CN1308657C - Method for measuring formation of seamless space stereomodel - Google Patents

Abstract

The invention discloses a method for generating a measurable seamless spatial three-dimensional model. The steps are as follows: sequentially number the aerial photos in the direction along the flight belt; ... slices to make orthophotos; using the digital terrain model, use double-numbered slices 2, 4, 6... to make auxiliary slices of orthophotos, and mosaic the digital orthophotos made by odd-numbered slices into a seamless area according to the ground coordinates , while recording the area range of each digital orthophoto image in the mosaic digital orthophoto image; point-to-point construction of a measurable seamless three-dimensional model. The three-dimensional model constructed by using the present invention breaks through the limitation of the stereo image pair range in photogrammetry, can be conveniently constructed and used without professional knowledge of photogrammetry, can truly restore and reproduce the three-dimensional terrain landscape model during photography, and can carry out Seamless three-dimensional roaming and browsing, and three-dimensional measurement and information collection can be performed on the model. It can be used for surveying and mapping, geology, forestry, electric power, urban planning, road and railway design and other related industries.

Description

A Method for Generating a Measurable Seamless Spatial Stereo Model

technical field

The invention belongs to the field of surveying and mapping science and technology, and relates to a method for generating a measurable seamless spatial three-dimensional model that is convenient to construct and use by using aerial images and a digital ground model (DEM).

Background technique

The nature we live in is a three-dimensional space. Most of the objects we see are three-dimensional. People are used to measuring an object with three parameters: length, width, and height. Most of the information in three-dimensional space is obtained through human eyes. As the saying goes, "Seeing is better than hearing a hundred times", which vividly describes the important role of the eyes, so the human eye is the most important organ for people to observe and perceive the world. Faced with the gorgeous and charming scenery of nature, people hope to find a new three-dimensional display method to reproduce the natural landscape realistically and three-dimensionally while admiring and sighing. Because traditional display methods are mostly two-dimensional projections of three-dimensional scenes, most of the stereoscopic depth information is lost, and people can only judge the depth level of objects in the scene by experience, which is very unreal. Through in-depth research on the human eye, people study the principle of stereoscopic vision of the human eye, thus making it possible to artificially realize stereoscopic display. Stereoscopic vision is extremely important to humans, and a world without stereoscopic levels would be unimaginable. People have produced stereoscopic vision effect through binocular observation. Normal people use their eyes to identify objects in three-dimensional space. When people watch a three-dimensional object, their eyes observe from slightly different angles on the left and right sides, so the optical images formed by the observed object on the retinas of the left and right eyes are slightly different. The so-called binocular parallax (Binocular Parallax) is also called physiological parallax. Parallax occurs mainly because there is a certain distance between the left and right eyes of a person, and the distance between the eyes of an adult is about 65mm. The generation of vision plays a very important role in the formation of stereo vision. When the optical images on the left and right retinas are transmitted to the optic nerve center of the brain at the same time, the left and right optical images with parallax are processed and fused by the optic nerve, and people can feel the three-dimensional level of the objects they see. This is artificial stereo vision.

In the field of photogrammetry, artificial stereo vision has been used for a long time. At the end of the 18th century, C. Pulfrich of the Jena Zeiss factory in Germany proposed the principle of stereoscopic observation, and in 1901 manufactured a stereoscopic coordinate measuring instrument, known in Germany as "the father of stereophotogrammetry" ". At the same time, it laid the foundation for stereo measurement for photogrammetry. Since then, the dual-image projection mapping, stereographic mapping instrument, analytical mapping instrument, and the full-digital digital mapping of the current digital photogrammetry workstation are all based on this principle.

The development of photogrammetry has a history of hundreds of years. It has experienced three stages of development: analog photogrammetry, analytical photogrammetry and digital photogrammetry. The spatial three-dimensional model of photography is restored through analog, analytical or digital methods. It is a main feature of photogrammetry to reproduce the features and topography of the area to be photographed, perform stereoscopic measurement on the model, and collect some basic geographic information. Since the establishment of the stereo model has to go through the complex process of photogrammetry of internal orientation, image pair orientation and absolute orientation, professional knowledge of photogrammetry is necessary. Therefore, this spatial model is basically established and used by photogrammetry workers. A patent for photogrammetry workers.

