements of engineering surfaces. Hasegawa et al. 8 employed fractal characteristics of the ARMA model in an approach to model a machined surface profiles. Carneiro et al. 9 measured the surface roughness using scanning probe microscopy, which includes more than 20 three-dimensional roughness parameters to characterize the surface topography. After capturing the images of surfaces using machine vision systems manufactured by various processes including shaping, milling, grinding, etc. Ramamoorthy et al. 10,11 have utilized the grey level intensity histograms, etc. for establishing new optical parameters for roughness evaluation. Ramamoorthy et al. 12 have also used stereometry techniques to get the three- dimensional depth profiles of such surfaces and successfully estimated the surface area and volume of the components. Most state of the art digital image magnification techniques suffer from the limitation that they do not introduce any new information to the original image. This lack of information, more precisely the absence of high spatial frequency components is responsible for the perceptible degradation of magnified images, which are reected, in blurred edges. Interpolation methods are usually employed in magnification of digital images. One of the best interpolation schemes namely cubic convolution developed by Keys 13 approximates the ideal sinc function by truncating it and this non-ideal interpolation cuts some high frequencies, which are present in the original image, leading to band limiting effects on the high resolution image. Although the cubic spline method generates a better high-resolution version of an image, computationally it is much more cumbersome compared to cubic convolution. Edge blurring is even more severe 229 continuous space step edge. The bi-level approximation serves as a local template on which the higher resolution sampling grid can then be superimposed (where disputed values in regions of local window overlap are averaged to smooth errors). The result is an image of increased resolution with noticeably sharper edges. Biancardi et al. 17 estimate the phases and frequencies of absent wave- forms of absent frequencies from the original low resolution image and then synthesize them in the high resolution image. This technique, like the one by Allebach and Wong, takes advantage of sub-pixel edge estimation from the low- resolution image to direct the subsequent polynomial interpolation step. There are limitations even in the widely accepted mechanical stylus methods such as evaluation of roughness, waviness and form error. Various electrical filters, cut off ratios and magnification are used during evaluation. Here in this work an attempt is made to digitally magnify the surface image. To test the quantification parameters evaluated using this method, a comparative study has been presented with the mechanical stylus parameters with complete analysis. It has been finally established that this digital magnification followed by qualitative evaluation of surface images could be very well used for engineering surfaces such as shaped, milled and ground surfaces. 2. Experimental procedure The experiments were carried out by preparing at specimens made by different machining processes, such as grinding, milling and shaping. Surfaces with different textures were obtained by controlling the machining parameters of these processes. The vision system consisted of a CCD camera, image processing software, a computer, an image processing board and a video monitor. The images of the surface of the work piece to be measured were captured by the camera and the frame grabber card digitized the image and stored it in the frame buffer. The digitized image was stored as an array of 512!480 with 8 bit pixels brightness resolution. Each pixel had a definite illumination intensity value. The grey scale analysis technique has been normally used for processing and analyzing the image. The digital image was transferred to a display subsystem. Here, the image data was converted to a standard television format and was displayed on a television monitor. 