数字图像处理模拟题(双语课)

Terms and concepts explanation

RGB：Red Green Blue 三原色红绿蓝

CMYK：cyan magenta yellow black 青、粉红、黄、黑

HSI: hue saturation intensity 色调、饱和度、亮度

FFT fast fourier transform 快速傅里叶变换

CWT continuous wavelet transform 连续小波变换

DCT discrete cosine transform 离散余弦变换

DFT discrete fourier transform 离散傅里叶变换

DWT discrete wavelet transform 离散小波变换

CCD charge-coupled device电荷耦合元件

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 （direct current component）直流分量的频率域GLH The 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 : there i s only one set of αk for any given f(x), then the ψk (x) are called basis functions

Multi-scale analysis多尺度分析

Gaussian function:Gaussian function In mathematics,is a function of the form:

for some real constants a 0, b, c 0, and e ≈ 2.718281828 (Euler’s number).对于一些真正的常量0,b,c 0,和e≈2.718281828(欧拉数)。

Sharpening filter ：锐化滤波器

Smoothing filter/convolution ：smoothing filter are used for blurring and for noise reduction

平滑滤波器用于模糊处理和降低噪声/卷积

Imageenhancement/imagerestoration image Enhancement the process of manipulating an i mage so that the result is more suitable than the original for a specific application.

图像增强处理是对图像进行的加工，使其结果对于特定的应用比原始图像更适合的一种处理。

Image restoration is an area that also deals with improving the appearance of an image. However, unlike enhancement, which is subjective, image restoration is objective.

图像复原也是一个改进图像外观的一个处理领域，然而与图像增强不同，图像增强是主观的，图像复原是客观的。

取样sampling: Digitizing the coordinate values is called sampling.对坐标值进行数字化称为.. 量话quantization：Digitizing the amplitude values is called quantization.对幅值数字化称为.空间分辨率：spatial resolution is a measure of the smallest discernible detail in an image.图像中可辨别的最小细节的度量

灰度分辨率：Intensity resolution refers to the smallest discernible change in intensity level.灰度分辨率是指在灰度级中可分辨的最小变化

空间域滤波：Spatial domain filtering

Frequency domain filtering：Frequency domain filtering with a variable frequency for the signal filtering 频率域滤波以频率作为变量对信号进行滤波

wavelet transforms are based on small waves,of varying frequency and limited duration.小波变换基于一些小型波，它具有变化的频率和有限的持续时间。

Image compression,the art and science of reducing the amount of data required to represent an image.图像压缩是一种减少描绘一幅图像所需数据量的技术和科学.

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.

Cite one example of spatial operation举一个空间操作的例子

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.

From the following processing result make a general comment about ideal highpass(figure B)and Gaussian highpass filter(figure D)

Answer：Gaussian highpass filter is more smooth than ideal highpass, even for small objects and thin lines with GHPF filter is also more clear

The original image, the ideal lowpass filter and Gaussian lowpass filter are shown be…B and C D and E are the results of the either filter B or C

a)Draw lines to connect the filters with their result 连线滤波器和处理结果

b)Explain the difference of the two filters 解释两者的区别

Answer：It is clear from this example that ideal lowpass filtering is not very practical实用,it has ringing properties. Over characteristics of Gauss filter is very flat, so it is not ringing

Blurred with a 3x3 smoothing mask would the resultant histograms still be the same? Draw the two histograms and explain your answer 模糊了一个3x3的平滑的掩膜？会得到的直方图仍然是相同的吗？画两图并解释你的答案

With the chromaticity diagram bellow give a brief description to the RGB color model. And these three colors enough to compose all visible colors?

用色度图给出的RGB颜色模型的简短描述。这三种颜色足以构成所有可见的颜色吗？

Answer：Images represented in the RGB color model consist of three component images, one for each primary color.

These three colors enough to compose all visible colors

What the result when applying an averaging mask with the size 1x1？

什么样的结果时，应用平均掩膜大小1x1？

不变

A mean filter is a linear filter but a median filter is not. WHY？

均值滤波器是一种线性滤波器，中值滤波器不是，为什么？

The basic principle of linear filtering is to replace the original image with the mean value of each pixel, but median filter replace the original image with the median value of each pixel.

The value of mean and median is different.

Develop an algorithm which implements frequency domain filtering by means of Fourier transform. 利用傅立叶变换实现了频率域滤波的算法。

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;

（1）将输入图像f（x，y）的（-1）x+y为中心的变换；

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

transform.

计算图像的DFT从（1）得到的功率谱f（u，v）的傅里叶变换。

Multiply by a filter function h(u,v)

乘以一个滤波器函数h(u,v) .

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

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

Multiply the result in (5) by（-1）x+y

The following matrix A is a 3x3 image and B is a 3x3 laplacian mask, what will be the resulting image?(Note that the elements beyond the border remain unchanged)

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

Develop an algorithm which computes the pseudo-color image by means of fourier transform

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

（频率域的基本滤波步骤）

Digital image histogram 编写一个函数计算数字图像直方图；

1)创建函数h：

function h=hist(x,N) 2)算法代码：（Untitled6.M）

[m,n]=size(x); a=imread('F:\Border Collie.jpg');

h=zeros(1,N); a=rgb2gray(a);

x=double(x); b=hist(a,256);

for i=1:m bar(b);

for j=1:n figure,imhist(a);

h(x(i,j)+1)=h(x(i,j)+1)+1;

end

end

Fundamental Steps in images Digital image Processing数字图像图像处理的

基本步骤

image acquisition图像采集—>image filter and enhancement图像滤波和增强

—>image restoration图像复原—>Color image processing彩色图像处理

—>wavelets and multiresolution processing小波与多分辨率处理—>compression （压缩）—>morphological processing(形态学处理)—>segmentation（分割）

—>representation and description（表示与描述）—>object recognition（目标识别）Lossless approaches—Hoffman Coding 无损方法- 霍夫曼编码

步骤：

create of source reductions by ordering the symbols under consideration and combining the lowest probability symbols into a single symbols that replaces them in the next source reduction.