This traditional three-dimensional model composed of left and right images is the basis and core of photogrammetry. Since its scope is limited to a small area where the two images overlap and the establishment process is complicated, it is only used as a photogrammetry work. A medium of geographic data collection by the author, after the data collection work is completed, it is discarded and never used again. Since the three-dimensional model contains all the information of the terrain surface during photography, and the information retained after data collection is very limited, it is a very regrettable thing to lose the three-dimensional model in vain. If we can construct a large-scale and conveniently constructed spatial three-dimensional model, it will enable geologists, foresters, planners, engineers and other industries who use aerial photos without the need for complex knowledge background of photogrammetry. Under the premise of the environment, building and using the spatial three-dimensional model in a simple way will make a significant contribution to the efficient planning, development and protection of natural resources. At the same time, non-professionals can sit at home and browse the realistic three-dimensional terrain through the spatial model Landscape models can greatly increase the utilization value of aerial photography results.

Contents of the invention

The problem to be solved by the present invention is to provide a method for generating a measurable seamless spatial three-dimensional model that is convenient to construct and use in a wide range. It can be easily constructed and used without professional knowledge of photogrammetry, can truly restore and reproduce the 3D terrain landscape model during photography, can perform seamless three-dimensional roaming and browsing, and can perform 3D measurement and information collection on the model .

The technical solution provided by the present invention is: a method for generating a measurable seamless spatial three-dimensional model, the steps of which are as follows:

(1) Sequentially number the aerial photos in the direction along the flight strip;

(2) Use the digital ground model to make orthophoto images with single-numbered slices 1, 3, 5..., and the specific production steps are as follows:

i) Project the grid at a certain interval on the XY plane onto the digital elevation model according to the orthographic projection to obtain the coordinates of the four corners of the grid (X _i , Y _i , Z _i )

ii) By the collinear condition equation

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}$

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}$

In the formula: x, y, -f are the space coordinates of the image point;

f is the focal length of the aerial photograph;

x ₀ , y ₀ are the coordinates of the principal point of the image;

X, Y, Z are the object space coordinates of the ground point;

X _S , Y _S , Z _S are the object space coordinates of the shooting site;

a _i , b _i , c _i (i=1, 2, 3) form nine direction cosines for the three outer orientation elements of the photo;

Transform the coordinates of the four corners intersecting with the digital ground model after step i) projection into the photo coordinate system according to the collinear conditional equation to obtain the corresponding image point coordinates ( _xi , y _i );

iii) Calculate the corresponding scan coordinates from the image point coordinates through the internal orientation transformation parameters

$\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; I</span>}\\ \mathrm{<span\; class="notranslate">\; J</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="C0214775200105.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]$

In the formula, m ₁ , m ₂ , n ₁ , n ₂ , I ₀ , J ₀ are internal orientation parameters;

iv) For the pixels in each block, the corresponding scan coordinates are interpolated according to the bilinear polynomial

I＝a ₀ +a ₁ X+a ₂ Y+a ₃ XY

J＝b ₀ +b ₁ X+b ₂ Y+b ₃ XY

In the formula, I and J are scanning coordinates, X and Y are ground coordinates, a _i and b _i are bilinear transformation coefficients

v) Grayscale interpolation

The four corner points of each surface element are calculated according to the collinear equation, and then converted into scanning coordinates by the internal orientation parameters, and the scanning coordinates of each block are calculated point by point according to the bilinear transformation, and then gray The intensity interpolation method interpolates the gray value of each pixel;

vi) Gray scale assignment

Assign each interpolated gray value to each corrected pixel one by one;

After each point is processed, a digital orthophoto is formed;

(3) Utilize the digital ground model, and use the double-numbered sheets 2, 4, 6... to make auxiliary sheets of the orthophoto. The process of making is similar to the process of the orthophoto, except that step i) uses variable-angle projection to introduce the projection of the parallax method The function is used to project instead of the orthographic projection when making an orthophoto, and the projection function of the parallax method introduced by the variable-angle projection is $P_i=\frac{{\mathrm{BZ}}_i}{h-Z_i},$ In the formula, P _i is the parallax of each point, Z _i is the elevation value of each point, B is the photographic baseline of the stereo pair, and H is the flying height when photographing; the specific production steps are as follows:

From the grid on the XY plane, according to the projection function of the parallax method introduced by the variable-angle projection, the projection direction is parallel to the XZ plane to introduce the parallax, and according to the calculation formula of the intersection point between the variable-angle projection light and the surface of the digital ground model, the grid four The corner points are projected to the digital elevation model to obtain the intersection point (X' _i Y' _i Z' _i ) of the projection line and the digital ground model, and the following calculation steps are the same as steps ii to vi of making an orthophoto;

(4) Mosaic the digital orthophotos produced by the odd number of slices into a seamless area according to the ground coordinates, and record the area range of the mosaic digital orthophotos of each digital orthophoto at the same time;

(5) Point-to-point construction of measurable seamless three-dimensional models.

