数字图像处理-作业题及部分答案.doc

1. 数字图像与连续图像相比具有哪些优点?连续图像f(x,y)与数字图像I(c,r)中各量的含义是什么?它们有何联系和区别? (To be compared with an analog image, what are the advantages of a digital image? Let f(x,y) be an analog image, I(r, c) be a digital image, please give explanation and comparison for defined variables: f/I, x/r, and y/c)

2. 图像处理可分为哪三个阶段? 它们是如何划分的？各有什么特点? (We can divide "image processing" into 3 stages, what are they? how they are divided? What are their features?)

答：低级处理---低层操作,强调图像之间的变换,是一个从图像到图像的过程;
中级处理---中层操作,主要对图像中感兴趣的目标进行检测和测量,从而建立对图像的描述,是一个从图像到数值或符号的过程;
高级处理---高层操作,研究图像中各目标的性质和相互联系,得出对图像内容含义的理解以及对原来客观场景的解释;

3. 试从结构和功能等角度分析人类视觉中最基本的几个要素是什么?什么是马赫带效应? 什么是同时对比度?它们反映了什么共同问题? (According to the structure and function of the eyes, what are the basic elements in human vision? What is the Mach Band Effect? What is Simultaneous Contrast? What common facts can we infer from both Mach Band Effect and Simultaneous Contrast?)

答：人的视觉系统趋向于过高或过低估计不同亮度区域边界的现象称为“马赫带”效应; 同时对比度指的是人的视觉系统对某个区域感觉到的亮度除了依赖于它本身的强度,还与背景有关.
马赫带效应和同时对比度现象表明人所感觉到的亮度并不是强度的简单函数.

4. 比较说明像素邻域、连接、通路以及连通基本概念的联系与区别。(Please compare the following conceptions and their distinction: (1) neighborhood; (2) adjacency; (3) path; (4) connectivity)

5 设有某图像子集中p(3,4),q(8,10)两像素点,试分别计算p和q之间的D4, D8, DE距离.(Given pixels p(3,4) and q(8,10), please calculate the following distance: D4, D8 and DE.)

6. 什么是采样和量化？什么是灰度分辨率与空间分辨率？它们如何影响图像视觉质量以及数据量大小？(What are the definition of Sampling and Quantization? What are the definition of grayscale resolution and spatial resolution? How Sampling and Quantization process affect the visual quality and date volume of an image?)

7. 试举出常用的三种图像灰度映射规则并绘出相应的映射曲线。(Please give three common gray-level mapping functions and their figure respectively)

8. 为什么一般情况下对离散图像的直方图均衡化并不能产生完全平坦的直方图？(Why digital image with histogram equalization process cannot obtain fully flat histogram?)

离散图像的灰度级数有限，只有当灰度级数趋近于无穷大时，直方图均衡化才能产生完全平坦的直方图

9. 试给出以下直方图均衡化的步骤及结果 (Please Do histogram equalization on the given histogram)
0 1 2 3 4 5 6 7 8
0.5
0.4
0.3
0.1
0
0.2
0.17
0.12
0.13
0.05
0.03
0.13
0.15
0.22

(a)

Computation procedure:

Grayscale
0
1
2
3
4
5
6
7
Original histgram
0.17
0.12
0.13
0.05
0.03
0.13
0.15
0.22
Accumulated histgram

Grayscale Round

Mapping

New histgram

10. 给定如下灰度图像，根据下列要求给出对正方形区域内四个象素进行空间滤波增强的结果： ①：设计一个大小为3x3的空间均值滤波器进行图像平滑；②：利用3x3的标准拉普拉斯算子进行图像锐化；③：以3x3的模板进行图像中值滤波；(Please filter pixels marked with rectangle: (1) using a 3*3 spatial averaging filter to perform image smoothing; (2) using a standard 3*3 Laplacian operator to perform image sharpening; (3) perform 3*3 median filtering)

11. 与均值平滑滤波器相比,中值滤波器有何优点? 请给出中值滤波实施步骤。(What advantages does median filter have, compared with averaging filter? Please list necessary procedures how to perform a median filter)

与均值平滑滤波器相比,中值滤波器能在消除噪声的同时保留图象的细节, 其实施步骤为:
1. 将模板在图中漫游,并将模板中心与图中某个象素位置重合;
2. 读取模板下各对应象素的位置灰度值;
3. 将这些灰度值从大到小排成列,找出排在中间位置的灰度值并将其赋给对应模板中心位置的象素;

12. 试简单叙述图像特征在空域与频域表示下的联系与区别。(When image is represented in spatial and frequency domains respectively, what similarity or differences do they have?)