Code each reduced source, starting with the smallest source and working back to the original source.

Simple programming with MATLAB

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

有卫星照片的夜晚如下。写一个程序用MATLAB来得知哪个照片是更亮的

代码：A=imread（’1.jgp’）;

B=imread(‘2.jpg’);

[m,n]=size(A);

for i=1:m

for j=1:n

sum1=sum1+A[I,j];

end

end

avg1=sum1/m*n;

[r,c]=size(B);

for i=1:m

for j=1:n

sum2=sum2+B[I,j];

end

end

avg2=sum2/m*n;

An 8x8 images f(i,j) has gray levels given by the following equation F(i,j)=|i-j| i,j=0,1………………………Write a program to find the output image obtained by applying a 3x3 median filter on the image f(i,j);note that the border pixels remain unchanged

有一个8x8图像f（i，j）灰度由以下公式得出

F（i，j）= | I-J | i，j = 0,1 ...........................

写一个程序来得出用中值滤波器采用3x3图像f（i，j）的输出图像；注意边界像素保持不变

Avaege filter均值滤波

function [r]=avgfilter(gray,n)

a(1:n,1:n)=1;

[row,col]=size(gray);

gray1=double(gray);

gray2=gray1;

for i=1:row-n+1

for j=1:col-n+1

c=gray1(i:i+(n-1),j:j+(n-1)).*a;

s=sum(sum(c));

gray2(i+(n-1)/2,j+(n-1)/2)=s/(n*n);

end

end

r=uint8(gray2);

>> avg3=avgfilter(noise,3);

>> avg5=avgfilter(noise,5);

>> avg7=avgfilter(noise,7);

>> subplot(221);imshow(noise);title('原噪声图');

>> subplot(222);imshow(avg3);title('3*3均值滤波图');

>> subplot(223);imshow(avg5);title('5*5均值滤波图');

>> subplot(224);imshow(avg7);title('7*7均值滤波图');

Winener filrer维纳滤波

>> figure;subplot(2,3,1);imshow(gray);title('原灰度图像');

>> noise2 = imnoise(gray,'gaussian',0,0.05);

>> subplot(2,3,3);imshow(noise2);title('高噪点处理后的图像');

>> winener3=wiener2(noise2,[3 3]);

>> winener5=wiener2(noise2,[5 5]);

>> winener9=wiener2(noise2,[9 9]);

>> subplot(2,3,4);imshow(winener3);title('维纳滤波器处理后的图像3*3');

>> subplot(2,3,5);imshow(winener5);title('维纳滤波器处理后的图像5*5');

>> subplot(2,3,6);imshow(winener9);title('维纳滤波器处理后的图像9*9');

median filter中值滤波

function [r]=midfilter(gray,n)

[row,col]=size(gray);

gray1=double(gray);

gray2=gray1;

for i=1:row-n+1

for j=1:col-n+1

c=gray1(i:i+(n-1),j:j+(n-1));

e=c(1,:);

for u=2:n

e=[e,c(u,:)];

end

mm=median(e);

gray2(i+(n-1)/2,j+(n-1)/2)=mm;

end

end

r=uint8(gray2);

>> mid3=midfilter(noise,3); >> mid5=midfilter(noise,5); >> mid7=midfilter(noise,7);

>> subplot(221);imshow(noise);title('原噪声图'); >> subplot(222);imshow(mid3);title('3*3中值滤波图'); >> subplot(223);imshow(mid5);title('5*5中值滤波图');

>> subplot(224);imshow(mid7);title('7*7中值滤波图');

>> img=imread('E:\university\数字图像处理\实验\4\test.jpg');

>> gray=togray(img);

>> subplot(2,3,1);imshow(gray);title('原灰度图像');

>> noise = imnoise(gray,'gaussian',0,0.02);

>> subplot(2,3,3);imshow(noise);title('高噪点处理后的图像');

>> adaptgray=adaptive(noise,3);

>> subplot(2,3,4);imshow(adaptgray);title('自适应局部降噪滤波器'); >> avg=avgfilter(noise,3);

>> subplot(2,3,5);imshow(avg);title('3*3算术均值滤波图像');

>> geo=geometric(noise,3);

>> subplot(2,3,6);imshow(geo);title('3*3几何均值滤波图像');

The theory of the Wiener filter

The Wiener filtering is optimal in terms of the mean square error. In other words, it minimizes the overall mean square error in the process of inverse filtering and noise smoothing. The Wiener filtering is a linear estimation of the original image. The approach is based on a stochastic framework. The orthogonality principle implies that the Wiener filter in Fourier domain can be expressed as follows:

where are respectively power spectra of the original image and the additive noise, and H( f1,f2) is the blurring filter. It is easy to see that the Wiener filter has two separate part, an inverse filtering part and a noise smoothing part. It not only performs the deconvolution by inverse filtering (highpass filtering) but also removes the noise with a compression operation (lowpass filtering).

Steps of Wiener filter design 维纳滤波器设计步骤

(1)Digitize a sample of the input signal s(t)

(2)Autocorrelate the input sample to produce and estimate of Rx

(3)Compute the Fourier transform of Rx to produce Px

(4)Obtain and digitize input sample to estimate Rxs

(5)Compute the Fourier transform of Rxs to produce Pxs

(6)Work out the transfer function by Eq.(51) or compute inverse Fourier transform of H0 to produce impulse response, h0