数字图像处理在光栅质量评定中的应用

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摘　要

计量光栅是一种常用而且又重要的光学器件，它在许多领域中都有广泛的应

用。在使用光栅之前，必须要对它的质量做一评定。虽然光栅作为产品，在出厂之

前已经通过质量检验，但在检验时，是通过显微镜对光栅进行观察，看光栅的条

纹是否规则，是否有明显的凸出或凹陷。使用的显微镜的放大倍数一般为 40 倍。

这是因为如果放大倍数太小，一些细微的细节将会观察不到；而放大倍数过大的

话，视场的范围将太小，因面如果要对光栅的每一部分都要观察到是十分困难的

这样检验起来会很麻烦。这是从客观方面来考虑的；同时在检验时，是通过肉眼

来观察的，不同的人去观察，得到的结论也可能会不同，所以检验结果受到检验

者个人的主观因素的影响也较大，这是从主观方面来考察的。因此，不论从主观

还是客观方面去考虑，这样的检验方法都有不足之处。

由于这些不足之处，有必要对用新的方法来检验光栅的质量做一研究。本文

的目的就是为了改进传统方法，利用计算机图像处理技术处理分析光栅的透射图

从而对光栅的质量进行检验、评定。

本课题至少有以下两方面的意义：

在本文所提出的方法中，检验光栅质量的过程中，经过显微镜放大后的

图像不是直接用肉眼来观察，而是通过传感器输入到监视器中通过计算

机来分析的。这样做一方面克服了显微镜放大倍数这一客观条件的限制

同时也避免了由肉眼观察所带来的主观方面的影响因素。

在检验时，只要用摄像系统采集得到光栅的透射图像，然后对该图像进

行一定的分析，就可以检验光栅的质量，因而检验系统结构简单、快捷。

有一定的实用价值

在本文中，作者主要做了以下工作：

图像的滤波及其方法的选择。

由于在采集光栅透射图像的过程中，可能存在位移、旋转等畸变。也可能由于

其它各种因素的干扰使图像产生噪声或使图像变模糊，因而首先需要对图像进行

平滑和增强等预处理, 这就是对图像的滤波。

在本文中通过分析比较，利用了一种新的滤波技术，即小波变换的方法来消

除图像中的噪声。小波变换是近年来得到迅速发展的一种新的信号处理方法，它

已经在许多领域里得到了重要的应用。小波滤波就是利用信号和噪声在各尺度下

的小波系数有所不同的特点，来对它们进行分离，从而达到滤波的目的。最后用

Matalb 模拟了所得到的结果，并对结果做了分析，模拟结果表明，滤波结果还是

相当理想的。

光栅图像条纹方向的确定

光栅的透射图像是一种典型的纹理图像，它由明暗相间的条纹组成，纹理比

较规则。因而在本文的分析中，条纹的方向是一个重要的参数，需要确定，在本

文的处理中将采用 Hough 变换的方法。

Hough 变换是于 1962 年在美国作为专利而被发表的，它对图像形状可以进行

有效的识别，而且对噪声的影响不太敏感，所以取得了很大的应用。在本文中根

据Hough 变换检测直线的原理，确定了光栅图像条纹的方向，并用Matlab 时进行

了模拟。模拟结果表明，该方法对光栅透射图像的处理效果好，可以达到要求。

图像的二值化算法的研究

以二值图像处理为中心的图像处理系统目前很多，这主要是因为这种系统处

理速度快，成本低，而且还能定义几何学的各种概念等。因此将图像转化成为二

值图像来处理是很有必要的。在本文中对光栅图像进行处理的过程中，也需要把

图像转化成为二值图像。

对图像时行二值化处理时，阈值的选取是一个关键问题，在本文中作者研究

了该问题，并结合本课题研究的目的，提出了一种确定阈值的算法，对该算法用

Matlab 进行了模拟，结果表明该算法是可行的。

评定指标的设计

本文的目的就是通过对光栅透射图像的分析提来评定光栅质量的好坏，要评

定，就必须有评定指标，这是评价光栅质量的关键。指标设计的好与坏，关系到

评价结果的可靠性。因而，本文在指标设计及综合评价分析上也做了一定的研究

并得到了比较满意的结果。

关键词：数字图像处理　光栅　小波变换　二值化　指标　质量评定

ABSTRACT

Metric raster is an important and useful optical instrument, and has been widely

used in various fields. We must access it’s quality before we use a raster. As products,

raster has passed the quality inspection before leaving factory, but the inspection is done

using the microscope to check if the stripe of the raster is regular, if there exists obvious

protrusion or concave. In general, the enlargement factor of the microscope is 40, if the

multiple is too small, the remoteness details can’t be observed. If the multiple is too

large, the visual field will be too small, making it difficult to observe each part of the

raster. Hence, this inspection method is difficult to implement. Further more, different

people may get different results because the results can only be observed by means of

human eyes using this inspection method. It’s easy to see that this inspection method

does have some disadvantages from both subjective or objective points of view.