3. Magnification of digital images Magnification of digital images is basically a problem of brightness interpolation in the input image which is lso a low resolution image. It starts with the geometric trans- formation of the input pixels which are mapped to a new position in the output image. A geometric transform is a vector function T that maps the pixel (x,y) to a new position 15 230 R. Kumar et al. / International Journal of Machine Tools & Manufacture 45 (2005) 228 -234 (x 0,y 0). T is defined by its two component equations: x Z T x； y； y 0 Z T x； y (1) Assume that the planar transformation given by Eq. (1) has been accomplished, and new point co-ordinates (x 0,y 0) obtained. The position of the point does not in general fit the discrete raster of the output image, and the collection of transformed points gives the samples of the output image with non-integer co-ordinates. Values on the interior grid are needed, and each pixel value in the output image raster can be obtained by brightness interpolation of some neighboring non-integer samples. The brightness interpolation problem is usually expressed in a dual way by determining the brightness of the original point in the input image that corresponds to the point in the output image lying on the discrete raster. Suppose that the brightness value of the pixel (x 0,y 0) in the output image needs to be computed, where x 0 and y 0 lie on the discrete raster (integer numbers). The co-ordinates of the point (x,y) in the original image can be obtained by inverting the planar transformation in Eq. (1) x ； y Z T x 0； y Generally, the real co-ordinates after inverse transformation do not fit the input image discrete raster, and so brightness is not known. The only information available about the originally continuous image function f(x,y) is its sampled version g s(lDx,kDy). To get the brightness value of the point (x,y) the input image is resampled. Let the result of the brightness interpolation be denoted by f (x,y), where n distinguishes different interpolation n methods. The brightness can be expressed by the convolu- tion equation: X X N N 0 x y K1 0 f x； y Z n g sl Dx； kDyh nx K lDx； y K kDy (2) lZKN kZKN The function h n is called the interpolation kernel and it is defined differently for different interpolation schemes. It s the neighborhood of the point at which brightness is desired. Usually, only a small neighborhood i use , outside which h m is zero. Therefore, the brightness interpolation is, in effect； input image resampling which generates the high resolution version of the input image. Three interpolation methods, which are used quite extensively for digit al image magnification, are Nearest neighborhood interpolation, Linear interpolation and Bicubic interpolation. In this paper, Cubic Convolution algorithm, originally proposed by Keys 13, has been employed to achieve the digital image magnification which is considered to be the most optimal scheme (the accuracy it offers compared to the computational burden). The reader is advised to refer to Ref. 13 for the exhaustive treatment of its concepts and mathematical description. 4. Improvement to image magnification There are various methods available to enhance the edges after magnification. Some are Linear Edge Crispening, Statistical Differencing, etc. Again Linear Edge Crispening can be performed by discrete convolution, unsharp masking and Fourier domain filtering depending upon the nature of image. For example, edge enhancement for scanned images is done by unsharp masking. In this case of discrete two- dimensional images, discrete convolution is most frequently used. While applying Edge Crispening, the mask should be of high-pass form, as edges are high frequency features. There are several 3!3 high-pass masks available for such a task. These masks possess the property that the sum of their elements is unity in order to avoid amplitude bias in the processed image. Out of several masks the one, which has been used in this work, is given below: K 1 K1 K1 2 6 H Z 4 K1 3 7 K1 5 9 K 1 K1 K1 5. Surface roughness estimation The surface roughness parameter used throughout in this study is the average surface roughness (R a) as it is the most widely used surface finish parameter by researchers and in industry as well. It is the arithmetic average of the absolute value of the heights of roughness irregularities from the mean value measured, that is ! X . n R Z j iy j n iZ1 where y i is the height of roughness irregularities from the mean value and n is the number of sampling data. In this study, a feature of the surface image, called the arithmetic average of the grey level G a, is used to predict the actual surface roughness of the workpiece. The arithmetic average of the grey level G a can be expressed as ffX a fi. G a Z jg 1 K g mj C jg 2 K g mj C/C jg n K g mj n where g 1,g 2,g 3,.,g n are the gray level values of a surface image along one line and g m is the mean of the grey values and this can be determined as ffX fi. g m Z g 1 C g 2 C/C g n n The grey level average (G a) has been calculated for all the surfaces after the images of the surface were captured. These G a values have been calibrated with the respective Ra values measured using a stylus profilometer. Multiple linear 16 Table 1 Machining