RU2714525C1 - Method for determining the mean square error of spatial coordinates of points of the analyzed object from image processing obtained by different cameras with arbitrary values of orientation elements - Google Patents

Abstract

FIELD: data processing.

SUBSTANCE: proposed invention relates to photogrammetry, geodesy, cartography and can be used for constructing topographic plans and maps, three-dimensional models of terrain, buildings and structures, solving engineering and geodesic tasks, for building measurement drawings of facades of buildings, determining volume of displaced soil for open pits and various drifts, etc. and is realized in practice using a computer program. Disclosed method of determining the mean square error of spatial coordinates of points of the analyzed object from processing of intermittent images obtained by different survey cameras with arbitrary values of elements of external and internal orientation, in which object overlapping images are obtained; determining the focal distance of the camera as an internal orientation element; determining coordinates of images of points of the analyzed object, obtaining values of mean square errors of determining coordinates of images of points of the analyzed object. Further, the mean square error of the spatial coordinates of the points of the analyzed object is determined by taking the value of the focal distance of the camera and the coordinates of the image of the points on the image and taking the values of the mean square errors for the coordinates of the images of the points of the analyzed object on the image. Overlapping object images are obtained using different camera cameras; determining focal distance of different camera chambers; spatial coordinates of points of the analyzed object are determined by one or more pairs of images obtained by different survey cameras; determining linear and angular elements of external orientation of different survey cameras, having any values in spatial coordinate system, in which coordinates of points of analyzed object are determined. To determine the standard errors of spatial coordinates of the points of the analyzed object, the value of the focal distance of at least two survey cameras and the coordinates of the images of the points on two images are taken. When determining the mean square error of points of the analyzed object, linear and angular elements of external orientation of survey cameras and mean square errors with which linear and angular elements of external orientation of survey cameras are determined are used. When determining the mean square error of spatial coordinates of the points of the analyzed object, the coordinates of the images of the points on each picture and the mean square error with which each coordinate of the image of the points of the analyzed object is determined on each image are used. Determining the parallactical coefficient of the method of direct photogrammetric resection, taking into account the inclination of the survey basis relative to all three axes of the spatial coordinate system; determining parameters of influence of linear and angular elements of external orientation of a pair of images, elements of internal orientation of survey cameras, coordinates of images of points of the analyzed object, measured on a pair of photographs, on accuracy of determining spatial coordinates of points of the analyzed object; determining square of mean square error separately for each element of external and internal orientation of camera cameras, for each coordinate of images of points of analyzed object, measured on a pair of photographs, taking into account error, introduced by each element of external and internal orientation and each measured coordinate; determining total square of mean square error for each of three spatial coordinates of points of analyzed object, taking into account effect of mean square errors, with which elements of external and internal orientation and coordinates of images of points of the analyzed object, measured on a pair of images, are determined, and a mean square error of spatial coordinates of points of the analyzed object is determined.

EFFECT: high reliability of determining the mean square error of spatial coordinates of points of the analyzed object from image processing.

1 cl, 5 dwg, 13 tbl

Description

The present invention relates to the field of photogrammetry, geodesy, cartography and can be used to build topographic plans and maps, three-dimensional models of terrain, buildings and structures, solve engineering and geodetic problems, determine the volume of displaced soil for quarries and various mine workings, etc., applicable to images obtained by a shooting camera, the carrier of which is any aircraft: manned aircraft, artificial Earth satellite (AES), spacecraft (SC), unmanned aerial vehicle The military unit (UAV), etc., is applicable to images obtained by several UAVs (UAV group), is universal and can be used for military equipment.

Further, the applicant provides clarifications that are necessary to facilitate an unambiguous understanding of the essence of the claimed materials and to exclude contradictions and / or disputed interpretations when performing substantive examination.

The root-mean-square error is in probability theory and statistics the most common indicator of the dispersion of values of a random variable relative to its mathematical expectation [https: // ru-wiki. RMS error]. To simplify the perception of the text by the applicant in the context of the present description also uses the sign "error" to denote the sign "mean square error".

Spatial coordinates - in the context of the present description, by spatial coordinates, the applicant means rectangular (Cartesian) coordinates.

Image - under the sign image in the context of the present description, the applicant means photographic images obtained using a photographic camera (analog, digital).