Based on the facts mentioned above, it’s necessary to find a new way to inspect the

quality of raster. Using the technology about digital image processing, we will improve

the traditional method to analyze the quality of transmission image of raster and

appraise the quality of raster in the end.

This paper has at least two advantages as follows:

Using the method brought forward in this paper, the image enlarged with the

microscope is inputted to computer using a sensor and will be analyzed by

computer instead of human eyes during the course of inspection. This method

not only can eliminate the limitation of multiple of enlargement, but also can

avoid the subjective impacts of human eyes.

The inspection system is simple, practical, and easy to implement, because the

quality of raster can be appraised simply by collecting the transmission image

of the raster for analysis using computer.

What the author has mainly done in this paper is:

The filtering of image and the selection of approach

Because the image is likely to be displaced and rotated in the course of collection,

and the image is tend to include noise or become fuzzy because of some other factors.

Hence, it must be filtered before we analyze the transmission image of raster.

This paper has introduced a new method called Wavelet transform to handle the

image filtering. This technology about digital signal filtering has developed rapidly in

the past several decades and has played an important role in many important

applications in various fields. Depending on the characteristic that the signal and noise

has different wavelet coefficient in different scale, Wavelet transform successfully

separate noise from signal. Using Matlab, a very famous software in engineering

calculation, We simulated the result, and analyzed the result we have got, the result

indicated that the filtering approach is relatively effective.

Determine the directional angel of the stripe in the image

The transmission image of raster is a typical texture image, and the strip in the

image is quite formal. In this paper, the direction of the stripe is an important parameter

for the analysis of transmission image, so the determination of the directional angel of

the stripe is necessary. We finished this work based on the theory of Hough transform .

Hough transform was bring forward as patent in the U.S in 1962, it can effectively

identify the shape of image and isn’t very hypersensitive to the noise, so this approach

is widely adopted in various applications. In this paper, we advances an approach using

the Hough Transform to determine the transmission image’s stripe angle, the effective

result of this approach is validated by the simulation test using Matlab.

The study on algorithm about thresholding

Binary image has many advantages, like higher processing speed, lower cost, the

easier definitions about some geometrical concepts, and so on. Many systems are based

on binary image processing. So it is necessary to transform the color image to binary

image. In this paper, we also need transform the image to binary image in the course of

processing raster image.

To transform the image to binary image, the key problem is to determine the threshold.

We worked on this problem and brought forward a feasible and practical algorithm in

this paper. In the end, we simulated this algorithm using Matlab and the algorithm had

proved to be effective.

The designing of the index of assessing

Our purpose in this paper is to assess the quality of raster based on the analysis of

the transmission image of raster, so we must have some index about it, and this is the

key to quality assessing. The index designed can greatly influence our assessing result

and the reliability of the result. So in the paper we also worked on how to design the

index and on the overall evaluation analysis. And we got satisfactory results in the end.

