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毕业论文外文翻译-图像分割

毕业论文外文翻译-图像分割
毕业论文外文翻译-图像分割

图像分割

前一章的资料使我们所研究的图像处理方法开始发生了转变。从输人输出均为图像的处理方法转变为输人为图像而输出为从这些图像中提取出来的属性的处理方法〔这方面在1.1节中定义过)。图像分割是这一方向的另一主要步骤。

分割将图像细分为构成它的子区域或对象。分割的程度取决于要解决的问题。就是说当感兴趣的对象已经被分离出来时就停止分割。例如,在电子元件的自动检测方面,我们关注的是分析产品的图像,检测是否存在特定的异常状态,比如,缺失的元件或断裂的连接线路。超过识别这此元件所需的分割是没有意义的。

异常图像的分割是图像处理中最困难的任务之一。精确的分割决定着计算分析过程的成败。因此,应该特别的关注分割的稳定性。在某些情况下,比如工业检测应用,至少有可能对环境进行适度控制的检测。有经验的图像处理系统设计师总是将相当大的注意力放在这类可能性上。在其他应用方面,比如自动目标采集,系统设计者无法对环境进行控制。所以,通常的方法是将注意力集中于传感器类型的选择上,这样可以增强获取所关注对象的能力,从而减少图像无关细节的影响。一个很好的例子就是,军方利用红外线图像发现有很强热信号的目标,比如移动中的装备和部队。

图像分割算法一般是基于亮度值的不连续性和相似性两个基本特性之一。第一类性质的应用途径是基于亮度的不连续变化分割图像,比如图像的边缘。第二类的主要应用途径是依据事先制定的准则将图像分割为相似的区域,门限处理、区域生长、区域分离和聚合都是这类方法的实例。

本章中,我们将对刚刚提到的两类特性各讨论一些方法。我们先从适合于检测灰度级的不连续性的方法展开,如点、线和边缘。特别是边缘检测近年来已经成为分割算法的主题。除了边缘检测本身,我们还会讨论一些连接边缘线段和把边缘“组装”为边界的方法。关于边缘检测的讨论将在介绍了各种门限处理技术之后进行。门限处理也是一种人们普遍关注的用于分割处理的基础性方法,特别是在速度因素占重要地位的应用中。关于门限处理的讨论将在几种面向区域的分割方法展开的讨论之后进行。之后,我们将讨论一种称为分水岭分割法的形态学

图像分割方法。这种方法特别具有吸引力,因为它将本章第一部分提到的几种分割属性技术结合起来了。我们将以图像分割的应用方面进行讨论来结束本章。 10.1间断检测

在本节中,我们介绍几种用于检测数字图像中三种基本的灰度级间断技术:点、线和边缘。寻找间断最一般的方法是以3.5节中描述的方式对整幅图像使用一个模板进行检测。图10-1所示的3x3模板,这一过程包括计算模板所包围区域内灰度级与模板系数的乘积之和。就是说,关于式(3.5.3),在图像中任意点的模板响应由下列公式给出:

∑==+++=919

9...2211i wizi

z w z w z w R (10.1.1)

图10-1 一个一般的3*3模板

这里Zi 是与模板系数Wi 相联系的像素的灰度级。照例,模板响应是它的中心位置。有关执行模板操作的细节在3.5节中讨论。

10.1.1点检测

在一幅图像中,孤立点的检测在理论上是简单的。使用如图10-2(a)所示的模板,如果

|R| ≥ T (10.1.2)

我们说在模板中心的位置上已经检测到一个点。这里T 是一个非负门限,R 由式(10.1.1)给出。基本上,这个公式是测量中心点和它的相邻点之间加权的差值。基本思想就是:如果一个孤立的点(此点的灰度级与其背景的差异相当大并且它所在的位置是一个均匀的或近似均匀的区域)与它周围的点很不相同,则很容易被这类模板检测到。注意,图10-2(a)中的模板同图3.39(d)中给出的模板在拉

普拉斯操作方而是相同的。严格地讲,这里强调的是点的检测。即我们着重考虑

的差别是那些足以识别为孤立点的差异(由T决定)。注意,模板系数之和为零表

示在灰度级为常数的区域,模板响应为零。

(a)

(b)(c)(d)图10-2 (a)点检测模板,(b)带有通孔的涡轮叶片的X射线,(c)点检测的结果,(d)使用式(10.1.2)得到的结果(原图由X-TEK系统公司提供)

例10.1图像中孤立点的检浏

我们以图10-2(b)功为辅助说明如何从一幅图中将孤立点分割出来.这幅X

射线图显示了一个带有通孔的喷气发动抓涡枪叶片,通孔位于圈像的右上象限。

在孔中只嵌有一个黑色像素。图10-2(c)是将点检测模板应用于X射线图像后得

到的结果.图10-2(d)显示了当T取图10-2(c)中像素最高绝衬值的90%时,应用

式(10.1.2)所得的结果(门限选择将在10.3节中详细讨论)。图中的这个单一的

像素清晰可见(这个像素被人为放大以便印刷后可以看到)。由于这类检测是基于

单像素间断,并且检测器模板的区域有一个均匀的背景,所以这个检测过程是相

当有专用性的当这一条件不能满足时,本章中计论的其他方法会更适合检测灰度

级间断

10.1.2线检测

复杂程度更高一级的检测是线检测,考虑图10-3中显示的模板。如果第l

个模板在图像中移动,这个模板将对水平方向的线条(一个像素宽度)有更强的响

应。在一个不变的背景上,当线条经过模板的中间一行时会产生响应的最大值。画一个元素为1的简单阵列,并且使具有不同灰度级(如5)的一行水平穿过阵列,可以很容易验证这一点。同样的实验可以显示出图10-3中的第2个模板对于45°方向线有最佳响应;第3个模板对于垂直线有最佳响应;第4个模板对于

-45°方向线有最佳响应;这些方向也可以通过注释每个模板的优选方向来设置,即在这些方向上用比别的方向更大的系数(为2)设置权值。注意每个模板系数相加的总和为零,表示在灰度级恒定的区域来自模板的响应为零。