A single image is a single image (image) obtained by a camera.

A couple of pictures - in the context of the present description, this feature is synonymous with the “stereopair” feature used in a number of sources. Indicates two images that depict the same object under investigation.

Overlapping images are two or more images that depict the same object under investigation.

The shooting basis is a straight line segment connecting the design centers of two shooting cameras, i.e. a straight line segment connecting the centers of optical design of images forming a stereo pair.

Longitudinal parallax - the abscissa difference of the corresponding points of the images (pictures) that make up the stereo pair, i.e. the difference of coordinates x ₁ and x _{2 of the} image of the point of the investigated object in the first and second picture of a pair of images (stereo pairs).

Image processing - in the context of the present description, by the indicated attribute, the applicant refers to the process of acting on a material object, namely, on an analog or digital image (snapshot) using material means, namely, using any measuring tool or in manual mode, either in automatic mode or in semi-automatic mode, that is, using partially manual, partially automatic mode.

The claimed technical solution provides the opportunity to increase the reliability of determining the mean square error (error) of the spatial coordinates of any points of the investigated object (hereinafter - the object) from processing two or more overlapping, randomly located images obtained by different shooting cameras.

Attention should be paid to the relevance of solving this problem as a whole for economic and other activities, because errors in the coordinates on the basis of which topographic maps, cadastral maps, models of buildings and structures, etc. are created, directly determine the quality of the results of work (products) created on the basis of these coordinates. The use of false coordinates (that is, coordinates for which errors exceed acceptable values or coordinates for which errors are not defined) can lead to emergency and even catastrophic situations and consequences, for example, damage to underground utilities (gas pipelines, oil pipelines, electrical cables , water supply, sewage, metro lines) in the process of construction, repair, reconstruction, etc. It should be taken into account that factual errors sometimes exceed the permissible error by several times. For example, in the inventory with the required accuracy of 10 cm for the coordinates of the characteristic points of the boundaries of real estate in settlements (Order of the Ministry of Economic Development of Russia dated 01.03.2016 No. 90 [1]), the actual error sometimes reaches 60-80 cm and even more. Thus, improving the reliability of determining errors is an urgent problem in solving national economic problems, various types of activities and the implementation of various works.

In addition, increasing the reliability of determining the mean square error (error), with which the spatial coordinates of the terrain points (structures) are determined, allows us to establish the compliance of the obtained materials with the requirements of GOSTs, instructions, norms and rules used in geodesy, cartography, engineering and geodetic surveys, cadastre , for example, GOST R 56905-2016 “Conducting measurement and engineering-geodetic works on objects of cultural heritage. General requirements".

The objective of the claimed technical solution is to increase the reliability of determining the mean square error (error) in determining the spatial coordinates of any point of the object. The mean square error values are determined from the processing of overlapping images of the object (by measuring the coordinates of the images of any point in the images) for any values of the elements of the external and internal orientation of the shooting cameras necessary to determine the spatial coordinates of the points of the object, depending on the errors with which linear and angular elements of external and internal orientation of filming cameras, coordinates of image points.

A feature of the claimed technical solution is that the carriers of the shooting cameras, for example, a UAV group (several UAVs performing shooting) can be arbitrarily located in space relative to the axes of a rectangular spatial coordinate system in which the coordinates of the points of the object under study are determined, and relative to each other, when this overlapping image can be obtained with different technical characteristics of the shooting cameras.

The applicant has analyzed the state of the art in the indicated field of technology on Russian and foreign patent databases on the use of overlapping images (pictures) to determine the spatial coordinates of objects in order to increase the reliability of determining the error in the values of the spatial coordinates of the points of the studied object.

The analysis of the investigated prior art, performed by the applicant as a whole in the indicated technical field, allows us to conclude that the problem of increasing the reliability of determining the error of spatial coordinates obtained from processing overlapping images arbitrarily located relative to the axes of a rectangular coordinate system in which the coordinates are determined points of the investigated object, on the filing date of this application is very relevant and is not allowed to the essence in the proper degree.