Key words: Digital image processing, Raster, Wavelet Transform,

Thresholding, Index, Quality Assessing

目　录
摘要
ABSTRACT
第一章 绪　论..................................................................................................................1
§1.1 问题的提出..........................................................................................................1
§1.1.1 光栅简介............................................................................................................................1
§1.1.2 光栅质量的检验................................................................................................................2
§1.1.3 透射图像的采集................................................................................................................2
§1.1.4 本文所提出的方法............................................................................................................3
§1.1.5 本文研究的意义................................................................................................................4
§1.2 该领域目前的研究概况......................................................................................4
§1.2.1 数字图像处理简介............................................................................................................4
§1.2.2 目前研究概况....................................................................................................................5
§1.2.3 纹理图像处理研究概况...................................................................................................6
§1.3 本文的主要内容及结构......................................................................................7
§1.3.1 主要内容............................................................................................................................7
§1.3.2 结构安排............................................................................................................................7
第二章 数字图像的基本概念..........................................................................................9
§2.1 引言......................................................................................................................9
§2.2 图像模型..............................................................................................................9
§2.3 图像的数字化....................................................................................................10
§2.3.1 采样..................................................................................................................................10
§2.3.2 量化..................................................................................................................................11
§2.3.3 图像的矩阵表示..............................................................................................................11
§2.4 数字图像类型....................................................................................................12
§2.4.1 真彩色图像......................................................................................................................13
§2.4.2 灰度图像..........................................................................................................................13
§2.4.3 二值图像..........................................................................................................................13
§2.5 图像类型的转换................................................................................................13
§2.5.1 真彩色图像转换为灰度图像.........................................................................................14
§2.5.2 灰度图像转换为二值图像.............................................................................................14
第三章 图像的滤波........................................................................................................15
§3.1 引言....................................................................................................................15
§3.2 小波变换的概念................................................................................................15
§3.2.1 一维小波变换..................................................................................................................15
§3.2.2 正交多尺度分解..............................................................................................................16
§3.2.3 二维小波变换..................................................................................................................19
§3.3 小波变换滤波及算法........................................................................................21
§3.4 试验仿真............................................................................................................22

§3.4.1 仿真结果..........................................................................................................................22
§3.4.2 结果分析..........................................................................................................................25
第四章 图像条纹方向的确定........................................................................................28
§4.1 引言....................................................................................................................28
§4.2 HOUGH 变换的定义及性质...............................................................................28
§4.2.1 Hough 变换的定义..........................................................................................................28
§4.2.2 Hough 变换的性质..........................................................................................................30
§4.3 图像边缘的检测................................................................................................30
§4.3.1 Sobel 算子的概念...........................................................................................................30
§4.3.2 边缘的提取......................................................................................................................31
§4.4 用HOUGH 变换确定图像纹理的方向..............................................................31
§4.5 试验仿真............................................................................................................33
§4.5.1 仿真结果..........................................................................................................................33
§4.5.2 结果分析..........................................................................................................................34
第五章 图像的二值化....................................................................................................36
§5.1 引言....................................................................................................................36
§5.2 图像二值化的基本概念....................................................................................36
§5.2.1 静态门限..........................................................................................................................36
§5.2.2 一般动态门限..................................................................................................................36
§5.2.3 背景动态门限..................................................................................................................37
§5.3 阈值确定的理论分析........................................................................................37
§5.3.1 概述..................................................................................................................................37
§5.3.2 从布尔代数出发分析.....................................................................................................38
§5.3.3 从二元域出发分析..........................................................................................................41
§5.3.4 一点说明..........................................................................................................................42
§5.4 指标的权重的确定............................................................................................42
§5.4.1 定性分析..........................................................................................................................42
§5.4.2 理论分析..........................................................................................................................44
§5.4.3 权重的确定......................................................................................................................47
§5.5 算法描述............................................................................................................47
§5.5.1 算法分析..........................................................................................................................47
§5.5.2 算法流程图......................................................................................................................48
§5.6 试验仿真............................................................................................................49
§5.6.1 仿真结果..........................................................................................................................49
§5.6.2 结果分析..........................................................................................................................50
第六章 评价指标的设计................................................................................................51
§6.1 引言....................................................................................................................51
§6.2 统计指标............................................................................................................51
§6.2.1 样本空间..........................................................................................................................51
§6.2.2 均值..................................................................................................................................53

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摘要：

摘　要计量光栅是一种常用而且又重要的光学器件，它在许多领域中都有广泛的应用。在使用光栅之前，必须要对它的质量做一评定。虽然光栅作为产品，在出厂之前已经通过质量检验，但在检验时，是通过显微镜对光栅进行观察，看光栅的条纹是否规则，是否有明显的凸出或凹陷。使用的显微镜的放大倍数一般为40倍。这是因为如果放大倍数太小，一些细微的细节将会观察不到；而放大倍数过大的话，视场的范围将太小，因面如果要对光栅的每一部分都要观察到是十分困难的这样检验起来会很麻烦。这是从客观方面来考虑的；同时在检验时，是通过肉眼来观察的，不同的人去观察，得到的结论也可能会不同，所以检验结果受到检验者个人的主观因素的影响也较大，这是...

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