数字图像处理课件(冈萨雷斯第三版)复习材料

(1) 名词解释

RGB Red Green Blue，红绿蓝三原色

CMYK Cyan Magenta yellow blacK , 用于印刷的四分色

HIS Horizontal Situation Indicator 水平位置指示器

FFT Fast Fourier Transform Algorithm (method) 快速傅氏变换算法

CWT continuous wavelet transform 连续小波变换

DCT Discrete Cosine Transform 离散余弦变换

DWT DiscreteWaveletTransform 离散小波变换

CCD Charge Coupled Device 电荷耦合装置

Pixel: a digital image is composed of a finite number of elements,each of which has a particular lication and value,these elements are called pixel像素

DC component in frequency domain 频域直流分量

GLH Gray Level Histogram 灰度直方图

Mather(basic)wavelet：a function (wave) used to generate a set of wavelets, 母小波，用于产生小波变换所需的一序列子小波

Basis functions basis image 基函数基图像

Multi-scale analysis 多尺度分析

Gaussian function 高斯函数

sharpening fi l ter 锐化滤波器

Smoothing filter/convolution 平滑滤波器/卷积

Image enhancement /image restoration 图像增强和图像恢复

（2）问答题

1. Cite one example of digital image processing

Answer:In the domain of medical image processing we may need to inspect a certain class of images generated by an electron microscope to eliminate bright, isolated dots that are no interest.

2.Cite one example of frequency domain operation from the following processing result,

make a general comment about ideal highpass filter (figure B) and Gaussian highpass filter(figure D)

A.Original image

B.ideal highpass filter

In contrast to the ideal low pass filter, it is to let all the signals above the cutoff frequency fc without loss, and to make all the signals below the cutoff frequency of FC without loss of.

C.the result of ideal highpass filter

D.Gaussian highpass filter

High pass filter, also known as "low resistance filter", it is an inhibitory spectrum of the low frequency signal and retain high frequency signal model (or device). High pass filter can make the high frequency components, while the high-frequency part of the frequency in the image of the sharp change in the gray area, which is often the edge of the object. So high pass filter can make the image get sharpening processing

E.The result of Gaussian filter

3.The original image, the ideal lowpass filter and Gaussian lowpass filter are shown

below B nd C .D and E are the result of the either filter B or C

A.Draw lines to connect the filter with their result

B.Explain the difference of the two filters

Due to excessive characteristics of the ideal low-pass filter too fast Jun, it will produce a ringing phenomenon.Over characteristics of Gauss filter is very flat, so it is not ringing

4.What is the result when applying an averaging mask with the size 1X1?

5.State the concept of the Nyquist sampling theorem from the figure belovy

The law of sampling process should be followed, also called the sampling theorem and the sampling theorem. The sampling theorem shows the relationship between the sampling frequency and the signal spectrum, and it is the basic basis of the continuous signal discretization. In analog / digital signal conversion process, when the sampling frequency fs.max greater than 2 times the highest frequency present in the signal Fmax fs.max>2fmax, sampling digital signal completely retained the information in the original signal, the general practical application assurance sampling frequency is 5 ~ 10 times higher than that of the signal of the high frequency; sampling theorem, also known as the Nyquist theorem

6.A mean filter is a linear filter but a median filter is not, why?

Mean filter is a typical linear filtering algorithm, it is to point to in the target pixels in the image to a template, this template including its surrounding adjacent pixels and the pixels in itself.To use in the template to replace all the pixels of average pixel values.Linear filter, median filter, also known as the main method used in the bounded domain average method.

Median filter is a kind of commonly used nonlinear smoothing filter and its basic principle is to put the little value in a digital image or sequence to use value at various points in the field of a point at which the value to replace, its main function is to let the surrounding pixel gray value differences between larger pixel change with the surrounding pixels value close to the values, which can eliminate the noise of the isolated points, so median filter to filter out the salt and pepper noise image is very effective.

（3）算法题

1.The following matrix A is a 3*3 image and B is 3*3 Laplacian mask, what will be the resulting image? (Note that the elements beyond the border remain unchanged)

2.Develop an algorithm to obtain the processing result B from original image A

3.Develop an algorithm which computes the pseudocolor image processing by means of

fourier tramsform

Answer：

The steps of the process are as follow:

(1) Multiply the input image f(x,y) by （-1）x+y to center the transform;

(2) Compute the DFT of the image from (1) to get power spectrum F(u,v) of Fourier

transform.

(3) Multiply by a filter function h(u,v) .

(4) Compute the inverse DFT of the result in (3).

(5) Obtain the real part of the result in (4).

(6) Multiply the result in (5) by（-1）x+y

4.Develop an algorithm to generate approximation image series shown in the following figure b** means of down sampling

.

（4）编程题

There are two satellite photos of night as blew.Write a program with MATLAB to tell which is brighter

An 8*8 image f(i,i) has gray levels given by the following equation:

f(i,i)=|i-j|, i,j=0,1 (7)

Write a program to find the output image obtained by applying a 3*3 median filter on the image f(i,j) ;note that the border pixels remain unchanged.