The basic principle of the present invention is based on the stereoscopic vision principle of the human eye, based on the digital orthophoto image, using the original aerial photo and the digital ground model (DEM), the digital orthophoto image is generated by the odd-numbered slices, and the parallax is passed through the even-numbered slices. The function introduces parallax to generate a stereoscopic orthophoto auxiliary sheet that matches the orthophoto. The digital orthoimage and the corresponding auxiliary image together form a stereoscopic orthophoto. After seamless mosaic of the digital orthophoto, use the stereo The construction algorithm of the model and the auxiliary film together form a large-scale seamless three-dimensional virtual and measurable landscape model with no upper and lower parallax.

The three-dimensional model constructed by using the present invention breaks through the limitation of the stereo image pair range in photogrammetry, can be conveniently constructed and used without professional knowledge of photogrammetry, can truly restore and reproduce the three-dimensional terrain landscape model during photography, and can carry out Seamless three-dimensional roaming and browsing, and three-dimensional measurement and information collection can be performed on the model. It can be used for surveying and mapping, geology, forestry, electric power, urban planning, road and railway design and other related industries.

Description of drawings

Figure 1 is the parallax diagram generated by two points on the ground at different heights relative to the reference plane during the original photography;

Figure 2 is the same introduced disparity map as the original disparity;

Figure 3 is an orthophoto map;

Figure 4 is an orthophoto auxiliary film;

Fig. 5 is a diagram for calculating the intersection point of projected rays with variable angles and DEM;

Figure 6 is the photo number;

Fig. 7 is a flowchart of the present invention.

Detailed ways

First introduce the variable angle projection of the present invention and introduce the parallax method below.

As shown in Figure 1 and Figure 2, Figure 1 shows the parallax produced by two points on the ground at different heights relative to the reference plane during the original photography, and Figure 2 shows the α ₁ and α used to produce the same parallax as the original photography α ₂ Projection rays at two different angles, from the geometric relationship in Figure 1 and Figure 2, we can know:

$\mathrm{<span\; class="notranslate">\; tg</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="B\; Z"\; filenames="C0214775200105.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="1"\; label="B\; Z"\; filenames="C0214775200105.png"\; state="\{\{state\}\}">\; </figure-callout>}}{{\mathrm{<span\; class="notranslate">\; </span>}}_{}}$ $\mathrm{<span\; class="notranslate">\; tg</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; B</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, B is the photography baseline of the stereo pair, and H is the flight height during photography (the same below). Therefore, in order to be consistent with the parallax of the original photography, variable-angle projection is used to introduce parallax. Figures 3 and 4 show The principle of parallax is introduced by changing the angle, and the projection is parallel to the XZ plane. According to different ground elevations, the angle of the projection light at each point is different.

As can be seen from the geometric relationship in Figure 3 and Figure 4, the projection function of the variable angle introduction parallax method is:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; BZ</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In the formula, P _i is the parallax of each point; Z _i is the elevation value of each point.

It can be seen from the above formula that the elevation of any point in the stereoscopic orthographic image with parallax introduced by variable-angle projection can be obtained by the following formula:

${\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Since the intersection point of the projection function and the surface of the digital terrain model (DEM) must be calculated when generating the auxiliary stereoscopic orthophoto image, the intersection point (X′ _i Y′ _i Z′ _i ) of the variable-angle projection ray and the DEM surface is shown in Fig. 5 Shown, the geometric relationship in the figure shows:

${\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}$

In the formula $k=\mathrm{the\; tan}\mathrm{\&alpha;}=\frac{B}{Z_i}$

It should be noted that when the topographical fluctuations are large or the DEM grid is dense, when actually solving the intersection point of the variable-angle projection ray and the DEM, it is necessary to first determine which DEM grid interval the parallel ray falls on, and then use the above The formula solves the intersection of parallel rays and DEM.

The projection function of introducing the parallax method with variable angles has been described in detail above, and the steps of using the projection function to generate a measurable seamless spatial three-dimensional model are introduced below (see Figure 7):

(1) Collect the original data (original image, DEM and photo parameters); then number the aerial photos sequentially (1, 2, 3, 4, 5, 6...) in the direction along the flight belt, as shown in the figure 6.

