1. Technical route of geometrically accurate correction
(1) Selection of control points (GCP)
Geometrically accurate correction is to utilize the ground control points (GCP) to geographically correct geometrical distortions of remotely sensed images caused by various factors. That is, the geometric distortion process of the original TM image is simulated by the GCP data, and a certain correspondence between the original distorted image space and the standard space used for geographic mapping (the standard space chosen this time is the Gauss-Krüger projection space) is established. This correspondence is used to transform all the pixels in the distorted image space into the corrected image space, thus realizing geometric fine correction. This transformation is usually realized by polynomial fitting.
(2) Steps of geometric fine correction in PCI image processing system
a. Establish the coordinate system of the original image and the corrected image;
b. Select the GCP (ground control point) control point, and establish the ground spatial point file;
c. Conduct the GCP localization accuracy analysis by RMS (root of mean square) value.
c. Check the positioning accuracy of GCP by RMS (root of mean square) value;
d. Establish the morphology model by using the control point pairs, and geometrically correct the original image by using the model;
e. Conduct the accuracy analysis of geometrically fine corrections, and find out the corresponding points by using the standard maps (1:100,000 topographic maps) to make the comparisons and calculations, and then find out the accuracy value.
The processing flow is shown in Figure 2.2.1.
Figure 2.2.1 Geometric Precision Correction Process Flow Diagram of Satellite Imagery in Henan Province
2. Technical Realization of Geometric Precision Correction
(1) Determine the projection mode, and establish the spatial coordinate system of the original image and the corrected image correction
The projection of the map means that the surface of the earth's ellipsoid is the same as that of the map plane between the point and the point (or the line and the line). Let the geographical coordinates of a point on the earth's surface is Q, λ. The corresponding point on the map surface of the right-angle coordinates for x,y, then the equations of the two families of plane curves on the surface of the earth's longitude and latitude are:
Q=F1(x,y)
λ=F2(x,y)
For x,y, respectively, we can get
x=f1(Q, λ)
y=f2(Q, λ)
This is a system of spatial coordinates of map projections, which correspond to points between the surface of the earth's ellipsoid and map plane. p>y=f2(Q, λ)
In order to align with the topographic map of our country and conform to the practice of domestic cartography, the projection we adopt this time is the Gauss-Krüger projection (TM projection) common in our country, and the geo-referenced coordinates are TM-EO15 coordinate system.
Where: E015 indicates the adoption of Krassovsky ellipsoid parameters.
(2) Establishment of GCP ground space point file of GCP selection principles
a. GCP in the whole region as far as possible uniform distribution;
b. Each 1:100000 topographic map selected GCP points more than 8, in order to meet the 1:2500000 standard map frame 20 to 32 control points of reasonable control accuracy;
c. For can not be determine the feature points are not selected, so as not to affect the entire error statistics.
(3) Steps of GCP Selection for Establishing GCP Ground Spatial Point File
a. Find out the corresponding points with the 1:100000 topographic map and the original image, and label them on the original image and the topographic map respectively;
b. Read out the geographic coordinates (Cartesian coordinate system) of the selected corresponding points from 1:100000 topographic map;
c. Input the coordinates into the computer, and establish a coordinate system at the same time. coordinates into the computer, and at the same time create a GCP spatial coordinate file.
(4) Control point distribution and accuracy checking
The purpose of selecting control points is to determine the coefficients of the polynomials that realize the transformation from the original map space to the corrected space through the least-squares regression analysis of these control points. Using the GCP point dispersion diagram, the distribution of the selected GCP points is observed. If the distribution of GCP points is not balanced, the corresponding GCP points should be increased appropriately until satisfied; at the same time, the RMS value is observed for several times, and if it exceeds the coordinate range of one image element, the GCP points with large errors are deleted and the RMS value is reduced to ensure the accuracy.
a. Calculation mode of RMS
Remote sensing - Comprehensive survey and evaluation of land resources in Henan Province
Equation: σx - RMS error value in row direction; σy - RMS error value in column direction; xi - row coordinates of the ith control point in the original image obtained after correction of the original image; yi - column coordinates of the ith control point in the original image obtained after correction of the original image; xiorg- - the row coordinates of the original image corresponding to xi; yiorg - the column coordinates of the original image corresponding to xi; n - the number of control points; k - the number of terms (i.e., degrees of freedom) of the correction model used.
b. Mathematical model used in general (Table 2.2.1)
x=a0+a1x+a2y+a3xy+a4x2+a5y2+a6x2y+a7xy2+a8x3+a9y3
y=b0+b1x+b2y+b3xy+b4x2+b5y2+b6x2y+ b7xy2+b8x3+b9y3
Where: x, y - original image spatial coordinates, i.e., xi,yi in the RMS error formula; x, y - corrected image spatial pixel coordinates; ai, bi -- coefficients to be determined.
By iteratively calculating the RMS Ernor values of all GCPs through the above expression, it is possible to determine which GCP point has a large error, and at the same time, it is possible to determine the RMS Error value that finally meets the requirements.
Table 2.2.1 The number of terms (degrees of freedom) of the geometric fine correction model of TM image in Henan Province
(5) Implementation of geometric fine correction of TM image in Henan Province
Mathematical simulation of the geometric distortion process of the original image is carried out by using the data of the GCP control points, and the basic correspondence between the space of the original distorted image and the standard space for geographic mapping (correction space) is established. The basic correspondence between the original distorted image space and the standard space for geographic mapping (correction space) is established. Using this correspondence, all the elements in the distortion space are converted into the correction image space, thus realizing the accurate correction of the original image geometry. The specific processing is realized in the following steps:
a. Geometric transformation of pixel coordinates
More than 500 control points have been selected for the whole area of Henan Province. As the PCI image processing software can only select a maximum of 255 control points when performing geometric correction, the control points with large errors are repeatedly discarded. The remaining 255 control points are analyzed by least squares regression to determine the coefficients of the correction mathematical model, and thus the correction mathematical model is determined. Then each pixel coordinate on the original image is geometrically transformed using the calibration mathematical model to generate the coordinates of the corrected image, so as to achieve the geometric transformation of the pixel coordinates.
The correction mathematical model formula is
Forward transformation formula:
x′ = 1.76e+04 +0.033x +0.006105y
y′ = 1.474e+05 -0.005874x -0.03283y
Backward transformation formula:
x′= 4.592e+05 +29.33x -5.454y
y′ = -4.408e+06 +5.248x +29.48y
b. Determination of image element gray value
The gray value of image elements on the corrected space is equal to that of the *** yoke point of the original image space, and the gray value is transformed by bidirectional linear interpolation. That is, the four neighboring image element points around the *** yoke point are used to derive from linear interpolation. This method can make the image continuous and high accuracy, shortcomings of this algorithm with the change of gray value will lead to blurring of the image.
c. Accuracy test
In the completed geometrically accurate correction of the image randomly selected points, compared with the 1:100000 topographic map coordinates of the same points for cross-checking. After calculation, the majority of points accuracy of 0.4 mm, a small number of points error greater than or equal to 0.8 mm, to meet the design accuracy requirements.