-【数字图像处理】期末复习资料及期末模拟试卷(含答案)doc.doc

Digital Image Processing Examination 1. Fourier Transform problem. 1） For an image given by the function f(x,y)=(x+y)3 where x,y are continuous varibales; evaluate f(x,y)(x-1,y-2) and f(x,y)* (x-1,y-2),where is the Dorac Delta function.2） For the optical imaging system shoen below,consisting of an image scaling and two forward Fourier transforms show that the output image is a scale and inverted replica of the original image f(x,y).f(x,y)Scalingf(ax,by)FFg(x,y)_3) three binary images (with value 1 on black areas and value 0 elsewhere) are shown below. Sketch the continuous 2D FT of these images(dont do this mathematically, try to use instead the convolution theorem and knowledge of FTs of common functions)2. The rate distortion function of a zero memory Gaussian source of arbitary mean and variance 2 with respect to the mean-square error criterion isa) Plot this functionb) What is Dmaxc) If a distortion of no mor than 75% of the sources variance is allowed, what is the maximum compression that can be achieved?3. The PDF of an image is given by Pr(r) as shown below. Find the transform toconvert the images PDF to Pr(z). Assume continuity, and find the transform in terms of r and z. Explain the transformation.4. A certain inspection application gathers black & white images of parts as they travel along a conveyor belt. It is necessary to sort the parts into two categories: parts with holes and parts with-out holes. An example of an image that might be taken by the inspection camera is shown at the right.Propose a method to identify and locate the objects of each category in the image so that they can be picked up by a robotic system and placed in different bins. Assume that the imaging system knows where each image pixel is located on the conveyor belt at every point in time.Provide an annotated flow chart of the algorithm you propose.5. In a given application, an averaging mask is applied to input images to reduce noise and then a Laplacian mask is applied to enhance small details. Would mathematics predict that the result should be the same if the order of the operations were reversed? What practical issues would be encountered in computer implementation?Digital Image Processing Examination1. A preprocessing step in an application of microscopy is concerned with the issue of isolating individual round particles from similar particles that overlap in groups of two or more.Assuming that all particles are of the same size, propose a morphological algorithm that will produce an image that contains only the isolated (non-overlapping) particles that are not in contact with the boundary of the image.2. An image represented by a continuous function f(x, y) is w = 2 cm wide and h = 3 cm high. The image is to be converted to an array of pixels by a scanner whose response is zero above 80 lines/centimeter in both the horizontal and vertical directions. The discrete image is represented by an array f(n, m) where n and m take on integer values, 0 n N - 1, 0 m M-1.(a) Determine suitable values for N and M.(b) Assume that f(n, m) = f(na, mb). Determine the values of a and b.