From the investigated prior art, the inventors of patent No. 2681836 “A method for determining the spatial coordinates and angular position of a remote object” [2], the essence of which is a method for determining the spatial coordinates and angular position of a remote object using range-finding stations, which consists in using at least three range-finding stations, are identified stations spatially located at some distance from each other and from the object, within the line of sight of the object, while the coordinates of the range-finding stations of nations is determined in one of the selected coordinate systems, while the rangefinder stations point their rangefinders to the object and determine the distance to the remote object, after that the coordinates of the object are determined by the intersection of the spheres with the centers in three or more rangefinder stations, preliminary coordinates of the position of the object are calculated, characterized in that they perform the orientation of the ranging stations in sequential order, measure the distances between them, calculate and set the exact coordinate system, determine the coordinates of using the GLONASS / GPS equipment in the all-terrestrial coordinate system, determine the parameters of the transition from the all-terrestrial coordinate system to the exact coordinate system, determine the approximate coordinates of the unmanned aerial vehicle in the exact coordinate system specified by the rangefinding stations using the transition parameters from the all-terrestrial coordinate system into the exact coordinate system, calculate the horizontal and vertical pointing angles for each of the ranging stations d, point the rangefinder stations to the object, measure the distance from the rangefinder station to the reflectors mounted on the object, then based on the measured distances to each individual reflector, determine the coordinates of each reflector using the method of intersecting spheres from three or more rangefinder stations, determine the exact coordinates of an unmanned aerial vehicle apparatus in the exact coordinate system, as the average value between the coordinates of all reflectors, calculate the angular position of the unmanned aerial vehicle, i.e. e. determine the angles of roll, yaw, pitch, respectively, based on the previously calculated coordinates of the reflectors, then calculate in post-processing mode or in real time the spatial coordinates of the points on the ground according to the measured coordinates of their images obtained by the camera mounted on an unmanned aerial vehicle using the coordinates of an unmanned aerial vehicle apparatus and angular position of an unmanned aerial vehicle in the exact coordinate system calculated by the claimed method using integrated software package.

Otherwise, the essence of the known technical solution is to determine the spatial and angular position of the UAV (remote object) for determining in the post-processing mode (that is, after performing aerial photography) or in real time the spatial coordinates of the points of the object under study according to the measured coordinates of their images obtained by a shooting camera installed on the UAV, while this does not require the creation of reference points on the object under study. The accuracy of determining the spatial and angular position of the UAV (that is, elements of external orientation) in the known technical solution is high and is: 0.002-0.005 m (2-5 mm) for the spatial coordinates of the UAV; 1 ′ (60 ″ arc seconds) and better (in real time) for the angular position of the UAV. Therefore, in the claimed technical solution, the accuracy of determining the spatial coordinates of the points of the object under study from the images obtained from the UAV will also be high (millimeter, centimeter).

A disadvantage of the known invention in comparison with the claimed technical solution is that in the known invention the accuracy of determining the spatial coordinates of the points of the studied object, although it is high, however, to determine the error in determining the coordinates, the method used only for the case when the pictures (images) are horizontal (angles exterior orientation equal to zero or not exceed 3 °). In the claimed technical solution, it is possible to determine the error (error) with which the coordinates of the points of the object under study are determined by their overlapping images (pictures) obtained by shooting cameras having any values of linear and angular elements of external orientation.

That is, at the filing date of this application, there is an urgent problem of determining the errors of spatial coordinates obtained from processing overlapping images (images) having arbitrary, any spatial and angular position, obtained by different shooting cameras installed on UAVs, satellites, satellite, etc. P.

Further, the applicant provides information on the methods that are used to determine the errors with which the spatial coordinates of the points of the object are determined from processing their images.

From the studied prior art, it is well known that when performing ground surveying, aerial photography, and space shooting of an object of research, images are formed in a certain order, resulting in overlapping images of the object. Based on the measurement of images - according to the coordinates of the points of the object in the image, the spatial coordinates of these points are calculated in a rectangular coordinate system (Mikhailov A.P., Chibunichev A.G. Photogrammetry - M.: MIIGAiK Publishing House, 2016. 218-222s.) [3], (Nazarov A.S. Photogrammetry. - Minsk: TerraSystems, 2010, p. 161-167) [4].

The ability to measure a large number of points on an image allows you to build a digital terrain model, a digital terrain model, and a three-dimensional object model (3D model).