°

图10-3 线模板

令R1,R2,R3和R4。从左到右代表图10-3中模板的响应,这里R的值由式(10.1.1)给出。

假设4个模板分别应用于一幅图像,在图像中心的点,如果|Ri|>|Rj| ,

j≠i,则此点被认为与在模板i方向上的线更相关。例如,如果在图中的一点有|Ri|>|Rj| ,j=2,3,4,我们说此特定点与水平线有更大的联系。

换句话说,我们可能对检测特定方向上的线感兴趣。在这种情况下,我们应使用与这一方向有关的模板,并设置该模板的输出门限,如式(10.1.2)所示。换句话说,如果我们对检测图像中由给定模板定义的方向上的所有线感兴趣.只需要简单地通过整幅图像运行模板,并对得到的结果的绝对值设置门限即可。留下的点是有最强响应的点。对于一个像素宽度的线,这些响应最靠近模板定义的对应方向。下列例子说明了这一过程。

例 10.2特定方向上的线检测

图10-4(a)显示了一幅电路接线模板的数字化(二值的)图像。假设我们要找到一个像素宽度的并且方向为-45°的线条。基于这个假设,使用图10-3中最后一个模板。图10-4(b)显示了得到的结果的绝对值。注意,图像中所有水平和垂直的部分都被除去了。并且在图10-4(b)中所有原图中接近-45°方向的部分产生了最强响应。

(a)

(b)(c)

图10-4 线检测的说明。(a)二进制电路接线模板,(b)使用-45°线检测器

处理后得到的绝对值,(c)对图像(b)设置门限得到的结果为了决定哪一条线拟合模板最好,只需要简单地对图像设置门限。图10-4(c)显示了使门限等于图像中最大值后得到的结果。对于与这个例子类似的应用,让门限等于最大值是一个好的选择,因为输入图像是二值的,并且我们要寻找的是最强响应。图10-4(c)显示了在白色区所有通过门限检测的点。此时,这一过程只提取了一个像素宽且方向为-45°的线段(图像中在左上象限中也有此方向上的图像部分,但宽度不是一个像素)。图10-4(c)中显示的孤立点是对于模板也有相同强度响应的点。在原图中,这些点和与它们紧接着的相邻点,是用模板在这些孤立位置上生成最大响应的方法来定向的。这些孤立点也可以使用图10-2(a)中的模板进行检测,然后删除,或者使用下一章中讨论的形态学腐蚀法删除。

10.1.3边缘检侧

尽管在任何关于分割的讨论中,点和线检测都是很重要的,但是边缘检测对

于灰度级间断的检测是最为普遍的检测方法。本节中,我们讨论实现一阶和二阶数字导数检测一幅图像中边缘的方法。在3.7节介绍图像增强的内容中介绍过这些导数。本节的重点将放在边缘检测的特性上。某些前面介绍的概念在这里为了叙述的连续性将进行简要的重述。

基本说明

在3.7.1节中我们非正式地介绍过边缘。本节中我们更进一步地了解数字化边缘的概念。直观上,一条边缘是一组相连的像素集合。这些像素位于两个区域的边界上。然而,我们已经在2.5.2节中用一定的篇幅解释了一条边缘和一条边界的区别。从根本上讲,如我们将要看到的,一条边缘是一个“局部”概念,而由于其定义的方式,一个区域的边界是一个更具有整体性的概念。给边缘下一个更合理的定义需要具有以某种有意义的方式测量灰度级跃变的能力。

我们先从直观上对边缘建模开始。这样做可以将我们引领至一个能测量灰度级有意义的跃变的形式体系中。从感觉上说,一条理想的边缘具有如图10-5(a)所示模型的特性。依据这个模型生成的完美边缘是一组相连的像素的集合(此处为在垂直方向上),每个像素都处在灰度级跃变的一个垂直的台阶上(如图形中所示的水平剖面图)。

实际上,光学系统、取样和其他图像采集的不完善性使得到的边缘是模糊的,模糊的程度取决于诸如图像采集系统的性能、取样率和获得图像的照明条件等因素。结果,边缘被更精确地模拟成具有“类斜面”的剖面,如图10-5(b)所示。斜坡部分与边缘的模糊程度成比例。在这个模型中,不再有细线(一个像素宽的线条)。相反,现在边缘的点是包含于斜坡中的任意点,并且边缘成为一组彼此相连接的点集。边缘的“宽度”取决于从初始灰度级跃变到最终灰度级的斜坡的长度。这个长度又取决于斜度,斜度又取决于模糊程度。这使我们明白:模糊的边缘使其变粗而清晰的边缘使其变得较细。

图10-6(a)显示的图像是从图10-5(b)的放大特写中提取出来的。图10-6(b)显示了两个区域之间边缘的一条水平的灰度级剖面线。这个图形也显示出灰度级剖面线的一阶和二阶导数。当我们沿着剖面线从左到右经过时,在进人和离开斜面的变化点,一阶导数为正。在灰度级不变的区域一阶导数为零。在边缘与黑色一边相关的跃变点二阶导数为正,在边缘与亮色一边相关的跃变点二阶导数为负,沿着斜坡和灰度为常数的区域为零。在图10-6(b)中导数的符号在从亮到暗

的跃变边缘处取反。

(a)(b)

图10-5 (a)理想的数字边缘模型,(b)斜坡数字边缘模型。

斜坡部分与边缘的模糊程度成正比

图10-6 (a)由一条垂直边缘分开的两个不同区域,(b)边界附近的细

节显示了一个灰度级剖面图和一阶与二阶导数的剖面图由这些现象我们可以得到的结论是:一阶导数可以用于检测图像中的一个点是否是边缘的点(也就是判断一个点是否在斜坡上)。同样,二阶导数的符号可以用于判断一个边缘像素是在边缘亮的一边还是暗的一边。我们注意到围绕一条边缘,二阶导数的两条附加性质(1)对图像中的每条边缘二阶导数生成两个值(一个

不希望得到的特点);(2)一条连接二阶导数正极值和负极值的虚构直线将在边缘中点附近穿过零点。将在本节后面说明,二阶导数的这个过零点的性质对于确定粗边线的中心非常有用。

最后,注意到某些边缘模型利用了在进人和离开斜坡地方的平滑过渡(习题10.5)。然而,我们在接下来的讨论中将得出同样的结论。而且,这一点从我们使用局部检测进行处理就可以很明显地看出(因此,2.5.2节中对于边缘的局部性质进行了说明)。

尽管到此为止我们的注意力被限制在一维水平剖面线范围内,但同样的结论可以应用于图像中的任何方向上。我们仅仅定义了一条与任何需要考察的点所在的边缘方向相垂直的剖面线,并如前面讨论的那样,对结果进行了解释。

注:出自

Digital Image Processing 2nd Edition . Prentice Hall

Image Segmentation

The material in the previous chapter began a transition from image processing methods whose input and output are images, to methods in which the inputs are images, but the outputs are attributes extracted from those images (in the sense defined is Section 1.1). Segmentation is another major step in that direction.

