Question

新：求The ERDAS Field Guide第六章下半部分内容

谢谢了

Answer 1

例如：上面给出协方差矩阵的TM图像fj2，经主成分变换后形成新的图像fj2_pc，其协方差矩阵为
703.318 0 0 0 0 0 0
0 174.407 0 0 0 0 0
0 0 43.816 0 0 0 0
0 0 0 11.242 0 0 0
0 0 0 0 4.652 0 0
0 0 0 0 0 3.459 0
0 0 0 0 0 0 0.661
几何意义：
线性变换——坐标轴平移或旋转。
The process is easily explained graphically with an example of data in two bands. （讲解Page 153 - 155）
评论：数学的力量。反过来，图像处理加深对数学的理解。
PC方法常用于与其它方法相结合，如前面的Crisp和Resolution Merge。
英语总结：The different bands in a multispectral image can be visualized as defining an N-dimensional space where N is the number of bands. Each pixel, positioned according to its DN value in each band, lies within the N-dimensional space. This clustering of the pixels is termed the data structure.
The data structure can be considered a multidimensional hyperellipsoid. The principal axes of this data structure are not necessarily aligned with the axes of the data space. They are more directly related to the absorption spectra. You could view the axes that are largest for the data structure produced by the absorption peaks of special interest for a application.
For example, a geologist and a botanist are interested in different absorption features. They would want to view different data structures and therefore, different data structure axes. Both would benefit from viewing the data in a way that would maximize visibility of the data structure of interest.

Tasseled Cap（缨帽变换）
The Tasseled Cap transformation offers a way to optimize data viewing for vegetation studies. Research has produced three data structure axes that define the vegetation information content.
数学统计上最优的Principal Components方法不一定对各种应用都最优。这里的Tasseled Cap也是一种多维线性变换，但它的坐标轴平移或旋转朝最有利于观测植被地物的方向进行平移或旋转。
• Brightness—a weighted sum of all bands, defined in the direction of the principal variation in soil reflectance.
• Greenness—orthogonal to brightness, a contrast between the near-infrared and visible bands. Strongly related to the amount of green vegetation in the scene.
• Wetness—relates to canopy and soil moisture.
These rotations are sensor-dependent。For TM4 (第页).
缨帽变换系数的分析

RGB to IHS 及其逆计算
It is possible to define an alternate color space that uses intensity (I), hue (H), and saturation (S). This system is advantageous in that it presents colors more nearly as perceived by the human eye.
雷达图像的应用。