(2) Orthophoto production - digital orthophoto - seamless mosaic of orthophoto;

Use the digital terrain model DEM to make orthophoto images with single-numbered slices 1, 3, 5..., and the specific production steps are as follows:

i) Project the grid at a certain interval on the XY plane (generally equal to the grid size of the digital elevation model), and project it onto the grid digital elevation model according to the orthographic projection to obtain the coordinates of the four corners of the grid (X _i , Y _i , Z _i )

ii) By the collinear condition equation

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}$

In the formula: x, y, -f are the space coordinates of the image point;

f is the focal length of the aerial photograph;

x ₀ , y ₀ are the coordinates of the principal point of the image;

X, Y, Z are the object space coordinates of the ground point;

X _S , Y _S , Z _S are the object space coordinates of the shooting site;

a _i , b _i , c _i (i=1, 2, 3) form nine direction cosines for the three outer orientation elements of the photo;

Transform the coordinates of the four corners that intersect with the DEM after projection in step i) into the photo coordinate system according to the collinear condition equation to obtain the corresponding image point coordinates ( _xi , yi ₎ .

iii) Calculate the corresponding scan coordinates from the image point coordinates through the internal orientation transformation parameters

$\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; I</span>}\\ \mathrm{<span\; class="notranslate">\; J</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In the formula, m ₁ , m ₂ , n ₁ , n ₂ , I ₀ , J ₀ are internal orientation parameters;

iv) For the pixels in each block, the corresponding scan coordinates are interpolated according to the bilinear polynomial

I＝a ₀ +a ₁ X+a ₂ Y+a ₃ XY (7)

J＝b ₀ +b ₁ X+b ₂ Y+b ₃ XY

I, J are scan coordinates

X, Y are ground coordinates

a _i , b _i are bilinear transformation coefficients

v) Grayscale interpolation

The four corner points of each surface element are calculated according to the collinear equation, and then converted into scanning coordinates by the internal orientation parameters. For each block, the scanning coordinates are calculated point by point according to the bilinear transformation, and then gray The level interpolation method interpolates the gray value of each cell.

vi) Gray scale assignment

Assign each interpolated gray value to each corrected pixel one by one.

After each point is processed, a digital orthophoto is formed.

(3) Auxiliary image production - auxiliary film image;

Utilize the digital terrain model DEM, use double-number slices 2, 4, 6... to make auxiliary slices of the orthophoto, the process of making is similar to the process of the orthophoto, except that step i) use the projection function to project instead of making the orthophoto The specific production steps are as follows: from the grid on the XY plane, the parallax method is introduced according to the variable-angle projection, and the projection direction is parallel to the XZ plane to introduce parallax, and the calculation formula of the intersection point between the variable-angle projection light and the DEM surface is used. , project the four corners of the grid to the digital elevation model to obtain the intersection point (X′ _i Y′ _i Z′ _i ) of the projection line and the DEM. The following calculation steps are the same as steps ii to vi of making orthophotos.

(4) Mosaic the digital orthophotos produced by the odd number of slices into a seamless area according to the ground coordinates, and record the area range of the mosaic digital orthophotos of each digital orthophoto at the same time.

(5) Point-to-point construction of measurable seamless three-dimensional models.

Since there is no vertical parallax but only horizontal parallax between the digital orthophoto and the auxiliary film of the orthophoto, according to the basic principle of stereoscopic vision, as long as the same object is obtained from different positions, Two images can form stereoscopic vision. Since the digital orthophoto image and the corresponding auxiliary orthophoto image are from the left and right images when shooting, and the scales are the same, they meet the basic conditions for constructing stereoscopic vision, and there is no upper and lower parallax. Therefore, as long as the orthophoto is guaranteed Each point on the map corresponds point-by-point to the points on the orthophoto auxiliary sheet to form a three-dimensional geometric model. Because the digital orthophoto is seamless, the three-dimensional geometric model constructed based on the orthophoto is also seamless. The specific algorithm is as follows:

i) Take a point in the digital orthophoto, calculate the area of the digital orthophoto where the coordinates fall in the digital orthophoto before mosaic according to the ground of the point, find its photo number, and then find the corresponding orthophoto matching sheet .

ii) According to the ground coordinates of the point, find the corresponding point with the same name in the orthophoto matching sheet (that is, the point where the same object is imaged separately on the two images) to form a point pair in the three-dimensional model.

iii) After such point-by-point processing, it can be guaranteed that each point in the model is a stereoscopic point pair from the digital orthophoto and the digital orthophoto matching sheet, thereby forming a seamless stereoscopic model.