Segmentation subdivides an image into its constituent regions or objects. The level to which the subdivision is carried depends on the problem being solved. That is, segmentation should stop when the objects of interest in an application have been isolated. For example, in the automated inspection of electronic assemblies, interest lies in analyzing images of the products with the objective of determining the presence or absence of specific anomalies, such as missing components or broken connection paths. There is no point in carrying segmentation past the level of detail required to identify those elements.

Segmentation of nontrivial images is one of the most difficult tasks in image processing. Segmentation accuracy determines the eventual success or failure of computerized analysis procedures. For this reason, considerable care should be taken to improve the probability of rugged segmentation. In some situations , such as industrial inspection applications, at least some measure of control over the environment is possible at times. The experienced image processing system designer invariably pays considerable attention to such opportunities. In other applications, such as autonomous target acquisition, the system designer has no control of the environment. Then the usual approach is to focus on selecting the types of sensors most likely to enhance the objects of interest while diminishing the contribution of irrelevant image detail. A good example is the use of infrared imaging by the military to detect objects with strong heat signatures , such as equipment and troops in motion.

Image segmentation algorithms generally are based on one of two basic properties of intensity values: discontinuity and similarity. In the first category, the approach is to partition an image based on abrupt changes in intensity, such as edges in an image. The principal approaches in the second category are based on

partitioning an image into regions that are similar according to a set of predefined criteria. Thresholding, region growing, and region splitting and merging are examples of methods in this category.

In this chapter we discuss a number of approaches in the two categories just mentioned. We begin the development with methods suitable for detecting gray level discontinuities such as points, lines, and edges. Edge detection in particular has been a staple of segmentation algorithms for many years. In addition to edge detection per se, we also discuss methods for connecting edge segments and for "assembling" edges into region boundaries. The discussion on edge detection is followed by the introduction of various thresholding techniques . Thresholding also is a fundamental approach to segmentation that enjoys a significant degree of popularity, especially in applications where speed is an important factor. The discussion on thresholding is followed by the development of several region-oriented segmentation approaches. We then discuss a morphological approach to segmentation called watershed segmentation. This approach is particularly attractive because it combines several of the positive attributes of segmentation based on the techniques presented in the first part of the chapter. We conclude the chapter with a discussion on the use of motion cues for image segmentation.

10.1Detection of Discontinuities

In this section we present several techniques for detecting the three basic types of gray-level discontinuities in a digital image: points, lines, and edges. The most common way to look for discontinuities is to run a mask through the image in the manner described in Section 3.5. For the 3 x 3 mask shown in Fig. 10.1, this procedure involves computing the sum of products of the coefficients with the gray levels contained in the region encompassed by the mask. That is. with reference to Eq.

(3.5-3). the response of the mask at anv point in the image is given by

∑==+++=919

9...2211i wizi

z w z w z w R (10.1.1)

FIGURE 10.1 A general 3 x 3 mask.

where z; is the gray level of the pixel associated with mask coefficient Wi. As usual, the response of the mask is defined with respect to its center location. The details for implementing mask operations are discussed in Section 3.5.

10.1.1 Point Detection

The detection of isolated points in an image. is straightforward in principle. Using the mask shown in Fig. 10.2(a), we say that a point has been detected at the location on which the mask is centered if

|R| ≥ T (10.1.2)

where T is a nonnegative threshold and R is given by Eq. (10.1-1). Basically,this formulation measures the weighted differences between the center point and its neighbors. The idea is that an isolated point (a point whose gray level is significantly different from its background and which is located in a homogeneous or nearly homogeneous area) will be quite different from its surroundings, and thus be easily detectable by this type of mask. Note that the mask in Fig. 10.2(a) is the same as the mask shown in Fig. 3.39(d) in connection with Laplacian operations. However, the emphasis here is strictly on the detection of points. That is, the only differences that are considered of interest are those large enough (as determined by T, to be considered isolated points. Note that the mask coefficients sum to zero, indicating that the mask response will be zero in areas of constant gray level.

(a)

(b)(c)(d)FIGURE 10.2(a) Pointdetection mask. (b) X-ray image of a turbine blade with a porosity. (c) Result of point detection. (d) Result of using Eq. (10.1-2).(Original image courtesy of X-TEK Systems Ltd.)

EXAMPLE 10.1:Detection of isolated points in an image.

We illustrate segmentation of isolated points from an image with the aid of Fig.

10.2(6), which shows an X-ray image of a jet-engine turbine blade with a porosity in the upper, right quadrant of the image. There is a single black pixel embedded within the porosity. Figure 10.2(c) is the result of applying the point detector mask to the X-ray image, and Fig. 10.2(d) shows the result of using Eq. (10.1.2) with T equal to 90% of the highest absolute pixel value of the image in Fig. 10.2(c). (Threshold selection is discussed in detail in Section 10.3) The single pixel is clearly visible in this image (the pixel was enlarged manually so that it would be visible after printing). This -type of detection process is rather specialized because it is based on single-pixel discontinuities that have a homogeneous background in the area of the detector mask. When this condition is not satisfied, other methods discussed in this chapter are more suitable for detecting gray-level discontinuities.

10.1.2 Line Detection

The next level of complexity is line detection. Consider the masks shown in Fig.

10.3. If the first mask were moved around an image, it would respond more strongly to lines (one pixel thick) oriented horizontally. With a constant background, the maximum response would result when the line passed through the middle row of the mask. This is easily verified by sketching a simple array of 1's with a line of a different gray level (say, 5's) running horizontally through the array. A similar experiment would reveal that the second mask in Fig. 10.3 responds best to lines oriented at +450; the third mask to vertical lines; and the fourth mask to lines in the -450 direction . These directions can be established also by noting that the preferred direction of each mask is weighted with a larger coefficient (i.e., 2) than other possible directions. Note that the coefficients in each mask sum to zero, indicating a zero response from the masks in areas of constant gray level.

Horizontal +45° Vertical -45°

FIGURE 10.3 Line masks.