13. 分别画出低频增强滤波器, 高频增强滤波器转移函数曲线；(Please draw the transfer function curves for low-frequency filter and high-frequency filter respectively.)

14. 将高频增强和直方图均衡化结合起来使图像边缘锐化是一种常用的图像增强技术。请问以上两个操作的先后顺序对增强效果有影响吗？为什么？(In order to sharpen the edge of an image, it is common to use high-frequency emphasis and histogram equalization together. Does the sequence of implementing two technologies have effect on results? Why?)

15. 同态滤波的理论基础和依据是什么？请给出实施步骤。(What is the theory of homomorphic filtering? Please list the procedures to perform this filter)

同态滤波的目的是压缩图像整体范围的同时，扩张用户所感兴趣的细节特征的灰度级范围；其理论基础和依据是假设光照模型为照度分量与反射分量的乘积，由于照度分量变化缓慢，对应于频域中高频成分，而反射分量对应于频域中低频成分，故可通过减弱低频和增强高频的滤波处理实现上述的目的；

16. 试简单叙述图像增强与图像复原技术之间的联系与区别。(What are the relationship and difference between image enhancement and image restoration technology?)

17. 若成像系统为线性移不变系统，且仅受加性噪声n(x,y)干扰，即满足： g(x,y) = H[f(x,y)] + n(x,y), 请给出该系统下的图像退化模型并从冲激响应出发予以证明。(Give a linear, position-invariant image system and only additional noise n(x,y) is considered, namely, g(x,y)=H[f(x,y)]+n(x,y), Please give the image degradation model and prove it by starting with pulse response.)

18. 试给出估计图像退化函数的三种方式并简单叙述其基本思想。(Please summary three principal ways to estimate the degradation functions in image restoration and descript its theory in brief)

19. 逆滤波的基本原理是什么？试对其应用局限性及解决措施进行说明。(What is the theory of Inverse Filtering? Please give comments on its application limitation and propose some solutions)

逆滤波本质上是在忽略噪声影响情况下对退化图像进行滤波，其滤波函数为原退化系统响应函数的倒数，故当原退化系统响应函数取值为零时存在计算上的困难，或当取值较小时，受噪声的影响大；
解决措施： 频率受限，仅对零频附件的区域进行处理

20. 如图所示，设影像空间变换过程中某像素被映射到失真影像像素A,B,C,D内部点P(a,b),若A,B,C,D点的灰度值分别为GA=36, GB=76, GC=46, GD=66, a=0.7,b=0.6,试分别利用最近邻插值和双线性插值方法计算点P的灰度值GP. (As shown in figure, a pixel P is mapped within one grid with four pixels. The gray-levels of four pixels are GA=36, GB=76, GC=46, GD=66,and a=0.7,b=0.6. Please calculate the gray-levels of pixel P by using (1) nearest neighbor interpolation; (2)bilinear interpolation.)

21. 光的3基色指的是哪三种基本颜色?对应的3补色是什么?将一个补色和对应的光基色相混合产生何种颜色? 颜料的3基色指的是哪三种基本颜色?对应的3补色又是什么?将一个补色和对应的颜料基色相混合产生何种颜色? 光的3基色, 3补色与颜料的3基色, 3补色之间有何种关系? (Which are Primary Colors of Light? What are Secondary Colors of Light? What happen if we mix primary color of Light with its Secondary color of Light? Which are Primary Colors of Pigments? What are Secondary Colors of Pigments? What happen if we mix primary color of Pigments with its Secondary color of Pigments?)