It is also well known that the calculation of the spatial coordinates of the points of the investigated object according to the coordinates of their images is carried out by direct photogrammetric notching (Figure 1). To obtain the spatial coordinates of the points of the object under study by direct photogrammetric notching, it is necessary to have the values of the elements of the internal and external orientation of the images (images) (Nazarov AS, Photogrammetry. Minsk: TerraSystems, 2010, pp. 163-165) [4].

Elements of internal orientation - focal length, coordinates of the main point of the camera (image) (Limonov AN, Gavrilova LA Photogrammetry and remote sensing. - M .: Academic project. 2016. - from 122-123) [5].

Elements of external orientation - the spatial coordinates of the center of the projection and three image orientation angles (Limonov AN, Gavrilova LA Photogrammetry and remote sensing. - M.: Academic project. 2016. - p. 126-127) [5].

From the investigated prior art, the applicant has identified methods for determining the errors of the spatial coordinates of the points of the studied object obtained from image processing.

So, there is a known method in which the determination of errors with which the spatial coordinates of the points of the object under study are obtained is carried out on the basis of the values of the spatial coordinates of the reference points located on the object of study. An anchor point is a point whose geodetic coordinates are known and which is the starting point for photogrammetric constructions (Phototopography. Terms and definitions. GOST R 52369-2005, p.5) [6]. Some reference points not directly used in determining the spatial coordinates of the set of points of the object under study from image processing (hereinafter referred to as control points) are used to determine the errors with which the spatial coordinates of the set of points are obtained. At the end of the calculation, the values of the spatial coordinates of the control points are compared with the spatial coordinates of these control points obtained from image processing (A manual for photogrammetry, ed. Red V.I. Korableva. - M .: Nedra. 1970. p. 183) [7] . Control points outline at least three on a stereopair (Krasnopevtsev B.V. Photogrammetry. - M .: UPP "Reprography" MIIGAiK, 2008. p 93.) [8].

The known method is applied in practice and is illuminated, in particular, in the source (Instructions for photogrammetric work when creating digital topographic maps and plans. - M .: TsNIIGAiK, 2002. - 100 p. 31-32) [9].

The spatial coordinates of the control points are determined by geodetic measurements using geodetic equipment: GLONASS / GPS receivers, electronic total stations (Fig. 2, Fig. 3).

The main disadvantages of this method are:

1. The error in determining the spatial coordinates is not reliable, since the coordinates of the image of the point are not used in determining the error, namely, the error in determining the spatial coordinates established by the control points corresponds to the position of the control points, and the error in determining the spatial coordinates for all other points of the image is taken to be the error established only on control points.

2. The need to perform additional measurements at the facility before or after aerial photography using special geodetic equipment.

3. The inability in some cases to place control points on the test object in the required quantity and in the necessary areas of the test object due to special conditions, for example, due to the location of obstructing obstacles in the immediate vicinity of the object (fence, trees, building, etc. .), due to conditions dangerous to human activities.

4. The calculation of the error with which the spatial coordinates of the points of the studied object are determined is possible only after aerial photography has been performed.

The known method (Zharova N.E., Chibunichev A.G. Analysis of the accuracy of determining the coordinates of terrain points when using "random" stereo pairs of satellite images. News of higher educational institutions. Geodesy and aerial photography, No. 5, 2017, pp. 79-86.) [10], in which the use of "random" stereo pairs of satellite images is considered to determine the spatial coordinates of the points of the object under study. In the known method, “random stereopair” means two mono-images of the same territory (object) obtained by different space-based shooting systems, i.e. with satellite. The stereo pair is characterized by the following angles: convergence angle - C; asymmetry angle As; angle BIE - the height of the bisector of the angle of convergence (Fig. 4). The given angles are not angular elements of exterior orientation. When performing stereo shooting, the following tolerances on angular parameters are used: С - 30 ° ÷ 60 °; As <20 °; BIE - 60 ° ÷ 90 °. The selection of mono images for compiling “random stereopairs” is carried out subject to the optimal values for C, As, and BIE.