Let R1, R2, R3, and R4 denote the responses of the masks in Fig. 10.3, from left to right, where the R's are given by Eq. (10.1-1). Suppose that the four masks are run individually through an image. If, at a certain point in the image, |Ri| > |Rj|, for all j ≠i, that point is said to be more likely associated with a line in the direction of mask i. For example, if at a point in the image, |Ri|>|Rj|, for j = 2, 3. 4, that particular point is said to be more likely associated with a horizontal line. Alternatively, we may be interested in detecting lines in a specified direction. In this case, we would use the mask associated with that direction and threshold its output, as in Eq . (10.1.2). In other words, if we are interested in detecting all the lines in an image in the direction defined by a given mask, we simply run the mask through the image and threshold the absolute value of the result. The points that are left are the strongest responses, which,

for lines one pixel thick, correspond closest to the direction defined by the mask. The following example illustrates this procedure.

EXAMPLE 10.2:Detection of lines in a specified direction

Figure 10.4(a) shows a digitized (binary) portion of a wire-bond mask for an electronic circuit. Suppose that we are interested in finding all the lines that are one pixel thick and are oriented at-45". For this purpose, we use the last mask shown in Fig. 10.3.The absolute value of the result is shown in Fig. 10.4(b). Note that all vertical and horizontal components of the image were eliminated, and that the components of the original image that tend toward a -45° direction

(a)

(b)(c)

FIGURE 10.4 Illustration of line detection (a) Binary wirebond mask.

(b) Absolute value of result after processing with -45° line detector. (c) Result of thresholding image. (b) produced the strongest responses in Fig. 10.4(b).

In order to determine which lines best fit the mask, we simply threshold this image. The result of using a threshold equal to the maximum value in the image is

shown in Fig. 10.4(c).The maximum value is a good choice for a threshold in applications such as this because the input image is binary and we are looking for the strongest responses. Figure 10.4(c) shows in white all points that passed the threshold test. In this case, the procedure extracted the only line segment that was one pixel thick and oriented at -450 (the other component of the image oriented in this direction in the top, left quadrant is not one pixel thick). The isolated points shown in Fig.

10.4(c) are points that also had similarly strong responses to the mask. In the original image, these points and their immediate neighbors are oriented in such as way that the mask produced a maximum response at those isolated locations. These isolated points can be detected using the mask in Fig. 10.2(a) and then deleted, or they could be deleted using morphological erosion, as discussed in the last chapter.

10.1.3 Edge Detection

Although point and line detection certainly are important in any discussion on segmentation, edge detection is by far the most common approach for detecting meaningful discontinuities in gray level. In this section we discuss approaches for implementing first- and second-order digital derivatives for the detection of edges in an image. We introduced these derivatives in Section 3.7 in the context of image enhancement. The focus in this section is on their properties for edge detection. Some of the concepts previously introduced are restated briefly here for the sake continuity in the discussion.

Basic formulation

Edges were introduced informally in Section 3.7.1. In this section we look at the concept of a digital edge a little closer. Intuitively, an edge is a set of connected pixels that lie on the boundary between two regions. However, we already went through some length in Section 2.5.2 to explain the difference between an edge and a boundary. Fundamentally, as we shall see shortly, an edge is a "local" concept whereas a region boundary, owing to the way it is defined, is a more global idea. A reasonable definition of "edge" requires the ability to measure gray-level transitions in a meaningful way.

We start by modeling an edge intuitively. This will lead us to a formalism to

which "meaningful" transitions in gray levels can be measured. Intuitively, an ideal edge has the properties of the model shown in Figure 10.5(a). An ideal edge according to this model is a set of connected pixels (in the vertical direction here), each of which is located at an orthogonal step transition in gray level (as shown by the horizontal profile in the figure).

In practice, optics, sampling, and other image acquisition imperfections yield edges that are blurred, with the degree of blurring being determined by factors. such as the quality of the image acquisition system, the sampling rate, and illumination conditions under which the image is acquired. As a result, edges are more closely modeled as having a "ramplike" profile, such as the one shown in Figure 10.5(b). The slope of the ramp is inversely proportional to the degree of blurring in the edge. In this model. we no longer have a thin (one pixel thick) path. Instead, an edge point now is any point contained in the ramp, and an edge would then be a set of such points that arc connected. The "thickness" of the edge is determined by the length of the ramp. as it transitions from an initial to a final gray level. This length is determined by the slope, which. in turn is determined by the degree of blurring. This makes sense: Blurred edges tend to be thick and sharp edges tend to be thin.

Figure 10.6(a) shows the image from which the close-up in Fig. 10.5(b) was extracted. Figure 10.6(b) shows a horizontal gray-level profile of the edge between the two regions. This figure also shows the first and second derivatives of the gray-level profile. The first derivative is positive at the points of transition into and out of the ramp as we move from left to right along the profile: it is constant for points in the ramp: and is zero in areas of constant gray level.丁he second derivative is positive at the transition associated with the dark side of the edge, negative at the transition associated with the light side of the edge, and zero along the ramp and in areas of constant gray level. The signs of the derivatives in Fig. 10.6(b) would be reversed for an edge that transitions from light to dark.

a b

FIGURE 10.5 (a) Model of an ideal digital edge. (b) Model of a ramp edge. The

slope of the ramp is proportional to the degree of blurring in the edge.

FIGURE 10.6 (a) Two regions separated by a vertical edge. (b) Detail near the edge, showing a gray-level profile, and the first and second derivatives of the

profile

We conclude from these observations that the magnitude of the first derivative can be used to detect the presence of an edge at a point in an image (i.e.,to determine if a point is on a ramp). Similarly, the sign of the second derivative can be used to determine whether an edge pixel lies on the dark or light side of an edge. We note two additional properties of the second derivative around an edge: (7 ) II produces two values for every edge in an image (an undesirable feature); and (2) an imaginary straight line joining the extreme positive and negative values of the second derivative would cross zero near the midpoint of the edge. This zero-crossing property of the second derivative is quite useful for locating the centers of thick edges, as we show later in this section. Finally, we note that some edge models make use of a smooth transition into and out of the ramp (Problem 10.5). However, the conclusions at which we arrive in the following discussion are the same. Also, it is evident from this discussion that we are dealing here with local measures (thus the comment made in Section 2.5.2 about the local nature of edges).

Although attention thus far has been limited to a I -D horizontal profile. A similar argument applies to an edge of any orientation in an image. We simply define a profile perpendicular to the edge direction at any desired point and interpret the results as in the preceding discussion.