Answer:

1．Design an adaptive local noise reduction filter and apply it to an image with Gaussian noise. Compare the performance of the adaptive local noise reduction filter with arithmetic mean and geometric mean filter.

Answer:

clear

close all;

rt=imread('E:\数字图像处理\yy.bmp');

gray=rgb2gray(rt);

subplot(2,3,1);imshow(rt);

title('原图像') ;

subplot(2,3,2);imshow(gray);

title('原灰度图像') ;

rtg=im2double(gray);

rtg=imnoise(rtg,'gaussian',0,0.005)%加入均值为0，方差为0.005的高斯噪声

subplot(2,3,3);imshow(rtg);

title('高噪点处理后的图像');

[a,b]=size(rtg);

n=3;

smax=7;

nrt=zeros(a+(smax-1),b+(smax-1));

for i=((smax-1)/2+1):(a+(smax-1)/2)

for j=((smax-1)/2+1):(b+(smax-1)/2)

nrt(i,j)=rtg(i-(smax-1)/2,j-(smax-1)/2);

end

end

figure;

imshow(nrt);

title('扩充后的图像');

nrt2=zeros(a,b);

for i=n+1:a+n

for j=n+1:b+n

for m1=3:2

m2=(m1-1)/2;

c=nrt2(i-m2:i+m2,j-m2:j+m2);%使用7*7的滤波器

Zmed=median(median(c));

Zmin=min(min(c));

Zmax=max(max(c));

A1=Zmed-Zmin;

A2=Zmed-Zmax;

if(A1>0&&A2<0)

B1=nrt2(i,j)-Zmin;

B2=nrt2(i,j)-Zmax;

if(B1>0&&B2<0)

nrt2(i,j)= nrt2(i,j);

else

nrt2(i,j)=Zmed;

end

continue;

end

end

end

end

nrt3=im2uint8(nrt2);

figure;

imshow(nrt3);

title('自适应中值滤波图');

2.Implement Wiener filter with “wiener2” function of MatLab to an image with Gaussian noise and compare the performance with adaptive local noise reduction filter.

代码如下：

>> I=imread('E:\数字图像处理\yy.bmp');

>>J=rgb2gray(I);

>>K = imnoise(J,'gaussian',0,0.005);

>>L=wiener2(K,[5 5]);

>>subplot(1,2,1);imshow(K);title('高噪点处理后的图像');

>>subplot(1,2,2);imshow(L);title('维纳滤波器处理后的图像');

3. Image smoothing with arithmetic averaging filter (spatial convolution).

图像平滑与算术平均滤波(空间卷积)。

>> h=ones(3,3)/9;

>> h

h =

0.1111 0.1111 0.1111

0.1111 0.1111 0.1111

0.1111 0.1111 0.1111

>> x1=imfilter(x,h);

>> subplot(121);imshow(x);title('原图');

>> subplot(122);imshow(x1);title('经过（3*3）邻域平均后图');

>> h1=ones(5,5)/25;

>> h1

h1 =

0.0400 0.0400 0.0400 0.0400 0.0400

0.0400 0.0400 0.0400 0.0400 0.0400

0.0400 0.0400 0.0400 0.0400 0.0400

0.0400 0.0400 0.0400 0.0400 0.0400

0.0400 0.0400 0.0400 0.0400 0.0400

>> x2=imfilter(x,h1);

>> subplot(121);imshow(x);title('原图');

>> subplot(122);imshow(x2);title('经过（5*5）邻域平均后图');

4.Make a comparison of noise reduction by both median filter and averaging filter.

进行比较和中值滤波的降噪平均滤波器。

>> avgx=filter2(fspecial('average',5),x)/255;

>> midx=medfilt2(x,[5,5]);

>> subplot(131);imshow(x);title('原图');

>> subplot(132);imshow(avgx);title('经过（5*5）均值滤波图');

>> subplot(133);imshow(midx);title('经过（5*5）中值滤波图');

5.Develop a program to implement a Gradient Mask to obtain edge of an object (in compare with the function provided by Matlab)

开发一个程序来实现梯度面具来获取一个对象的边缘(与Matlab提供的函数)

>> subplot(231);imshow(j);title('原图');

>> eSoble=edge(j,'sobel');

>> subplot(232);imshow(eSoble);title('Soble 图');

>> ePrewitt=edge(j,'prewitt');

>> subplot(233);imshow(ePrewitt);title('Prewitt 图');

>> eRobert=edge(j,'roberts');

>> subplot(234);imshow(eRobert);title('Robert 图');

>> eLog=edge(j,'log');

>> subplot(235);imshow(eLog);title('Log 图');

>> eCanny=edge(j,'canny');

>> subplot(236);imshow(eCanny);title('Canny 图');

6.Image enhancement with High-Boost Filtering Mask and compare with the result of the operation defined by equation

图像增强与High-Boost 过滤面罩和与方程定义的操作的结果

>> subplot(131);imshow(j);title('原图');

