同济大学摄影测量学课件

1、1,Photogrammetry摄影测量学,关泽群,同济大学 测量与国土信息工程系,Chapter 5 Digital Image and Feature Extraction,Contents,5.1 Image Sampling and Resampling 5.2 Point Feature Extraction 5.3 Line Feature Extraction,4,DIGITAL IMAGERY,A digital image is a regular array of pixels, or picture elements, and is described in terms

2、of its geometry and its radiometry. 数字影像是一个灰度矩阵g,矩阵中每个元素gi,j,是一个灰度值,对应着光学影像或实体的一个微小区域,称为像元素或像元或像素（Pixel=Picture element ）。各像元素的灰度值gi,j,代表其影像经采样与量化了的“灰度级”,数字影像或数字化影像,6,To Obtain Digital Image,Each pixel of a digital image is a direct or indirect sample of the continuous incident light distribution. A

3、 digital sensor samples incident light directly. (可以直接装在空间飞行器中的扫描式传感器、数码相机、以及加有特殊装置的工业摄像机直接获得) An example of indirect sampling is scanning a piece of film and converting it into a digital image. (也可利用影像数字化器（如扫描仪等）对摄取的像片经过采样、量化获得地形测图中航测通常使用),7,Pixels may be arranged in any regular pattern, but in pra

4、ctice most sampling grids are square or rectangular (一般为矩形格网) . Hexagonal grids(六角形格网) have some theoretical advantages but have seldom been implemented. The ratio between pixel width and pixel height is known as the aspect ratio（纵横比）; a square pixel has an aspect ratio of one.,Pixel, IFOV and GSD,8

5、,Digital images are often described in terms of their pixel size, but can also be specified in terms of the instantaneous field of view (IFOV)瞬时视场, which is the angle determined by the pixel size and the focal length. As shown in Fig. , as the focal length decreases or the pixel size increases, the

6、IFOV increases.,Figure. Instantaneous field of view (IFOV) and ground sample distance (GSD),A larger IFOV means that one pixel covers a larger portion of the scene or, equivalently, that the image will have lower spatial resolution.,9,Figure . Instantaneous field of view (IFOV) and ground sample dis

7、tance (GSD),Instantaneous field of view (IFOV) 瞬时视场 ground sample distance (GSD) 地面采样间隔(距离),Another measure related to pixel size is the ground sample distance (GSD), which is the projection of the pixel size onto the ground plane (Fig. ).,Pixel, IFOV and GSD,10,This is often used erroneously as a s

8、ynonym for resolution. In fact, the resolution of a digital image is determined by both the sensor geometry and by factors external to the sensor, such as atmospheric conditions, platform motion, etc. The actual resolution may be as good as indicated by the GSD, but in practical applications it is o

9、ften lower.,Pixel, IFOV and GSD,11,IFOV and GSD Calculation,A satellite imaging system has pixels that are 0.015 ram square and a focal length of 1000mm. What is (the IFOV? What is the GSD at nadir, assuming an orbital altitude of 650 km?,SOLUTION The IFOV is,and the GSD is GSD = IFOV(650,000) = 9.7

10、5 m,1. Digital Image Sampling,13,Digital images sample a continuous analog input image at discrete points and assign a discrete intensity value at each point. How can we determine whether all the information in the original image is present in its sampled digital form or, equivalently, what spatial

11、sampling rate is required to fully capture the input?,14,The answer to this question relies on sampling theory. Sampling theory states that a band-limited signal with a highest frequency of can be exactly reconstructed with a sampling rate of 2. （当采样频率大于信号中最高频率的2倍时，采样之后的数字信号完整地保留了原始信号中的信息） In terms

12、of wavelength, a signal with a minimum wavelength of must be sampled with a sample spacing of no greater than /2. The theoretical minimum sampling rate required is known as the Nyquist rate.,15,What happens if we dont sample at a high enough rate? The higher-frequency components of the signal, which