From:

Introduction to Algorithms Digital Image Processing 2nd Edition . Prentice Hall

1.先打开金山词霸自动取词功能,然后阅读文献;

2.遇到无法理解的长句时,可以交给Google处理,处理后的结果猛一看,不堪入目,可是经过大脑的再处理后句子的意思基本就明了了;

3.如果通过Google仍然无法理解,感觉就是不同,那肯定是对其中某个“常用单词”理解有误,因为某些单词看似很简单,但是在文献中有特殊的意思,这时就可以通过CNKI的“翻译助手”来查询相关单词的意思,由于CNKI的单词意思都是来源与大量的文献,所以它的吻合率很高。

另外,在翻译过程中最好以“段落”或者“长句”作为翻译的基本单位,这样才不会造成“只见树木,不见森林”的误导。

四大工具:

1、Google翻译:https://www.docsj.com/doc/2b2021940.html,/language_tools

google,众所周知,谷歌里面的英文文献和资料还算是比较详实的。我利用它是这样的。一方面可以用它查询英文论文,当然这方面的帖子很多,大家可以搜索,在此不赘述。回到我自己说的翻译上来。下面给大家举个例子来说明如何用吧

比如说“电磁感应透明效应”这个词汇你不知道他怎么翻译,

首先你可以在CNKI里查中文的,根据它们的关键词中英文对照来做,一般比较准确。

在此主要是说在google里怎么知道这个翻译意思。大家应该都有词典吧,按中国人的办法,把一个一个词分着查出来,敲到google 里,你的这种翻译一般不太准,当然你需要验证是否准确了,这下看着吧,把你的那支离破碎的翻译在google里搜索,你能看到许多相关的文献或资料,大家都不是笨蛋,看看,也就能找到最精确的翻译了,纯西式的!我就是这么用的。

2、CNKI翻译:https://www.docsj.com/doc/2b2021940.html,

CNKI翻译助手,这个网站不需要介绍太多,可能有些人也知道的。主要说说它的有点,你进去看看就能发现:搜索的肯定是专业词汇,而且它翻译结果下面有文章与之对应(因为它是CNKI检索提供的,它的翻译是从文献里抽出来的),很实用的一个网站。估计别的写文章的人不是傻子吧,它们的东西我们可以直接拿来用,当然省事了。网址告诉大家,有兴趣的进去看看,你们就会发现其乐无穷!还是很值得用的。https://www.docsj.com/doc/2b2021940.html,

3、网路版金山词霸(不到1M):

https://www.docsj.com/doc/2b2021940.html,/6946901637944806

4、有道在线翻译:https://www.docsj.com/doc/2b2021940.html,/?keyfrom=fanyi.logo

翻译时的速度:

这里我谈的是电子版和打印版的翻译速度,按个人翻译速度看,打印版的快些,因为看电子版本一是费眼睛,二是如果我们用电脑,可能还经常时不时玩点游戏,或者整点别的,导致最终SPPEED变慢,再之电脑上一些词典(金山词霸等)在专业翻译方面也不是特别好,所以翻译效果不佳。在此本人建议大家购买清华大学编写的好像是国防工业出版社的那本《英汉科学技术词典》,基本上挺好用。再加上网站如:google CNKI翻译助手,这样我们的翻译速度会提高不少。

具体翻译时的一些技巧(主要是写论文和看论文方面)

大家大概都应预先清楚明白自己专业方向的国内牛人,在这里我强烈建议大家仔细看完这些头上长角的人物的中英文文章,这对你在专业方向的英文和中文互译水平提高有很大帮助。

我们大家最蹩脚的实质上是写英文论文,而非看英文论文,但话说回来我们最终提高还是要从下大工夫看英文论文开始。提到会看,我想它是有窍门的,个人总结如下:

图像处理中值滤波器中英文对照外文翻译文献

中英文资料对照外文翻译 一、英文原文 A NEW CONTENT BASED MEDIAN FILTER ABSTRACT In this paper the hardware implementation of a contentbased median filter suitabl e for real-time impulse noise suppression is presented. The function of the proposed ci rcuitry is adaptive; it detects the existence of impulse noise in an image neighborhood and applies the median filter operator only when necessary. In this way, the blurring o f the imagein process is avoided and the integrity of edge and detail information is pre served. The proposed digital hardware structure is capable of processing gray-scale im ages of 8-bit resolution and is fully pipelined, whereas parallel processing is used to m inimize computational time. The architecturepresented was implemented in FPGA an d it can be used in industrial imaging applications, where fast processing is of the utm ost importance. The typical system clock frequency is 55 MHz. 1. INTRODUCTION Two applications of great importance in the area of image processing are noise filtering and image enhancement [1].These tasks are an essential part of any image pro cessor,whether the final image is utilized for visual interpretation or for automatic an alysis. The aim of noise filtering is to eliminate noise and its effects on the original im age, while corrupting the image as little as possible. To this end, nonlinear techniques (like the median and, in general, order statistics filters) have been found to provide mo re satisfactory results in comparison to linear methods. Impulse noise exists in many p ractical applications and can be generated by various sources, including a number of man made phenomena, such as unprotected switches, industrial machines and car ign ition systems. Images are often corrupted by impulse noise due to a noisy sensor or ch annel transmission errors. The most common method used for impulse noise suppressi on n forgray-scale and color images is the median filter (MF) [2].The basic drawback o f the application of the MF is the blurringof the image in process. In the general case,t he filter is applied uniformly across an image, modifying pixels that arenot contamina ted by noise. In this way, the effective elimination of impulse noise is often at the exp ense of an overalldegradation of the image and blurred or distorted features[3].In this paper an intelligent hardware structure of a content based median filter (CBMF) suita ble for impulse noise suppression is presented. The function of the proposed circuit is to detect the existence of noise in the image window and apply the corresponding MF

图像分割毕业设计

目录 摘要........................................................... I Abstract......................................................... I I 第1章绪论 (1) 1.1图像分割概述 (1) 1.2图像分割特征 (1) 1.3图像分割的发展及现状 (1) 1.4研究的背景与意义 (2) 第2章数字图像处理 (3) 2.1发展概况 (3) 2.2主要目的 (4) 2.3常用方法 (4) 2.4应用领域 (5) 2.5研究方向 (7) 2.6基本特点 (7) 2.7MATLAB软件 (8) 第3章阈值分割 (10) 3.1图像二值化 (10) 3.2阈值分割基本原理 (10) 3.3阈值分割方法定义 (11) 3.4阈值分割描述 (11) 3.5阈值分割分类 (12) 第4章阈值分割方法 (13) 4.1直方图法 (13)