parameters used for grinding and the roughness values Speed (rpm) Ga parameter 15.09 10.54 9.03 12.17 14.94 8.73 15.93 14.33 9.13 , optical R. Kumar et al. / International Journal of Machine Tools & Manufacture 45 (2005) 228 -234 Table 3 Machining parameters used for shaping and the roughness values Speed (rpm) 12 18 24 18 24 18 18 12 18 24 12 24 24 Feed (mm/stroke) 0.2 0.2 0.2 0.6 0.6 0.2 0.4 0.4 0.4 0.4 0.2 0.2 0.4 Depth of cut (mm) 0.5 0.5 0.5 0.5 0.5 1 1 1 0.5 0.5 1 1 1 Ga parameter 22.31 17.21 21.07 24.95 28.31 14.86 19.1 18.92 29.62 19.61 18.7 20.44 17.23 , optical R a (mm), stylus parameter 19.06 19.83 21.34 24.58 26.55 20.38 26.63 25.31 27.74 23.44 21.36 22.14 24.72 231 1801 2204 2593 1809 1501 2000 1800 2202 2593 Depth of cut (doc) (mm) 50 50 50 30 30 30 80 80 80 R a (mm), stylus parameter 0.51 0.49 0.48 0.52 0.53 0.49 0.51 0.48 0.46 regression equations have been developed for each of the machining processes based upon the data presented in Tables 1-3. They are as follows: (a) Grinding: K5 R Z 0:52 K 1:9 !10 speed K 0:00044 doc a C 0:003322 Ga (b) Milling: R a Z K0:97 C 0:0003 speed K 0:00694 feed C 0:415 doc C 0:1985 Ga (c) Shaping R a Z 7:182 C 0:0683 speed C 11:44 feed C 5:61 doc C 0:328 Ga 6. Magnification and surface roughness Earlier research work 18 carried out on roughness evaluation of surfaces using machine vision involved Table 2 Machining parameters used for milling and the roughness values Speed (rpm) 125 250 90 90 125 180 90 125 63 63 90 125 Feed (mm/min) 22.4 22.4 22.4 45 45 45 45 45 45 22.4 22.4 22.4 Depth of cut (mm) 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 Ga , optical parameter 15.61 19.35 21.30 18.23 28.89 16.99 27.16 19.04 17.71 21.36 25.51 26.46 R a (mm), sty- lus parameter 2.17 2.94 3.51 2.69 4.45 2.44 4.75 3.02 2.46 3.41 4.41 4.65 correlating the spectra of such surfaces to the roughness values and these have been shown to follow power law behavior. Profile of such surfaces were shown to be self- affined which implies that when magnified, increasing details of roughness emerge and appear similar to the original profile. In this paper an attempt has been made to correlate the grey level average (G a) values obtained from the images with their respective surface roughness and study the behavior of such a correlation at various degrees of image magnification for the three machining operations. Consequently, images of workpieces captured by machine vision were magnified by factors 2, 5, 10 and 20 using the magnification technique mentioned in Section 3 and improved by Linear Edge Crispening algorithm. The feature of the image under study, G a, was extracted and a correlation between G a and surface roughness R a was established on the basis of data given in Tables 4-6 (for three machining processes). Based on the values of correlation coefficient so obtained, plots have been drawn between the magnification factor and correlation coefficient from the data and are shown in Fig. 1 for three machining processes. 7. Results and discussion Based on the cubic convolution algorithm, the digital imag s of mach ned work pieces h ve be n magnified or Table 4 Variation of G a with varying magnification factors for ground surfaces Ga (1!) 8.73 10.54 9.03 9.13 14.33 12.17 14.94 15.93 G a (2!) 23.58 20.01 20.83 23.41 26.32 17.85 21.95 21.87 G a (5!) 36.73 38.88 36.12 30.36 37.25 35.6 44.15 44.02 G a (10!) 40.33 41.5 36.72 32.42 39.33 42.17 47.34 46.5 G a (20!) 41.39 46.92 35.51 34.57 43.36 46.56 50.28 48.14 R a (mm) 0.49 0.49 0.48 0.46 0.48 0.52 0.53 0.51 17 232 Table 5 R. Kumar et al. / International Journal of Machine Tools & Manufacture 45 (2005) 228-234 Basically the accuracy of the interpolation technique to Variation of G a with varying magnification factors for milled surfaces G a (1!) 15.62 19.35 21.31 18.23 17.71 21.36 25.51 26.46 G a (2!) 18.98 20.73 23.47 19.73 32.51 18.83 29.53 21.72 G a(5!) 29.95 33.23 36.49 31.59 33.45 39.91 37.86 42.27 G a (10!) 28.42 35.28 40.86 33.77 36.89 43.26 48.11 50.31 G a (20!) 34.47 43.60 45.18 39.04 41.48 44.57 53.25 56.05 R a (mm) 2.17 2.94 3.51 2.69 2.46 3.41 4.41 4.65 Table 6 Variation of G a with varying magnification factors for shaped surfaces G a (1!) 22.31 17.21 21.07 24.95 19.11 29.63 19.61 G a (2!) 24.2 17.38 22.17 26.42 27.79 15.98 17.91 G a (5!) 35.35 33.11 34.52 38.42 44.51 48.17 36.12 G a (10!) 38.86 35.71 37.04 39.43 48.39 50.24 39.92 G a (20!) 