13、 correspond to the fine details in the image, are incorrectly interpreted as lower-frequency components. These erroneous components confuse the overall signal reconstruction, a phenomenon known as aliasing（混淆）.,16,For digital images, the lens and the pixel both act as apertures, limiting the maximum

14、 detail visible in the image. For most aerial cameras, the lens (and film, if a scanner is used) usually have much higher resolution than the commonly used pixel sizes can record, so the pixel size determines the effective aperture.,Digital Image Sampling,Sampling 对实际连续函数模型离散化的量测过程 Sampling point 被量

15、测的“点”是小的区域-像素 Sampling interval 矩形的长与宽通常称为像素的大小,Sampling theorem (One-dimensional image）,Band-limited function,Sampling Processing,Sampling interval - x,fl is cutoff frequency(Nyquist rate),当采样间隔能使在函数g(x)中存在的最高频率中每周期取有两个样本时，则根据采样数据可以完全恢复原函数g(x),Digital Image Expression,Frequency domain,Fourier trans

16、form,2. Digital Image Resampling,23,DIGITAL IMAGE RESAMPLING,We often need to resample a digital image into a different geometry, for example, to create an orthophoto. Any type of geometric transformation, including similarity, affine, projective, polynomial, etc. , can be applied to a digital image

17、 in exactly the same way as to any two-dimensional set of coordinates.,Image matching,Reference images (主图像) Matching image (辅图像),25,However, once we have calculated the new image coordinates, which are often fractional, we must decide which gray value to assign to them. A new value must be interpol

18、ated from the pixels neighboring the coordinates; a number of mathematical techniques are available.,Image resampling theorem,当欲知不位于矩阵（采样）点上的原始函数g(x,y)的数值时就需进行内插，此时称为重采样（resampling）,Non-sampling point,Image resampling method,Digital image,Sinc sampling function,28,Three common resampling methods:,Bi

19、-linear interpolation Bi-cubic convolution(cost of more computation. ) Nearest neighbor interpolation,Bi-linear interpolation,Convolution kernel is a triangle function,11,12,21,22,p,Y,X,y1,y2,a,b,y,1- y,x,1- x,x2,x1,Bi-linear interpolation,Bi-linear interpolation computation,Hadamard product,Weighte

20、d average,Bi-linear interpolation computation,Bi-cubic convolution,Convolution kernel is a cubic function,p,11,12,13,14,21,31,41,22,23,24,32,33,34,42,43,44,Y,x,y,x,Bi-cubic convolution demo,Bi-cubic convolution computation,Bi-cubic convolution computation,Nearest neighbor interpolation,直接取与P(x,y)点位置

21、最近像元N的灰质值为核点的灰度作为采样值,A comparison of three resampling methods,最邻近像元法最简单，计算速度快且能不破坏原始影像的灰度信息。但其几何精度较差，。前两种方法几何精度较好，但计算时间较长，特别是双三次卷积法较费时，在一般值况下用双线性插值法较宜。,3. Locating Conjugate Epipolar lines and Image Resampling, According to the principles of analytical photogrammetry According to the coplanarity con

22、dition,Two methods for locating conjugate epipolar lines,Photographic baseline,Coordinate transformation,According to the principles of analytical photogrammetry,Tilt image,Horizontal image,v = 某常数即表示某一核线,C=v,在“水平”影像上获取核线影像,u=k Sampling interval,Locating epipolar lines in Horizontal image,同名核线的v坐标值相

23、等,Locating conjugate points,核线的重排列（重采样）,是否是采样点？,Horizontal image,Tilt image,Epipolar line rearrangement (resampling),Linear interpolation demo,Linear interpolation,Epipolar line,y1,k, The nearest pixel method,n 1tgK,Epipolar line rearrangement (resampling),对每条核线而言K是常数,Linear interpolation, According