4.2迭代法 (14) 4.3最大类间方差法 (17) 4.4小结 (20) 第5章最大类间方差法的改进 (21) 结论 (27) 参考文献 (28) 致谢 (29)

通常人们只对图像的某个区域感兴趣,为了能够把感兴趣的区域提取出来,就得对图像进行分割。图像分割就是把图像分成一些具有不同特征而有意义的区域,以便进一步的图像处理与分析。图像分割是图像处理的关键,在灰度图像中分割出有意义区域的最基本方法是设置阈值的分割方法。选择阈值的主要方法有:直方图法,迭代法,最大类间方差法。本文主要比较三种方法的优缺点,并对其中的最大类间方差法进行优化,改进分割效果。 关键词:阈值直方图迭代法最大类间方差法

毕业论文外文翻译模版

吉林化工学院理学院 毕业论文外文翻译English Title(Times New Roman ,三号) 学生学号:08810219 学生姓名:袁庚文 专业班级:信息与计算科学0802 指导教师:赵瑛 职称副教授 起止日期:2012.2.27~2012.3.14 吉林化工学院 Jilin Institute of Chemical Technology

1 外文翻译的基本内容 应选择与本课题密切相关的外文文献(学术期刊网上的),译成中文,与原文装订在一起并独立成册。在毕业答辩前,同论文一起上交。译文字数不应少于3000个汉字。 2 书写规范 2.1 外文翻译的正文格式 正文版心设置为:上边距:3.5厘米,下边距:2.5厘米,左边距:3.5厘米,右边距:2厘米,页眉:2.5厘米,页脚:2厘米。 中文部分正文选用模板中的样式所定义的“正文”,每段落首行缩进2字;或者手动设置成每段落首行缩进2字,字体:宋体,字号:小四,行距:多倍行距1.3,间距:前段、后段均为0行。 这部分工作模板中已经自动设置为缺省值。 2.2标题格式 特别注意:各级标题的具体形式可参照外文原文确定。 1.第一级标题(如:第1章绪论)选用模板中的样式所定义的“标题1”,居左;或者手动设置成字体:黑体,居左,字号:三号,1.5倍行距,段后11磅,段前为11磅。 2.第二级标题(如:1.2 摘要与关键词)选用模板中的样式所定义的“标题2”,居左;或者手动设置成字体:黑体,居左,字号:四号,1.5倍行距,段后为0,段前0.5行。 3.第三级标题(如:1.2.1 摘要)选用模板中的样式所定义的“标题3”,居左;或者手动设置成字体:黑体,居左,字号:小四,1.5倍行距,段后为0,段前0.5行。 标题和后面文字之间空一格(半角)。 3 图表及公式等的格式说明 图表、公式、参考文献等的格式详见《吉林化工学院本科学生毕业设计说明书(论文)撰写规范及标准模版》中相关的说明。

概率论毕业论文外文翻译

Statistical hypothesis testing Adriana Albu,Loredana Ungureanu Politehnica University Timisoara,adrianaa@aut.utt.ro Politehnica University Timisoara,loredanau@aut.utt.ro Abstract In this article,we present a Bayesian statistical hypothesis testing inspection, testing theory and the process Mentioned hypothesis testing in the real world and the importance of, and successful test of the Notes. Key words Bayesian hypothesis testing; Bayesian inference;Test of significance Introduction A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study (not controlled). In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level. The phrase "test of significance" was coined by Ronald Fisher: "Critical tests of this kind may be called tests of significance, and when such tests are available we may discover whether a second sample is or is not significantly different from the first."[1] Hypothesis testing is sometimes called confirmatory data analysis, in contrast to exploratory data analysis. In frequency probability,these decisions are almost always made using null-hypothesis tests. These are tests that answer the question Assuming that the null hypothesis is true, what is the probability of observing a value for the test statistic that is at [] least as extreme as the value that was actually observed?) 2 More formally, they represent answers to the question, posed before undertaking an experiment,of what outcomes of the experiment would lead to rejection of the null hypothesis for a pre-specified probability of an incorrect rejection. One use of hypothesis testing is deciding whether experimental results contain enough information to cast doubt on conventional wisdom. Statistical hypothesis testing is a key technique of frequentist statistical inference. The Bayesian approach to hypothesis testing is to base rejection of the hypothesis on the posterior probability.[3][4]Other approaches to reaching a decision based on data are available via decision theory and optimal decisions. The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis. The critical region is usually denoted by the letter C. One-sample tests are appropriate when a sample is being compared to the population from a hypothesis. The population characteristics are known from theory or are calculated from the population.

外文翻译---特征空间稳健性分析:彩色图像分割

附录2:外文翻译 Robust Analysis of Feature Spaces: Color Image Segmentation Abstract A general technique for the recovery of significant image features is presented. The technique is based on the mean shift algorithm, a simple nonparametric procedure for estimating density gradients. Drawbacks of the current methods (including robust clustering) are avoided. Feature space of any nature can be processed, and as an example, color image segmentation is discussed. The segmentation is completely autonomous, only its class is chosen by the user. Thus, the same program can produce a high quality edge image, or provide, by extracting all the significant colors, a preprocessor for content-based query systems. A 512 512 color image is analyzed in less than 10 seconds on a standard workstation. Gray level images are handled as color images having only the lightness coordinate. Keywords: robust pattern analysis, low-level vision, content-based indexing

图像分割技术与MATLAB仿真

中南民族大学 毕业论文(设计) 学院: 计算机科学学院 专业: 自动化年级:2012 题目: 图像分割技术与MATLAB仿真 学生姓名: 高宇成学号:2012213353 指导教师姓名: 王黎职称: 讲师 2012年5月10日

中南民族大学本科毕业论文(设计)原创性声明 本人郑重声明:所呈交的论文是本人在导师的指导下独立进行研究所取得的研究成果。除了文中特别加以标注引用的内容外,本论文不包含任何其他个人或集体已经发表或撰写的成果作品。本人完全意识到本声明的法律后果由本人承担。 作者签名:年月日