(6) Three-dimensional display (complementary color method or stroboscopic method) and measurement of three-dimensional models

Using liquid crystal glasses as a stereoscopic observation device (other methods can also be used), using the double buffer stereoscopic display mechanism of Open GL to send each stereoscopic point pair to the left and right display buffers respectively, and the 3D stereoscopic model can be observed through the liquid crystal glasses. After the parallax of each point is measured by three-dimensional mapping, the elevation information of each point can be calculated through the previous formula for calculating the elevation from the parallax. At the same time, its plane position can be obtained from the digital orthophoto.

Claims (1)

1. A method for generating a measurable seamless spatial three-dimensional model, the steps of which are as follows: (1) Sequentially number the aerial photos in the direction along the flight strip; (2) Use the digital ground model to make orthophoto images with single-numbered slices 1, 3, 5..., and the specific production steps are as follows: i) Project the grid at a certain interval on the XY plane onto the digital elevation model according to the orthographic projection to obtain the coordinates of the four corners of the grid (X _i , Y _i , Z _i ) ii) By the collinear condition equation $\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}$ $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>}$ In the formula: x, y, -f are the space coordinates of the image point; f is the focal length of the aerial photograph; x ₀ , y ₀ are the coordinates of the principal point of the image; X, Y, Z are the object space coordinates of the ground point; X _S , Y _S , Z _S are the object space coordinates of the shooting site; a _i , b _i , c _i (i=1, 2, 3) form nine direction cosines for the three outer orientation elements of the photo; Transform the coordinates of the four corners intersecting with the digital ground model after step i) projection into the photo coordinate system according to the collinear conditional equation to obtain the corresponding image point coordinates ( _xi , y _i ); iii) Calculate the corresponding scan coordinates from the image point coordinates through the internal orientation transformation parameters $\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; I</span>}\\ \mathrm{<span\; class="notranslate">\; J</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]$ In the formula, m ₁ , m ₂ , n ₁ , n ₂ , I ₀ , J ₀ are internal orientation parameters; iv) For the pixels in each block, the corresponding scan coordinates are interpolated according to the bilinear polynomial I＝a ₀ +a ₁ X+a ₂ Y+a ₃ XY J＝b ₀ +b ₁ X+b ₂ Y+b ₃ XY In the formula, I and J are scanning coordinates, X and Y are ground coordinates, a _i and b _i are bilinear transformation coefficients v) Grayscale interpolation The four corner points of each surface element are calculated according to the collinear equation, and then converted into scanning coordinates by the internal orientation parameters, and the scanning coordinates of each block are calculated point by point according to the bilinear transformation, and then gray The intensity interpolation method interpolates the gray value of each pixel; vi) Gray scale assignment Assign each interpolated gray value to each corrected pixel one by one; After each point is processed, a digital orthophoto is formed; (3) Utilize the digital ground model, and use double-numbered sheets 2, 4, 6... to make auxiliary sheets of the orthophoto. The process of making is similar to the process of the orthophoto, except that step i) introduces the projection of the parallax method by using variable-angle projection The function is used to project instead of the orthographic projection when making an orthophoto, and the projection function of the parallax method introduced by the variable-angle projection is $P_i=\frac{B{Z}_i}{h-Z_i},$ In the formula, P _i is the parallax of each point, Z _i is the elevation value of each point, B is the photographic baseline of the stereo pair, and H is the flying height when photographing; the specific production steps are as follows: From the grid on the XY plane, according to the projection function of the parallax method introduced by the above-mentioned variable-angle projection, the projection direction is parallel to the XZ plane to introduce parallax, and according to the calculation formula of the intersection point between the variable-angle projection light and the surface of the digital ground model, the grid Project the four corner points to the digital elevation model to obtain the intersection point (X′ _i Y′ _i Z′ _i ) of the projection line and the digital ground model, and the following calculation steps are the same as steps ii to vi of making orthophotos; (4) Mosaic the digital orthophotos produced by the odd number of slices into a seamless area according to the ground coordinates, and record the area range of the mosaic digital orthophotos of each digital orthophoto at the same time; (5) Point-to-point construction of measurable seamless three-dimensional models.

Images