>> H=[-1 -1 -1;-1 -9 -1;-1 -1 -1];

>> xhigh=filter2(H,j);

>> subplot(132);imshow(xhigh,[]);title('高通滤波');

>> jdouble=double(j);

>> M=[1 1 1;1 1 1;1 1 1]/9;

>> xmask=double(xhigh);

>> xmask2=filter2(M,xmask);

>> xm=xmask-xmask2;

>> subplot(133);imshow(xm);title('掩膜处理');

7．Count the number of pixels for each gray levels. 计算像素的数量为每个灰色的水平。 1,,1,0,-=L j f j Λ

1,,1,0,-=L j n j Λ

>> jpg=imread('F:19.jpg');

>> grayjpg=rgb2gray(jpg);

>> imshow(grayjpg);

>> [m,n]=size(jpg);

>> figure(1);

>> imshow(jpg);

>> gp=zeros(1,256);

????+?-=)

,(),(),(),(),(22y x f y x f y x f y x f y x g

for i=1:256

gp(i)=length(find(jpg == (i-1)));

end figure,bar(0:255,gp);

8．Estimate probabilities of each gray levels. 估计每个灰度级的概率。

1,,1,0,/)(-==L j n n f P j j f Λ

[m,n]=size(jpg);

figure(1);

imshow(jpg);

gp=zeros(1,256); %创建一个全零矩阵，1×256，计算各灰度出现的概率

for i=1:256

gp(i)=length(find(jpg == (i-1)))/(m*n);

end

figure,bar(0:255,gp);

9．Calculate cumulative distribution function of each gray levels. 计算每个灰度级的累积分布函数。

1,,,1,0,)()(0-==∑=L k j f P f C k

j j f ΛΛ

S1=zeros(1,256);

tmp=0;

for i=1:256

tmp=tmp+gp(i);

S1(i)=tmp; %各灰度的累计概率

end

figure,plot(S1);

10. Calculate gray levels of output image. 计算输出图像的灰度值

g = EQ (f) 1,,,,1,0,-=P k i g i ΛΛ

]5.0)()[(min min max ++-=g f C g g INT g i

newGp=zeros(1,256); %计算新的各灰度出现的概率

S2=zeros(1,256);

for i=1:256

S2(i)=round(S1(i)*256); %将取整后的值存储在S2

end

for i=1:256

newGp(i)=sum(gp(find(S2==i)));

end

figure,bar(0:255,newGp);

11．Develop a program to decompose the two images into coefficients and then fuse the corresponding coefficients to obtain a fusion result.

Observe the experiment result by trying different wavelets provided by Matlab and make necessary comparisons.

x1=imread('E:bwb.jpg');

x1=rgb2gray(x1);

x1=double(x1)/255;

x2=imread('E:bwb.jpg');

x2=rgb2gray(x2);

x2=double(x2)/255;

subplot(221)

imshow(x1)

title('图1')

subplot(222)

imshow(x2)

title(' 图2')

[ca1,ch1,cv1,cd1]=dwt2(x1,'haar');

[ca2,ch2,cv2,cd2]=dwt2(x2,'haar');

[row,col]=size(ca1);

for i=1:row

for j=1:col

ca(i,j)=(ca1(i,j)+ca2(i,j))/2;

if abs(ch1(i,j))>abs(ch2(i,j))

ch(i,j)=ch1(i,j);

elseif abs(ch1(i,j))

ch(i,j)=ch2(i,j);

cv(i,j)=cv1(i,j);

else

ch(i,j)=ch2(i,j);

cv(i,j)=cv2(i,j);

end

if abs(cd1(i,j))>abs(cd2(i,j))

cd(i,j)=cd1(i,j);

else

cd(i,j)=cd2(i,j);

end

end

end

x=idwt2(ca,ch,cv,cd,'haar');

imwrite(x,'a.png');

subplot(223)

imshow(x)

title('融合之后的图片')

12.Develop a program with db2 wavelets decomposition to enhance the detail of the image.

x1=imread('E:bwb.jpg');

x1=rgb2gray(x1);

x2=imread('E:bwb.jpg');

x2=rgb2gray(x2);

subplot(1,3,1)

imshow(x1)

title('图像一')

subplot(1,3,2)

imshow(x2)

title('图像二')

x1=double(x1);

x2=double(x2);

zt=3;

wtype='haar';

[c0,s0]=wavedec2(x1,zt,wtype);

[c1,s1]=wavedec2(x2,zt,wtype);

k=size(c1);

c=zeros(1,k(2));

temp=zeros(1,2);

c(1:s1(1,1))=(c0(1:s1(1,1))+c1(1:s1(1,1)))*0.5;

p=waverec2(c,s0,wtype);

p=uint8(p);

subplot(1,3,3)

imshow(p)

title('融合之后的图像')

（5）短文

要求：

应用课程所学知识写一篇关于图像处理典型应用方面的短文，要求写：题目、关键字、正文（不少于150字）。