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图像分割技术研究及MATLAB仿真 摘要:作为一项热门的计算机科学技术,图像分割技术已经在我们生活中越来越普及。顾 名思义这项技术的目的就是,将目标图像从背景图像中分离出去。由于这些被分割的图像区域在某些属性上很相近,因此图像分割与模式识别以及图像压缩编码有着密不可分的关系。完成图像分割所采用的方法各式各样,所应用的原理也不同。但他们的最终目的都是把图像中性质相似的某些区域归为一类,把性质差异明显的不同区域分割开来。通常在分割完成之后,我们就要对某些特定区域进行分析、计算、评估等操作,因而分割质量的好坏直接影响到了下一步的图像处理[1],因此图像分割是图像处理的一个关键步奏。图像分割技术在各个领域都有着及其重要的意义;在工业上有卫星遥感,工业过程控制监测等等;在医学方面,水平集的分割方法还可以通过医学成像帮助医生识别模糊的病变区域;在模式识别领域还可应用到指纹扫描、手写识别、车牌号识别等等。 本课题的研究内容是对图像分割技术的几种常用的方法进行综述和比较,并基于其中一种方法进行MATLAB仿真测试,给出性能分析比较结果。 关键字:图像分割,MA TLAB仿真,模式识别 Image Segmentation and Matlab Simulation Abstract:Image segmentation is to image representation for the physically meaningful regional connectivity set, namely according to the prior knowledge of target and background, we on the image of target and background of labeling and localization, then separate the object from the background. Because these segmented image regions are very similar in some properties, image segmentation is often used for pattern recognition and image understanding and image compression and coding of two major categories. Because the generated in the segmented region is a kind of image content representation, it is the image of visual analysis and pattern recognition based and segmentation results of quality of image analysis, recognition and interpretation of quality has a direct impact. Image segmentation it is according to certain features of the image (such as gray level, spectrum, texture, etc.) to a complete picture of the image is segmented into several meaningful area. These features made in a certain region of consistent or similar, and between different regions showed significantly different. Image segmentation technology in various fields have most of the field and its important significance in digital image processing, image segmentation has a wide range of applications, such as industrial automation, process control, online product inspection, image coding, document image processing, remote sensing and medical image analysis, security surveillance, as well as military, sports and other aspects. In medical image processing and analysis, image segmentation for body occurrence of three-dimensional display of the diseased organ or lesion location determination and analysis plays an effective role in counseling; in the analysis and application of road traffic conditions,

毕业论文 外文翻译#(精选.)

毕业论文(设计)外文翻译 题目:中国上市公司偏好股权融资:非制度性因素 系部名称:经济管理系专业班级:会计082班 学生姓名:任民学号: 200880444228 指导教师:冯银波教师职称:讲师 年月日

译文: 中国上市公司偏好股权融资:非制度性因素 国际商业管理杂志 2009.10 摘要:本文把重点集中于中国上市公司的融资活动,运用西方融资理论,从非制度性因素方面,如融资成本、企业资产类型和质量、盈利能力、行业因素、股权结构因素、财务管理水平和社会文化,分析了中国上市公司倾向于股权融资的原因,并得出结论,股权融资偏好是上市公司根据中国融资环境的一种合理的选择。最后,针对公司的股权融资偏好提出了一些简明的建议。 关键词:股权融资,非制度性因素,融资成本 一、前言 中国上市公司偏好于股权融资,根据中国证券报的数据显示,1997年上市公司在资本市场的融资金额为95.87亿美元,其中股票融资的比例是72.5%,,在1998年和1999年比例分别为72.6%和72.3%,另一方面,债券融资的比例分别是17.8%,24.9%和25.1%。在这三年,股票融资的比例,在比中国发达的资本市场中却在下跌。以美国为例,当美国企业需要的资金在资本市场上,于股权融资相比他们宁愿选择债券融资。统计数据显示,从1970年到1985年,美日企业债券融资占了境外融资的91.7%,比股权融资高很多。阎达五等发现,大约中国3/4的上市公司偏好于股权融资。许多研究的学者认为,上市公司按以下顺序进行外部融资:第一个是股票基金,第二个是可转换债券,三是短期债务,最后一个是长期负债。许多研究人员通常分析我国上市公司偏好股权是由于我们国家的经济改革所带来的制度性因素。他们认为,上市公司的融资活动违背了西方古典融资理论只是因为那些制度性原因。例如,优序融资理论认为,当企业需要资金时,他们首先应该转向内部资金(折旧和留存收益),然后再进行债权融资,最后的选择是股票融资。在这篇文章中,笔者认为,这是因为具体的金融环境激活了企业的这种偏好,并结合了非制度性因素和西方金融理论,尝试解释股权融资偏好的原因。

大学毕业论文---软件专业外文文献中英文翻译

软件专业毕业论文外文文献中英文翻译 Object landscapes and lifetimes Tech nically, OOP is just about abstract data typing, in herita nee, and polymorphism, but other issues can be at least as importa nt. The rema in der of this sect ion will cover these issues. One of the most importa nt factors is the way objects are created and destroyed. Where is the data for an object and how is the lifetime of the object con trolled? There are differe nt philosophies at work here. C++ takes the approach that con trol of efficie ncy is the most importa nt issue, so it gives the programmer a choice. For maximum run-time speed, the storage and lifetime can be determined while the program is being written, by placing the objects on the stack (these are sometimes called automatic or scoped variables) or in the static storage area. This places a priority on the speed of storage allocatio n and release, and con trol of these can be very valuable in some situati ons. However, you sacrifice flexibility because you must know the exact qua ntity, lifetime, and type of objects while you're writing the program. If you are trying to solve a more general problem such as computer-aided desig n, warehouse man ageme nt, or air-traffic con trol, this is too restrictive. The sec ond approach is to create objects dyn amically in a pool of memory called the heap. In this approach, you don't know un til run-time how many objects you n eed, what their lifetime is, or what their exact type is. Those are determined at the spur of the moment while the program is runnin g. If you n eed a new object, you simply make it on the heap at the point that you n eed it. Because the storage is man aged dyn amically, at run-time, the amount of time required to allocate storage on the heap is sig ni fica ntly Ion ger tha n the time to create storage on the stack. (Creat ing storage on the stack is ofte n a si ngle assembly in structio n to move the stack poin ter dow n, and ano ther to move it back up.) The dyn amic approach makes the gen erally logical assumpti on that objects tend to be complicated, so the extra overhead of finding storage and releas ing that storage will not have an importa nt impact on the creati on of an object .In additi on, the greater flexibility is esse ntial to solve the gen eral program ming problem. Java uses the sec ond approach, exclusive". Every time you want to create an object, you use the new keyword to build a dyn amic in sta nee of that object. There's ano ther issue, however, and that's the lifetime of an object. With Ian guages that allow objects to be created on the stack, the compiler determines how long the object lasts and can automatically destroy it. However, if you create it on the heap the compiler has no kno wledge of its lifetime. In a Ianguage like C++, you must determine programmatically when to destroy the