(c) Determine constants A, B, C, D, E such that the DFT of f can be expressed as(d) Find numbers (P1, P2) such that F(u + jP1, v + kP2) = F(u, v) for any integers j, k, u, v.3. The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model. SymbolProbabilitya0.2e0.3i0.1o0.2u0.1!0.14. The gradient of a function f (x) is defined asComputationally, the first derivative is implemented by calculating the difference between adjacent pixels.(a) Is the following a linear operator?(b) State how would you implement the above operator using differences between pixels.(c) A Sobel operator uses two masks, Hx and Hy to process an image. Explain why are two masks needed and what do they measure?(d) Write down the masks Hx and Hy, and identify them in the following figures:5. The three images shown were blurred using square averaging masks of sizes n=23, 25 , and 45, respectively. The vertical bars on the left lower part of (a) and (c) are blurred, but a clear separation exists between them. However, the bars have merged in image (b), in spite of the fact that the mask that produced this image is significantly smaller than the mask that produced image (c). explain this.Digital Image Processing Examination1. An image array f(m, n) of size M1 N1 is to be convolved with a filter array h(m, n) of size M2 N2 to produce a new image array g(m, n).1) Write a pseudo code program that describes a method to compute g(m, n) through the use of Fourier transforms. The result should be the same size as would be achieved with direct convolution.2) Modify the algorithm so that it does the correlation f h rather than the convolution.2. You have the job of designing an algorithm that will count the number of objects with holes and the number of objects without holes in images of the kind shown here. Assume that the images are binary with 0 corresponding to black and 1 corresponding to white. The imaging system is of low quality and produces images that are corrupted with salt and pepper noise.The objects do not overlap or touch, but may be close to each other in any direction. They may be of any shape or size. The algorithm should not be confused by the salt and pepper noise, and should not count noise pixels as objects.Write a pseudo-code description of your algorithm. You may also include a block diagram and other information to make it understandable to a programmer. State any assumptions you make, such as: “Objects must contain at least 50 pixels.”least 50 pixels.”3. Suppose that an image has the gray-level probability density functions shown. Here, p1(z) corresponds to objects and p2(z) corresponds to the background. Assume that p1=p2 and find the optimal threshold between object and back ground pixels.4. The Sobel operator computes the following quantity at each location (x, y) in an image array, A:Gxj,k=(Aj+1,k+1+2Aj+1,k+Aj+1,k-1)-(Aj-1,k+1+2Aj-1,k+Aj-1,k-1) Gyj,k=(Aj-1,k-1+2Aj,k-1+Aj+1,k-1)-(Aj-1,k+1+2Aj,k+1+Aj+1,k+1) Gj,k = |Gxj,k| + |Gyj,k|The position of Aj, k is column j and row k of the array.The operation is implemented as the convolution of the image array A with two masks, Mx and My followed by the magnitude operation.1) Write a 3 3 array for each mask, Mx and My.2) What mathematical operation on an image array is approximated by the Sobel operator? Show how the Sobel operator is related to the mathematical operation.5. Answer the following questions about morphological image processing.