41.28 43.11 40.32 44.85 53.49 55.28 40.43 R a (mm) 19.06 19.83 21.34 24.58 26.63 27.74 23.44 provide image magnification depends on its convergence 3 rate. Cubic convolution 13 offers a O(h ) convergence rate whereas cubic spline has a fourth order convergence rate, 4 i.e. O(h ). It means removing or altering the conditions on interpolation kernel to achieve a higher convergence rate, which in turn demands higher computational effort to derive interpolation coefficients. So there is a trade off between accuracy offered by an interpolation technique and efficiency in terms of computational effort it requires. Moreover, it is implemented quite easily by modern digital computers and image processors. Although the present algorithm is the optimal choice, it cannot prevent the perceptible degradation of edges fully. a wide range of magnification index ranging from 2! to 20! going in steps, suitable for future task of determining surface roughness and also to assess the effectiveness of improvement scheme once applied to them. Cubic convolu- tion remains as one of the best methods for magnification of digital images in terms of preserving edge details when compared to other methods, the blurring of edges has been found to be reduced substantially 13. It is a great advantage, as the edges inuence the image parameters decisively, and effective preservation of edges is essential for all image-processing applications including surface roughness determination. The computational simplicity offered by cubic convolution method cannot be abandoned for the slightly better result given by cubic spline method. Fig. 1. Variation of correlation coefficient with magnification factor for three machining processes. Fig. 2. A 100!100 image (topmost) of a ground surface. Its 2! magnified (middle) and magnified and improved image (bottommost). 18 R. Kumar et al. / International Journal of Machine Tools & Manufacture 45 (2005) 228 -234 233 edges, e.g. ground surfaces where the grain structure can be clearly seen after applying this algorithm. As the index of magnification increases, the effectiveness of the algorithm decreases, which is on the expected lines. Regression equations developed gave a maximum error of 2% and an average error of 0.7% in case of grinding, a maximum error of 6.34% and an average error of 1.2% in case of milling and finally a maximum error of 8.2% and an average error of 3.72% in case of shaping. This trend can be explained from the fact that large local variations in surface characteristics of milled and shaped surfaces, as compared to the ground one, cause slightly more inaccurate correlation between G a and R a. Finally, as seen from the plots in Fig. 1, there is an increase in the correlation coefficient with the magnification index and this increment is more marked in the case of ground components compared to milled and shaped ones. As mentioned earlier, owing to large local variations in surface roughness in the case of milled and shaped surfaces, magnification algorithm becomes increasingly ineffective with magnification index. This in turn means that magnified images of milled and shaped surfaces cannot predict the actual or true surface characteristics of a very small region of the image (which is subject to magnification), as compared to the magnified image of a ground workpiece, since large and irregular surface feature variation renders it difficult for the magnification algorithm to interpolate the brightness value of a pixel from that of its adjacent pixels correctly. Whereas in case of grinding, uniform surface texture helps magnification scheme to predict (through interpolation, as such is the nature of algorithm) values which are remarkably closer to the actual ones. It has also been observed that the plots in Fig. 1 follow the power law. 8. Conclusions The present work clearly indicates that the Machine vision approach can be used to evaluate the surface roughness of m chined surfaces and during evaluation, a good linear relationship between R a and G a is observed with a high level of accuracy. Cubic convolution interpolation method proved to be the optimal choice for magnification of digital images and subsequent image improvement can be done by Linear Edge Crispening algorithm. The calculation of G a, optical roughness value, from these magnified and improved images had a better correlation (i.e. higher correlation coefficient) with the average surface roughness (R a) measured for the components manufactured using the machining operations shaping, milling and grinding, indicating its effectiveness in application to measurement of surface roughness using machine vision system. It can also be inferred that this scheme of optical roughness estimation seems more promising for machining operations Fig. 3. A 100!100 image (topmost) of a milled surface. Its 2! magnified (middle) and magnified and improved image (bottommost). Some amount of blurring can be seen in every magnified image. To calculate the surface roughness pa