22. 试比较说明RGB颜色模型和HSI颜色模型. (Please give comments on RGB and HSI color models.)

23. 什么是伪彩色图像处理？试给出伪彩色图像处理的两种常用方式。(What is pseudo-color image processing? please give two common methods for pseudo-color image processing )

24. 什么是数据冗余？图像中的数据冗余包含哪三个方面？分别解释之 (What is “data redundancy”? Which kinds of data redundancies can be found in digital image compression? Please describe them respectively.)

25. 图像压缩性能评价常采用的准则有哪些?各有什么特点? (Which are the commonly used criteria to evaluate performance of image compression? And what character do the criteria has?

26. 请给出图像压缩模型(解码/译码),并对其不同构件的功能进行解释. (Please give comprehensive model on image compression (encoding and decoding) and have brief explain on different part of model.)

27. 对下表中的信源符号进行哈夫曼编码,并给出码字、平均码长和编码效率。(Please use the Huffman coding algorithm to encode the symbols in the table and give its Binary code, average length of the code and the code efficiency.)

Source Symbol
V1

V1
V1
V1
V1
V1
Probability
1/8
1/4
1/32
1/2
1/32
1/16
Binary Code

28. 假定白色像素为起始, 试对下列二值序列进行行程编码：1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 (Suppose the first pixel is white, please encode the binary symbols using the run-length coding algorithm)

29. 无损预测编码的基本思想是什么？为什么对预测误差进行编码比直接对原始数据进行编码的效率要高？(What is the theory of lossless predictive coding? Why can we get a higher efficiency when we encode the prediction, compared to the encoding of raw data?)

无损预测编码基本思想是不直接对原始数据进行量化与编码，而是利用线性预测技术去除象素间的相关性，对预测值与原始数据值之间的差异进行量化与编码；

30. 变换编码的基本思想是什么？正交变换选取的依据是什么？(What is the theory of “transform coding”? and on what we depend to select the orthogonal transformation?)

其基本思想是先对图像进行变换，使得变换域中数据间的相关性减小或互不相关，从而减小冗余度，在进行量化与编码；正交变换编码具有如下特点:
a) 熵保持. 正交变换不丢失信号,通过传输变换系数来传送信息;
b) 能量集中. 变换域中的能量集中于少数变换系数上,大多数的系数数值都很小,故对能量小的系数可粗糙量化象素间的或完全忽略;
c) 去相关. 正交变换能够去除冗余, 变换系数的相关性为零或较小;

31. 试借助集合概念从五个方面对图像分割给出完整的定义。（Please give accurate definition on image segmentation）

32. 利用Hough变换进行边缘连接的基本思想是什么? 试给出Hough变换检测直线段的基本步骤. (What is the theory of “Hough Transformation”? Please describe the steps using Hough Transformation to link discrete edgels into straight line segment.)

33. 一阶微分算子和二阶微分算子进行边缘检测的依据是什么?试分别给出两算子一种模板表示，并指明是何种算子。（Why the first-order derivative and second-order derivative operators can detect the image edge? Please list masks for two operators respectively and name it clearly.）

一阶微分检测边缘的依据是边缘灰度曲线的一阶导数具有极值,如Roberts梯度算子,其模板为:

1

-1
1

-1

二阶微分检测边缘的依据是边缘灰度曲线的二阶导数过零点,如拉普拉斯算子,其模板为:
-1
-1
8
-1
-1
-1
-1
-1
-1
0
-1
4
-1
0
-1
-1
0
0

34. 区域生长的基本思想是什么？在实际应用区域生长法时需要解决哪三个问题？（What is the theory of “region growing”? what kind of three issues should we overcome when we use “region growing” approach?）

三个需要解决的问题：
a) 选择一组能正确代表所需区域的种子像素；
b) 确定在生长过程中能将相邻像素合并的准则；
c) 制定让生长过程停止的条件或准则；

35. 试基于4－方向链码，分别给出图中轮廓的归一化链码、差分链码。（Please give normalized chain code, first difference of chain code for following boundary based on 4-code.）