(a) Shown below are two tables with expressions that relate to binary morphological image processing. Associate each expression in the left table with one from the right table. (b) A well-known morphological algorithm uses the following iteration with a structuring element B.(1) Initialize Xp = 1 for some pixel (2)(3) If then set X = Y and repeat (2)An original set A is shown in (A) and an initial pixel p 2 A is shown in (B). The result after one iteration of the algorithm with structuring elementis shown in (C). Fill in the result of the next two iterations by marking the appropriate pixels for the set Y in (D) and (E). In frame (F) show the result for Y that would be reached after a large number of iterations.Digital Image Processing Examination1. Consider the edge model depicted below. Sketch the gradient and Laplacian of the signal. It is not needed to compute exact numerical values in your answer. Plot of approximate shapes of the responses will be sufficient.2. The white bars in the test pattern shown are 7pixels wide and 210 pixels high. The separation between bars is 17 pixels. What would this image look like after application of .1) A 3*3 arithmetic mean filter?2) A 7*7 median filter.3) A 9*9 contraharmonic mean filter with Q=13. The video coding system introduced in the class utilizes several major components inter-frame motion estimation, motion compensated prediction, DCT, Huffman coding, and quantization.(a) When an encoded signal can be used to reconstruct the exact value of the original signal, we say the encoding method is lossless; otherwise, its called lossy. A lossy coding technique introduces distortion to the signal.Which component in the above video coding system is lossy?(b) The motion compensation process in the encoder generates a motion vector and prediction errors for each image block in the video signal. Suppose during the transmission of the encoded video stream, one motion vector is lost (e.g., due to the network erasure error). What will be the visual effects of such transmission errors on the decoded image sequence?4.Consider a black-and-white image consisting of round and rectangular objects, as shown in the image below. Assume the sizes of the objects are fixed and known. We also know that the width and length of the rectangles are larger than the diameter of the circles. None of the rectangles are tilted. In general, the objects may overlap with each other.Design a morphological operation based system to automatically detect all the instances of the rounds objects that overlap with rectangular objects.5. An image A, represented by an N M array of bytes, has a uniform brightness histogram. It is desired transform A into an image B in a way that produces a triangular brightness histogramDescribe a process that will accomplish the transformation. If possible, derive an equation for the transformation function. At a minimum, sketch the transformation function and indicate how you would use it in a program to compute the array B.