The disadvantages of this method is that the determination of the error with which the spatial coordinates of the points of the studied object are determined is based on the values of the spatial coordinates of the reference (control) points located on the object of research, in contrast to the claimed technical solution, in which the determination of the error (mean square error ) is carried out according to the elements of external and internal orientation and according to the errors with which they are determined, as well as according to the coordinates of the points in the image SRI (pictured) and errors with which they are identified.

The closest in essence and coinciding features with the claimed technical solution, chosen by the applicant as a prototype, is a method in which the determination of the spatial coordinate error is considered for a pair of planned images for which the tilt angles of the images do not exceed 3 ((Krasnopevtsev B.V. Photogrammetry . - M .: UPP "Reprography" MIIGAiK, 2008. from 77-79.) [8]. The essence of the prototype is a method in which the determination of errors in determining coordinates with respect to a pair of planned images is considered in which the angle of inclination of the images does not exceed 3 °, and the photographing basis is almost horizontal and directed along one of the axes of the coordinate system in which the coordinates of the object under study are determined. Such a coordinate axis, as a rule, is the X axis. To determine the error in determining spatial coordinates points of the object under study for a pair of images, the relationship formulas of the coordinates of the object points and the coordinates of their images on a pair of images are used for the ideal shooting case, when all three corner elements are oriented ia are zero. In the known method, errors in determining coordinates are determined by errors in measuring the basis of shooting, errors in measuring the coordinates of the image of a point on the left (first) picture, errors in measuring longitudinal parallax and are calculated by the formulas 1), 2), 3):

where:

M _X , M _Y , M _Z - errors (errors) in determining the spatial coordinates of X, Y, Z;

f is the focal length of the camera;

In - the basis of shooting in the scale of the image;

H - shooting height (distance to the subject);

x ₁ , y ₁ - coordinates of the image of the point in the first (left) image;

m _x1 , m _y1 - error (error) in measuring the coordinates x, y of the point image;

m _p - error (error) of the longitudinal parallax measurement.

In the prototype, it is noted that the values of the errors obtained by this method will be overestimated, since the effects of other sources of errors are not taken into account. As a result, for real images, the errors (errors) in determining the spatial coordinates will be greater, i.e. the accuracy of determining the coordinates will be lower.

The disadvantages of the prototype is the lack of reliability of determining the mean square error (error) of the spatial coordinates of the points of the investigated object from image processing, because:

- there is no way to determine the errors of the spatial coordinates of the points of the investigated object from the processing of overlapping images obtained by different shooting cameras, as in the known method using the same shooting camera;

- linear and angular elements of exterior orientation that have any values in the spatial coordinate system in which the coordinates of the points of the object are determined are not taken into account;

- the value of the focal length of only one shooting camera and the coordinates of the images of the points in only one image are taken into account;

- errors in measuring the coordinates of the image for each image of a pair of images are not taken into account, errors in measuring the coordinates of the image are assumed to be the same for the first and second images;

- errors of linear and angular elements of the exterior orientation of the survey cameras and errors with which linear and angular elements of the external orientation of the survey cameras are determined are not taken into account;

- errors of elements of interior orientation of the shooting camera are not taken into account - mean square errors with which focal lengths and coordinates of the main points of the shooting camera (image) are determined;

- the slope of the survey basis is not taken into account relative to all three axes of the spatial coordinate system, in which the coordinates of the points of the object under study are determined, i.e. the angular position of the survey basis relative to the axes of the rectangular coordinate system is not taken into account.

The claimed technical solution is aimed at eliminating the disadvantages of the prototype and at implementing the following technical results, namely, increasing the reliability of determining the mean square error (error) of the spatial coordinates of the points of the object under study from image processing, while:

- Images obtained by different shooting cameras;

- linear and angular elements of exterior orientation are taken into account, having any values in the spatial coordinate system in which the coordinates of the points of the object are determined;

- take into account the value of the focal length of different shooting cameras and the coordinates of the image points on two pictures of the stereo pair;

- the errors of measuring the coordinates of the image of points on a pair of images of a stereo pair are taken into account;

- the errors of linear and angular elements of the external orientation of different survey cameras and the errors with which the linear and angular elements of the external orientation of the survey cameras are taken into account;

- the errors of the elements of the interior orientation of the shooting cameras are taken into account - the mean square errors with which the focal lengths and coordinates of the main points of the shooting cameras are determined;

- the slope of the survey basis is taken into account relative to all three axes of the spatial coordinate system, in which the coordinates of the points of the object under study are determined, i.e. the angular position of the survey basis with respect to the axes of a rectangular coordinate system is taken into account.

