数字图像处理复习提纲

第一章1、What is an image?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. Image：A reflection from real world with infinite details ,Usually two- or three-dimensional2、What is a digital image?When x,y,and the intensity values of f are all finite, discrete quantities有限的离散量.digital image：An image which is“discretized离散,”Two-dimensional collection of light intensity values光强度值(or gray values灰度值) 。

Matrix矩阵, two-dimensional function 二维函数3、What is digital image processing?The field of digital image processing refers to processing digital images by means of a digital computer.digital image processing: deals with the manipulation and analysis of pictures by a computer.4、pixel is the term used most widely to denote the elments of a digital image5 Important steps in a typical image processing system（Fundamental steps in digital image processing ）Image Acquisition图像采集→Image filtering and enhancement图像滤波和加强→Segmentation分割→Feature selection 特征提取→Representation & description描述→Object recognition对象识别第二章1、Gray level:denote monochromatic intensity.表示单色强度2、Three basic quantities to describe the quality of a chromatic（有颜色的，彩色的）light source:Radiance（辐射）is the total amount of energy that flows from the light source.源自于光源的总能量Luminance (measured in lumens (lm))（流明）Gives a measure of the amount of energy an observer perceives from a light source.Brightness （亮度）Embodies the achromatic notion of intensity.体现了无色的强度概念3、空间分辨率和灰度分辨率的概念A widely used definition of spatial resolution空间分辨率is simply the smallest number of discernible line pairs per unit distance.Gray-level resolution 灰度分辨率：similarly refers to the smallest discernible change in gray level.5、Distance measures距离测量Euclidean distance欧氏距离De(p,q)=[(x-s)2+(y-t)2]1/2D4 distance(also called city-block distance)between p and q is defined as D4(p,q)=|x-s|+|y-t|D8 distance (also called chessboard distance)棋盘距离between p and q is defined as D8(p,q)=max(|x-s|,|y-t|)6、Sampling（采样）: digitize the coordinate valuesQuantization（量化）: digitize the amplitude values7、Adjacency（邻接性）（1）4-adjacency: p and q with intensity from V and q is in N4(p)（2）8-adjacency: p and q with intensity from V and q is in N8(p)（3）m-adjacency(mixed adjacency): p and q having intensity from V andq is in N4(p), or q is in ND(p) and N4(p) N4(q) has no pixels whose values are from V第三章1、Spatial domain（空域）refers to image plane itself,and image processing methods in this category are based on direct manipulation of pixels in an image.Frequency Domain （频域）Based on modifying the Fourier transform of an image.3、Border Processing边界处理Limiting the excursions of the center of the mask to be at a distance no less than (n-1)/2 pixels from the border. Padding the image by adding rows and columns of 0’s, or padding by replicating rows or columns.用边缘复制补在图像之外4、Smoothing Spatial Filters平滑滤波Smoothing filters are used for blurring(模糊)and for noise reduction(降噪).The output (response) of a smoothing, linear spatial filter is simply the average of the pixels contained in the neighborhood of the filter mask.Order-Statistics（nonlinear）Filters顺序统计滤波Order-statistics filters are nonlinear spatial filters whose response is based on ordering (ranking) the pixels contained in the image area encompassed by the filter, and then replacing the value of the center pixel with the value determined by the ranking result.Sharpening Spatial Filter锐化滤波5、First-Order Derivative傅里叶变换一阶特性：①Must be zero in flat segments (areas of constant gray-level values).②Must be nonzero at the onset of a gray-level step or ramp.③Must be nonzero along ramps.Second-Order Derivative 傅里叶变换的二阶特性①must be zero in flat areas;②must be nonzero at the onset and end of a gray-level step or ramp;③must be zero along ramps of constant slope.第四章1、the important characteristic that a function(傅里叶变换特征)：express in either a Fourier series or transform,can be reconstructed (recovered) completely via an inverse process ,with no loss of information.