外文翻译----数字图像处理方法的研究

The research of digital image processing technique 1 Introduction Interest in digital image processing methods stems from two principal application areas: improvement of pictorial information for human interpretation; and processing of image data for storage, transmission, and representation for autonomous machine perception. This chapter has several objectives: (1)to define the scope of the field that we call image processing; (2)to give a historical perspective of the origins of this field; (3)to give an idea of the state of the art in image processing by examining some of the principal area in which it is applied; (4)to discuss briefly the principal approaches used in digital image processing; (5)to give an overview of the components contained in a typical, general-purpose image processing system; and (6) to provide direction to the books and other literature where image processing work normally is reporter. 1.1What Is Digital Image Processing? An image may be defined as a two-dimensional function, f(x, y), where x and y are spatial (plane) coordinates, and the amplitude of f at any pair of coordinates (x, y) is called the intensity or gray level of the image at that point. When x, y, and digital image. The field of digital image processing refers to processing digital images by means of a digital computer. Note that a digital image is composed of a finite number of elements, each of which has a particular location and value. These elements are referred to as picture elements, image elements, pels, and pixels. Pixel is the term most widely used to denote the elements of a digital image. We consider these definitions in more formal terms in Chapter2. Vision is the most advanced of our senses, so it is not surprising that images play the single most important role in human perception. However, unlike human who are limited to the visual band of the electromagnetic (EM) spectrum, imaging machines cover almost the entire EM spectrum, ranging from gamma to radio waves. They can operate on images generated by sources that human are not accustomed to associating with image. These include ultrasound, electron microscopy, and computer-generated images. Thus, digital image processing encompasses a wide and varied field of application. There is no general agreement among authors regarding where image processing stops and other related areas, such as image analysis and computer vision, start. Sometimes a distinction is made by defining image processing as a discipline in which both the input and output of a process are images. We believe this to be a limiting and somewhat artificial boundary. For example, under this definition, even the trivial task of computing the average intensity of an image (which yields a single number) would not be considered an image processing operation. On the other hand, there are fields such as computer vision whose ultimate goal is to use computer to

图像分割算法的研究与实现本科学士学位毕业论文

TP391.41 学士学位论文(设计) 论文题目图像分割算法研究与实现 作者姓名 指导教师 所在院系 专业名称 完成时间

毕业设计(论文)原创性声明和使用授权说明 原创性声明 本人郑重承诺:所呈交的毕业设计(论文),是我个人在指导教师的指导下进行的研究工作及取得的成果。尽我所知,除文中特别加以标注和致谢的地方外,不包含其他人或组织已经发表或公布过的研究成果,也不包含我为获得及其它教育机构的学位或学历而使用过的材料。对本研究提供过帮助和做出过贡献的个人或集体,均已在文中作了明确的说明并表示了谢意。 作者签名:日期: 指导教师签名:日期: 使用授权说明 本人完全了解大学关于收集、保存、使用毕业设计(论文)的规定,即:按照学校要求提交毕业设计(论文)的印刷本和电子版本;学校有权保存毕业设计(论文)的印刷本和电子版,并提供目录检索与阅览服务;学校可以采用影印、缩印、数字化或其它复制手段保存论文;在不以赢利为目的前提下,学校可以公布论文的部分或全部内容。 作者签名:日期:

学位论文原创性声明 本人郑重声明:所呈交的论文是本人在导师的指导下独立进行研究所取得的研究成果。除了文中特别加以标注引用的内容外,本论文不包含任何其他个人或集体已经发表或撰写的成果作品。对本文的研究做出重要贡献的个人和集体,均已在文中以明确方式标明。本人完全意识到本声明的法律后果由本人承担。 作者签名:日期:年月日 学位论文版权使用授权书 本学位论文作者完全了解学校有关保留、使用学位论文的规定,同意学校保留并向国家有关部门或机构送交论文的复印件和电子版,允许论文被查阅和借阅。本人授权大学可以将本学位论文的全部或部分内容编入有关数据库进行检索,可以采用影印、缩印或扫描等复制手段保存和汇编本学位论文。 涉密论文按学校规定处理。 作者签名:日期:年月日 导师签名:日期:年月日

毕业论文外文翻译模板

农村社会养老保险的现状、问题与对策研究社会保障对国家安定和经济发展具有重要作用,“城乡二元经济”现象日益凸现,农村社会保障问题客观上成为社会保障体系中极为重要的部分。建立和完善农村社会保障制度关系到农村乃至整个社会的经济发展,并且对我国和谐社会的构建至关重要。我国农村社会保障制度尚不完善,因此有必要加强对农村独立社会保障制度的构建,尤其对农村养老制度的改革,建立健全我国社会保障体系。从户籍制度上看,我国居民养老问题可分为城市居民养老和农村居民养老两部分。对于城市居民我国政府已有比较充足的政策与资金投人,使他们在物质和精神方面都能得到较好地照顾,基本实现了社会化养老。而农村居民的养老问题却日益突出,成为摆在我国政府面前的一个紧迫而又棘手的问题。 一、我国农村社会养老保险的现状 关于农村养老,许多地区还没有建立农村社会养老体系,已建立的地区也存在很多缺陷,运行中出现了很多问题,所以完善农村社会养老保险体系的必要性与紧迫性日益体现出来。 (一)人口老龄化加快 随着城市化步伐的加快和农村劳动力的输出,越来越多的农村青壮年人口进入城市,年龄结构出现“两头大,中间小”的局面。中国农村进入老龄社会的步伐日渐加快。第五次人口普查显示:中国65岁以上的人中农村为5938万,占老龄总人口的67.4%.在这种严峻的现实面前,农村社会养老保险的徘徊显得极其不协调。 (二)农村社会养老保险覆盖面太小 中国拥有世界上数量最多的老年人口,且大多在农村。据统计,未纳入社会保障的农村人口还很多,截止2000年底,全国7400多万农村居民参加了保险,占全部农村居民的11.18%,占成年农村居民的11.59%.另外,据国家统计局统计,我国进城务工者已从改革开放之初的不到200万人增加到2003年的1.14亿人。而基本方案中没有体现出对留在农村的农民和进城务工的农民给予区别对待。进城务工的农民既没被纳入到农村养老保险体系中,也没被纳入到城市养老保险体系中,处于法律保护的空白地带。所以很有必要考虑这个特殊群体的养老保险问题。

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