Indices
Indices are used to create output images by mathematically combining the DN values of different bands(波段间的algebra，P180).
Applications
• Indices are used extensively in mineral exploration and vegetation analysis to bring out small differences between various rock types and vegetation classes.
• Indices can also be used to minimize shadow effects in satellite and aircraft multispectral images. Black and white images of individual indices or a color combination of three ratios may be generated.
Integer Scaling Considerations
由于波段比值可能变动很大，计算结果重新定标取整问题在这里特别突出。
Index Examples （P182-183）
（回顾第一章的Figure 1-6图，帮助理解植被指数等。）
Hyperspectral Image Processing
Hyperspectral image processing is, in many respects, simply an extension of the techniques used for multispectral data sets; indeed, there is no set number of bands beyond which a data set is hyperspectral. Thus, many of the techniques or algorithms currently used for multispectral data sets are logically applicable. What is of relevance in evaluating these data sets is not the number of bands per se, but the spectral bandwidth of the bands (channels). As the bandwidths get smaller, it becomes possible to view the data set as an absorption spectrum rather than a collection of discontinuous bands. Analysis of the data in this fashion is termed imaging spectrometry.
A hyperspectral image data set is recognized as a three-dimensional pixel array（Figure 65）（6-23）.
A data set with narrow contiguous bands can be plotted as a continuous spectrum and compared to a library of known spectra. A serious complication in using this approach is assuring that all spectra are corrected to the same background.
At present, it is possible to obtain spectral libraries of common materials. The JPL and USGS mineral spectra libraries are included in ERDAS IMAGINE. These are laboratory-measured reflectance spectra of reference minerals, often of high purity and defined particle size. The spectrometer is commonly purged（净化） with pure nitrogen to avoid absorbance by atmospheric gases. Conversely, the remote sensor records an image after the sunlight has passed through the atmosphere (twice) with variable and unknown amounts of water vapor, CO2. The unknown atmospheric absorbances superimposed upon the Earth’s surface reflectances makes comparison to laboratory spectra or spectra taken with a different atmosphere inexact. Indeed, it has been shown that atmospheric composition can vary within a single scene. This complicates the use of spectral signatures even within one scene.
A number of approaches have been advanced to help compensate for this atmospheric contamination of the spectra.
Fourier Analysis
Image enhancement techniques can be divided into two basic categories: point and neighborhood. Point techniques enhance the pixel based only on its value, with no concern for the values of neighboring pixels. These techniques include contrast stretches (nonadaptive), classification, and level slices. Neighborhood techniques enhance a pixel based on the values of surrounding pixels. As a result, these techniques require the processing of a possibly large number of pixels for each output pixel. The most common way of implementing these enhancements is via a moving window convolution. However, as the size of the moving window increases, the number of requisite calculations becomes enormous. An enhancement that requires a convolution operation in the spatial domain can be implemented as a simple multiplication in frequency space—a much faster calculation.
In ERDAS IMAGINE, the FFT is used to convert a raster image from the spatial (normal) domain into a frequency domain image. The FFT calculation converts the image into a series of two-dimensional sine waves of various frequencies. The Fourier image itself cannot be easily viewed, but the magnitude of the image can be calculated, which can then be displayed either in the Viewer or in the FFT Editor. Analysts can edit the Fourier image to reduce noise or remove periodic features, such as striping. Once the Fourier image is edited, it is then transformed back into the spatial domain by using an IFFT. The result is an enhanced version of the original image.
The basic premise（前提） behind a Fourier transform is that any one-dimensional function, f(x) (which might be a row of pixels), can be represented by a Fourier series consisting of some combination of sine and cosine terms and their associated coefficients.
176页上的图72
A Fourier transform is a linear transformation that allows calculation of the coefficients necessary for the sine and cosine terms to adequately represent the image. This theory is used extensively in electronics and signal processing. Therefore, DFT has been developed. Because of the computational load in calculating the values for all the sine and cosine terms along with the coefficient multiplications, a highly efficient version of the DFT was developed and called the FFT.
DFT ——177上的公式，FFT 快速算法
e-j2π(ax+by) = cos2π(ax+by) -jsin2π(ax+by)
The raster image generated by the FFT calculation is not an optimum image for viewing or editing. Each pixel of a fourier image is a complex number (i.e., it has two components: real and imaginary). For display as a single image, these components are combined in a root-sum of squares operation（傅利叶变换的模作为像元值来显示 u,v图像）. Also, since the dynamic range of Fourier spectra vastly exceeds the range of a typical display device, the Fourier Magnitude calculation involves a logarithmic function.
Finally, a Fourier image is symmetric about the origin (u, v = 0, 0). If the origin is plotted at the upper left corner, the symmetry is more difficult to see than if the origin is at the center of the image. Therefore, in the Fourier magnitude image, the origin is shifted to the center of the raster array.
178页上的图73（Figure 6-31）
另外，182页上图75表明傅利叶变换与卷积模板处理方法的关联，也请注意。
Radar Imagery Enhancement
The nature of the surface phenomena involved in radar imaging is inherently different from that of visible/infrared (VIS/IR) images. When VIS/IR radiation strikes a surface it is either absorbed, reflected, or transmitted. The absorption is based on the molecular bonds in the (surface) material. Thus, this imagery provides information on the chemical composition of the target.
When radar microwaves strike a surface, they are reflected according to the physical and electrical properties of the surface, rather than the chemical composition. The strength of radar return is affected by slope, roughness, and vegetation cover. The conductivity of a target area is related to the porosity of the soil and its water content. Consequently, radar and VIS/IR data are complementary; they provide different information about the target area. An image in which these two data types are intelligently combined can present much more information than either image by itself.