24、 to the principles of analytical photogrammetry According to the coplanarity condition,Two methods for locating conjugate epipolar lines,Mathematical Concepts in Photogrammetry,49,交汇确定地面点坐标,INTERSECTION (Space Intersection空间前方交会),Intersection refers to the determination of a points position in objec

25、t space by intersecting the image rays from two or more images.,50,The Coplanarity geometry,Figure illustrates a pair of overlapping frame photographs and a pair of conjugate image points.,The epipolar geometry,C,C,x,x and X are coplanar,A,S1,S2,l1,a1,a2,l2,Conjugate epipolar lines,an epipolar plane

26、 = plane containing baseline (1-D family),an epipolar line = intersection of epipolar plane with image (always come in corresponding pairs),Conjugate points is at conjugate epipolar lines,The epipolar geometry,s1,s2,p,Conjugate epipolar lines in the tilt images,x,y,z,u,q,v,w,p,q,Locating left epipol

27、ar line,The equation of left epipolar line,The equation of right epipolar line,Locating right epipolar line,Parameter determination,Relatively oriented double-image,Contents,5.1 Image Sampling and Resampling 5.2 Point Feature Extraction 5.3 Line Feature Extraction,Point Feature Extraction,Point feat

28、ures such as definite points, corner points have high accuracy. The operator for point feature extraction is usually called the interest operator.,Point feature with grey value differences,Moravec operator,Moravec于1977年提出利用灰度方差提取点特征的算子,r,c,（1）Get the interest value IV,（2）If the value M is larger tha

29、n a threshold given, then the point is taken as a candidate point,Moravec operator take a window of 5x5 pixel with the pixel as the centre and the quadratic sums of grey value differences along the four major directions.,确定窗口大小,（3）Feature point is taken from the extremum point of candidate point,For

30、stner operator,计算各像素的Roberts梯度和像素（c，r）为中心的一个窗口的灰度协方差矩阵，在影像中寻找具有尽可能小而接近圆的误差椭圆的点作为特征点。,（l）Calculate Roberts gradient of pixels,Forstner operator steps,（2）Obtain the covariance matrix for displacements,（3） Get the interest value q and w,DetN代表矩阵N之行列式,trN代表矩阵N之迹,(4） Obtain candidate point,当 同时 ，该像元为待选点,

31、（5） Feature point is taken from the extremum point of candidate point,即在一个适当窗口中选择最大的待选点,Contents,5.1 Image Sampling and Resampling 5.2 Point Feature Extraction 5.3 Line Feature Extraction,Line Feature Extraction,线特征是指影像的“边缘”与“线”,“边缘”可定义为影像局部区域特征不相同的那些区域间的分界线，而“线”则可以认为是具有很小宽度的其中间区域具有相同的影像特征的边缘对,Diffe

32、rence operator 、Laplace operator 、LOG operator etc. are usual methods,Line feature for House,Line feature for road,Line feature with grey value differences,一、Difference operator,1Gradient operator,Difference operator,对于一给定的阈值T，当时，则认为像素（i，j）是边缘上的点。,近似,Roberts gradient operator,Directional difference

33、operator,Direction of line and edge,Sobel operator,考察它上下、左右邻点灰度的加权差。与之接近的邻点的权大：,Prewitt operator and Sobel operator,加大模扳抑制噪声,Prewitt operator,Sobel operator,Second order difference operator,Directional second order difference operator,Laplace operator,Convolution kernel Mask,取其符号变化的点，即通过零的点为边缘点，因此通常也称其为零交叉（zero-Crossing）点,Laplace operator,Laplacian of gaussian operator （LOG）,首先用高斯函数先进行低通滤波，然后利用拉普拉斯算子进行高通滤波并提取零交叉点，,Gaussian function,Low-pass filters,Edge detection,LOG算子以为卷积核，对原灰度函数进行卷积运算后提取零交叉点为边缘,Laplacian of gaussian operator （LOG）,Sobel,Make comparison between