求The ERDAS Field Guide第十章内容

求The ERDAS Field Guide第十章内容
谢谢

ntroduction
Raw, remotely sensed image data gathered by a satellite or aircraft are representations of the irregular surface of the Earth. Even images of seemingly flat areas are distorted by both the curvature of the Earth and the sensor being used. This chapter covers the processes of geometrically correcting an image so that it can be represented on a planar surface, conform to other images, and have the integrity of a map.
Rectification is the process of transforming the data from one grid （or coordinate）system into another grid system using a geometric transformation. Since the pixels of the new grid may not align with the pixels of the original grid, the pixels must be resampled. Resampling is the process of extrapolating data values for the pixels on the new grid from the values of the source pixels.
(与纯坐标校正不同,图像的校正还涉及像元值重采样的问题.）
Registration（校准、配准）
Registration is the process of making an image conform to another image. A map coordinate system is not necessarily involved.
Georeferencing（地理坐标化）
Georeferencing refers to the process of assigning map coordinates to image data. Georeferencing, by itself, involves changing only the map coordinate information in the image file. The grid of the image does not change. （图像与坐标系配准时格网本身不变）
用户应注意：
Geocoded data are images that have been rectified to a particular map projection and pixel size, and usually have had radiometric corrections applied. It is possible to purchase image data that is already geocoded. Geocoded data should be rectified only if they must conform to a different projection system or be registered to other rectified data.
Latitude/Longitude
Orthorectification
Orthorectification is a form of rectification that corrects for terrain displacement（地形位移改正）. In relatively flat areas, orthorectification is not necessary, but in mountainous areas, orthorectification is recommended.
When to Rectify
Rectification is necessary in cases where the pixel grid of the image must be changed to fit a map projection system or a reference image.
When to Georeferenc Only
An image with no distortion and no any map coordinate needs to be georeferenced. It is a much simpler process than rectification. This involves redefining:
• the map coordinate of the upper left corner of the image
• the cell size (the area represented by each pixel)
Disadvantages of Rectification
During rectification, the data file values of rectified pixels must be resampled to fit into a new grid of pixel rows and columns. An unrectified image is more spectrally correct than a rectified image.
classification
Some analysts recommend classification before rectification.
Rectification Steps
1. Locate GCPs.
2. Compute and test a transformation.
3. Create an output image file with the new coordinate information in the header. The pixels must be resampled to conform to the new grid.
（与GIS课相比,这里多了第三步.）
Ground Control Points
GCPs are specific pixels in an image for which the output map coordinates (or other output coordinates) are known. GCPs consist of two X,Y pairs of coordinates:
• source coordinates—usually data file coordinates in the image being rectified
• reference coordinates—the coordinates of the map or reference image to which the source image is being registered.
Minimum Number of GCPs
k =（n + 1）(n + 2 ) / 2
一般采用大于K的GCPs,通过最小二乘法求解.
Polynomial Transformation
Polynomial equations are used to convert source file coordinates to rectified map coordinates. Depending upon the distortion in the imagery, the number of GCPs used, and their locations relative to one another, complex polynomial equations may be required to express the needed transformation.
(教材上有太多的通俗解释,可跳过之.)
Linear Transformations
1st-order：
x = a1 x + b1 y + c1
y = a2 x + b2 y + c2
Nonlinear Transformations
2nd-order：
x = a1 x2 + b1 y2 + c1 xy + d1 x + e1 y + f1
y = a2 x2 + b2 y2 + c2 xy + d2 x + e2 y + f2
Higher Order Polynomials
RMS Error 及GCPs评价问题（选引教材上P356）
Residuals and RMS Error Per GCP
参见：
Figure 10-11: Residuals and RMS Error Per Point
Figure 10-12: RMS Error Tolerance
Evaluating RMS Error
要点：只要GCPs的RMS可允许,尽可能用低次的多项式转换.
One should start with a 1st-order transformation unless it is known that it does not work. It is possible to repeatedly compute transformation matrices until an acceptable RMS error is reached.
Most rectifications are either 1st-order or 2nd-order. The danger of using higher order rectifications is that the more complicated the equation for the transformation, the less regular and predictable the results are. To fit all of the GCPs, there may be very high distortion in the image.
After each computation of a transformation and RMS error, there are four options:
• Throw out the GCP with the highest RMS error, assuming that this GCP is the least accurate.
• Tolerate a higher amount of RMS error.
• Increase the complexity of transformation, creating more complex geometric alterations in the image. A transformation can then be computed that can accommodate the GCPs with less error.
• Select only the points for which you have the most confidence.
Resampling Methods
帮助理解“GCP转换——重采样”的思路：
1、基于足够数量质量的GCPs,采用多项式变换,求取源图像坐标与参照图像坐标之间的转换关系.
2、求取源图像端点（右上左下等）在参照图像坐标系中的坐标（定范围）.
3、给定转换后图像的格网大小,及每个像元的“新”坐标.
xi = x0 + ( i – 1 ) Δx , yj = y0 + ( j – 1 ) Δy
4、基于“新”坐标反算转换后图像每个像元的源图像坐标,即求得在源图像中的相应位置,再利用该点邻近的或周边的源图像像元值,内插求出该点应取的像元值.
The next step in the rectification/registration process is to create the output file. Since the grid of pixels in the source image rarely matches the grid for the reference image, the pixels are resampled so that new data file values for the output file can be calculated.
3 resampling methods are supported in ERDAS IMAGINE.
In all methods, the number of rows and columns of pixels in the output is calculated from the dimensions of the output map, which is determined by the geometric transformation and the cell size. The output corners (upper left and lower right) of the output file can be specified. The default values are calculated so that the entire source file is resampled to the destination file.
To determine an output pixel’s value, the rectified coordinates of the pixel are retransformed back to the source coordinate system using the inverse of the transformation.（我把这一句话加在这儿,有利于理解思路.）
3 resampling methods supported in ERDAS IMAGINE are:
Nearest neighbor （最邻近采样）
—uses the value of the closest pixel to assign to the output pixel value.
参见：
Figure 10-14
Bilinear interpolation（双线性内插）
—uses the data file values of four pixels in a 2 × 2 window to calculate an output value with a bilinear function.
参见：
Figure 10-15
Cubic convolution（三次卷积内插）
以上三种内插法可参照去年教材§4.3.4.2.