二维离散公式：2、Some basic properties of frequency domain :频域特性1)The slowest varying frequency component(u=v=0) corresponds to the average gray-level of an image .2) Move away from the origin of the transform result,the low frequencies correspond to the slowly varyingcomponents3）Move away further,the higher frequencies correspond to faster an faster gray-level changes:edges,noise3、Basic steps of filtering in frequency domain频域滤波基本步骤1) Multiply the input image by (-1)(x+y) to center the transform,2)Compute F(u,v), the DFT the image from .3) Multiply F(u,v) by a filter function H(u,v).4) Compute the inverse DFT of the result in .5) Obtain the real part of the result in .6)Multiply the result in by (-1)(x+y) .4、低通滤波和高通滤波器的概念Lowpass filter: a filter attenuates high frequencies while “passing”low frequencies.Highpass filter:a filter attenuates low frequencies while “passing”high frequencies.5、Homomorphic Filtering 同态滤波基本步骤（照射分量对应慢变换，反射分量对应快变换）1)illumination component of an image generally is characterized by slow spatial variations, while the reflectance component tends to vary abruptly particularly at the junctions of dissimilar objects.2)These characteristics lead to associating the low frequencies of the Fourier transform of the logarithm of an image with illumination and high frequencies with reflectance.3)Although, these associations are rough approximations, they can be used to advantage in image enhancement.6、Fourier series: any periodical function can be expressed as the sum of sines and/or cosines of different frequncies, each multiplied by a different coefficent7、Fourier transform ：functions that are not periodical can be expressed as the integral of sines and/or cosines multiplied by a weighing function(4) 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) [m,n]=size(x); h=zeros(1,N); x=double(x); for i=1:m for j=1:n h(x(i,j)+1)=h(x(i,j)+1)+1; end end 2)算法代码：（Untitled6.M ） a=imread('F:\Border Collie.jpg'); a=rgb2gray(a); b=hist(a,256); bar(b); figure,imhist(a);第五章1、A model of the image degradation/restoration process图像退化/恢复的基本模型2、Estimation of noise parameters(估算噪声参数)(1)Periodic noise —Observe the frequency spectrum（2）Random noise with unknown PDFs1）Case 1: imaging system is available ——Capture images of “flat” environment2）Case 2: noisy images available⏹Take a strip from constant area⏹Draw the histogram and observe it⏹Measure the mean and variance3、各种滤波器：(1)Order-statistics filters1) Midpoint filters：it works best for randomly distributed noise(随机噪声),like Gausssian or uniform noise.2)Alpha-trimmed mean filters：the alpha-trimmed filters is useful in situation involving multiple types ofnoise,such as a combination of salt and pepper noise and Gaussian noise.3)Max/min filters：The filter is useful for finding the darkest points in an image.Also it reduces salt noise as aresult of the min operation.4)Median filters: particularly effective in the presence of impulse noise, also called salt-and pepper noise becauseof its appearance as white and black dots superimposed on an image.(2) mean filter1)Harmonic mean filter(谐波均值滤波):The Harmonic mean filter works well for salt noise ,but fails for forpepper noise.It does well also with other types of noise like Gaussian noise.2)Contra-harmonic mean filter (逆谐波均值滤波)：when Q=-1, it refers to Harmonic mean filter; when Q=0, itrefers to Arithmetic mean filter ; when Q>0, it can eliminate pepper noise ; when Q<0, it can eliminate salt noise ;3)Arithmetic mean filter(几何均值滤波器)4)Geometric mean filter(算术均值滤波器)第六章1、RGB: the three colors: red（R）, green（G）and blue（B）are referred to as primary colors of human vision.Three characteristics to distinguish colors:1) Brightness(亮度): embodies the achromatic notion of intensity.2) Hue (色调): represent dominant color as perceived by an observer.3)Saturation(饱和度): proportion to the amount of white light added2、secondary colors二次色：Magenta(品红)=red+blue Cyan(青色)=green+blue Yellow=red+green3、CMYK:Magenta , Cyan , Y ellow , Black4、HSI:HSI format Where I stands intensity, or brightness. H and S denote Hue and Saturation, respectively.5、pseudo-color（伪彩色）：assigning a color to a particular monochrome intensity or range of intensity6、Chromaticity(色度): hue ans saturation taken together4、最近邻域内插Nearest neighbor interpolation(1)利用最近邻域内插算法实现数字图像的放大和缩小。