模拟试卷一1.对将一个像素宽度的8通路转换到4通路提出一种算法。2.（A）试提出一种过程来求一个 邻域的中值？（B）试提出一种技术，逐像素地移动领域的中心来更新中值。（会了）3.证明如式 所示的拉普拉斯变换是各向同性的（旋转不变）。需要下列轴旋转 角的坐标方程： 其中 为非旋转坐标，而 为旋转坐标。4.获得对应于式子 到式子 的带阻滤波器的带通滤波器的等式。5.给定 的图象，那么一个 级金字塔是减少还是增加了表示图象所需的数据量？压缩或扩展率是多少？6.考虑灰度级数据12，12，13，13，10，13，57，54的一条8像素的线。这条线已经经过精度为6比特的均匀量化。构造它的3位IGS编码。7.一个零记忆高斯信源率失真函数如下： 请绘制出这个函数的曲线。8.证明二元表达式 的正确性。模拟试卷一参考答案1.2.（A）在数字上拣取为 的值，它的中值是 的最大值。（B）一旦值已经被分类一次，我们仅仅是删除在缓慢移动向附近的轨迹的值，插入首要移动的值到分类排列的最恰当位置。3.4.带通滤波器是从1减去带阻滤波器获得的：然后：（a） 理想的带通滤波器：（b） Butterworth带通滤波器：（c） 高斯带通滤波器：5.数据的数量在这个 级金字塔中是被限定在4/3之内的：又因为 ,因此我们可以得到以下的结果:6.7.8.模拟试卷二1.考虑以下所示的图像分割：（A） 令 并计算p和q间的4，8，m通路的最短长度。如果在这两点间不存在特殊通路，请解释原因。（B） 对 重复上题。2.使用式 给出的拉普拉斯变换的定义，证明将一幅图像减去其相应拉普拉斯图像等同于对图像做反锐化掩模处理。3.证明式子 的正确性。4.说明二维正弦函数的傅里叶变换是共轭脉冲对：提示：用式 的连续傅里叶变换并以指数项描述正弦。5.给定 的图像，那么一个 级金字塔是减少还是增加了表示图像所需的数据量？压缩或扩展率是多少？6.考虑灰度级数据12，12，13，13，10，13，57，54的一条8像素的线。这条线已经经过精度为6比特的均匀量化。构造它的3位IGS编码。7.画出下类图形的中轴：（1） 一个圆（2） 一个方形8.有一幅包含水平的、垂直的、45度的和-45度直线的二值图像。给出一组3*3模板。这些模板可以用于检测这些直线中1个像素长度的间断。假设直线的灰度级是1并且背景的灰度级为0。模拟试卷二参考答案1.（A）当 的时候，p和q两点之间不可能存在特殊通路4，因为从p到q之间的点都是4，并且都有从V获得值。下图中的（a）就显示了这一条件，是没有办法到达q的。最短的8通路可在图（b）中看出，它的长度是4。m通路的最短长度是5。这两个是这一题中的唯一的最短通路。（B） 时，最短的4通路的一种可能显示在图（c）中，它的长度是6。它可以十分容易地变换为另一条从p到q的同样长度的4通路。最短的8通路的一种可能（并不是唯一的）显示在图（d）中，它的长度是4。m通路的长度是6，它也不是唯一的。2.考虑到以下公式：当 表示 的平均值在一个预先确定的附近是 的圆心，包括中心的像素和它的四个紧靠着的点。在上述的公式最后一条行中的注入常数如比例因素，我们可以得出：这个等式的右边被看作是公式 的反锐化掩模定义。从而，就证明了，将一幅图像减去其相应拉普拉斯图像等同于对图像做反锐化掩模处理。3.我们首先知道 ，于是：4.运用正弦函数的指数、幂定义：从而得出：以下是函数的傅里叶变换：和：1的傅里叶变换给了最初的动力，而指数替换了最初的动力，因此：5.数据的数量在这个 级金字塔中是被限定在 之内的：又因为 ,因此我们可以得到以下的结果:6.7.8.模拟试卷三1.使用式 给出的拉普拉斯变换的定义，证明将一幅图像减去其相应拉普拉斯图像等同于对图像做反锐化掩模处理。2.式 （其中 ）和式 （其中 ）所示的 与 一组傅里叶变换对。对于 ，将式 代入式 ，会发现左右两边相等。再重复该过程，对于 ，将式 代入 。需要用到下面的指数正交性质：3.考虑在x方向均匀加速导致的图像模糊问题。如果图像在 静止，并用均匀加速 加速，对于时间T，找出模糊函数 ，可以假设快门开关时间忽略不计。4.以下列基本要素计算二元组 的扩展系数并写出对应的扩展:以二元实数集合 为基础的 和 。5.使用正切角的方法划分方形边界的图。6.有一幅包含水平的、垂直的、45度的和-45度直线的二值图象。给出一组3*3模板。这些模板可以用于检测这些直线中1个像素长度的间断。假设直线的灰度级是1并且背景的灰度级为0。7.画出5*5大小的图象的灰度共生矩阵，图像由交错的1和0的跳棋棋盘图案组成。位置算子P定义为“右边的一个像素”。模拟试卷三参考答案1.考虑到以下公式：当 表示 的平均值在一个预先确定的附近是 的圆心，包括中心的像素和它的四个紧靠着的点。在上述的公式最后一条行中的注入常数如比例因素，我们可以得出：这个等式的右边被看作是公式 的反锐化掩模定义。从而，就证明了，将一幅图像减去其相应拉普拉斯图像等同于对图像做反锐化掩模处理。2.通过直接将 中的 代替 中的F（u）得出：3. 和 ，这是涅耳余弦和正弦的积分。4.根据公式： 可得：所以，5.6.7.模拟试卷四1.考虑以下所示的图象分割：（A） 令 并计算p和q间的4，8，m通路的最短长度。如果在这两点间不存在特殊通路，请解释原因。（B） 对 重复上题。2.（A）试提出一种过程来求一个 邻域的中值？（B）试提出一种技术，逐像素地移动领域的中心来更新中值。3.证明如式 所示的拉普拉斯变换是各向同性的（旋转不变）。需要下列轴旋转 角的坐标方程：其中 为非旋转坐标，而 为旋转坐标。4.证明式子 的正确性。5.获得对应于式子 到式子 的带阻滤波器的带通滤波器的等式。6.说明二维正弦函数的傅里叶变换 是共轭脉冲对：提示：用式 的连续傅里叶变换并以指数项描述正弦。7.考虑灰度级数据12，12，13，13，10，13，57，54的一条8像素的线。这条线已经经过精度为6比特的均匀量化。构造它的3位IGS编码。8.一个零记忆高斯信源率失真函数如下：请绘制出这个函数的曲线。模拟试卷四参考答案1.（A）当 的时候，p和q两点之间不可能存在特殊通路4，因为从p到q之间的点都是4，并且都有从V获得值。下图中的（a）就显示了这一条件，是没有办法到达q的。最短的8通路可在图（b）中看出，它的长度是4。m通路的最短长度是5。这两个是这一题中的唯一的最短通路。（B） 时，最短的4通路的一种可能显示在图（c）中，它的长度是6。它可以十分容易地变换为另一条从p到q的同样长度的4通路。最短的8通路的一种可能（并不是唯一的）显示在图（d）中，它的长度是4。m通路的长度是6，它也不是唯一的。2.（A）在数字上拣取为 的值，它的中值是 的最大值。（B）一旦值已经被分类一次，我们仅仅是删除在缓慢移动向附近的轨迹的值，插入首要移动的值到分类排列的最恰当位置。3. 4.我们首先知道 ，于是：5.带通滤波器是从1减去带阻滤波器获得的：然后：（a） 理想的带通滤波器：（b） Butterworth带通滤波器：（c） 高斯带通滤波器：6.运用正弦函数的指数、幂定义：从而得出：以下是函数的傅里叶变换：和：1的傅里叶变换给了最初的动力，而指数替换了最初的动力，因此：7.8. （注：专业文档是经验性极强的领域，无法思考和涵盖全面，素材和资料部分来自网络，供参考。可复制、编制，期待你的好评与关注）