The essence of the claimed invention is a method for determining the mean square error of the spatial coordinates of the points of the studied object from the processing of intermittent images obtained by different shooting cameras with arbitrary values of the elements of external and internal orientation, which consists in the fact that receive overlapping images of the object; determine the focal length of the camera as an element of interior orientation; determine the coordinates of the images of the points of the investigated object, get the mean square errors of determining the coordinates of the images of the points of the studied object; next, the mean square error of the spatial coordinates of the points of the object under study is determined, for which they take the value of the focal length of the camera and the coordinates of the image points on the image; then take the mean square errors for the coordinates of the images of the points of the investigated object in the picture, characterized in that the overlapping images of the object are obtained using different shooting cameras; determine the focal length of different shooting cameras; the spatial coordinates of the points of the investigated object are determined by one or more pairs of images obtained by different shooting cameras; determine linear and angular elements of the external orientation of different survey cameras having any values in the spatial coordinate system in which the coordinates of the points of the object under study are determined; to determine the mean square errors of the spatial coordinates of the points of the object under study, take the value of the focal length of at least two shooting cameras and the coordinates of the images of the points in two images; in addition to the focal length value of the shooting cameras, the coordinates of the main points of at least two shooting cameras and the mean square errors with which the focal lengths and coordinates of the main points of the shooting cameras are used; when determining the mean square error of the points of the investigated object, linear and angular elements of the exterior orientation of the survey cameras and the mean square errors with which the linear and angular elements of the exterior orientation of the survey cameras are used are used; when determining the mean square error of the spatial coordinates of the points of the object under study, use the coordinates of the images of the points in each image and the mean square error with which each image coordinate of the points of the object under study in each image is determined; determine the parallactic coefficient of the direct photogrammetric notching method, taking into account the slope of the survey basis relative to all three axes of the spatial coordinate system, in which the coordinates of the points of the object under study are determined; determine the parameters of the influence of linear and angular elements of the external orientation of the pair of images, the elements of the internal orientation of the shooting cameras, the coordinates of the images of the points of the investigated object, measured on a pair of images, on the accuracy of determining the spatial coordinates of the points of the studied object; determine the square of the mean square error separately for each element of the external and internal orientation of the shooting cameras, for each coordinate of the images of the points of the investigated object, measured on a pair of images, taking into account the error that each element of external and internal orientation and each measured coordinate makes; determining the total square of the mean square error for each of the three spatial coordinates of the points of the object under study, taking into account the influence of the mean square errors with which the elements of external and internal orientation and image coordinates of the points of the object under study, measured on a pair of images, are determined; determine the mean square error of the spatial coordinates of the points of the investigated object; when the number of pairs of images is more than one, the mean square errors of the points of the studied object are determined as the statistical average for the number of pairs of pictures used to determine the coordinates of the points of the studied object.

The claimed technical solution is illustrated in Fig.1 - Fig.17.

In FIG. 1 shows a General view of the position of a pair (2) of images when determining the spatial coordinates of the points of the object by direct photogrammetric notching, where:

OXYZ - a system of rectangular coordinates in which the spatial of the object under study is determined;

I is the point of the object;

P ₁ - the first (left) picture of a pair of pictures;

P ₂ - the second (right) picture of a pair of pictures;

S ₁ - the center of the projection of the image P ₁ ;

S ₂ - the center of the projection of the image P ₂ ;

i ₁ - image of point I in the image P ₁ ;

i ₂ is the image of point I in the image P ₂ ;

- вектор положения точки объекта в системе координат OXYZ;

- the position vector of the point of the object in the coordinate system OXYZ;

- векторы, определяющие соответственно положение центра проекции S₁ и S₂ в системе координат OXYZ;

- vectors that respectively determine the position of the center of the projection S ₁ and S ₂ in the coordinate system OXYZ;

- вектор базиса съемки;

- shooting basis vector;

o ₁ x ₁ y ₁ - a flat coordinate system for measuring images in the image P ₁ ;

o ₂ x ₂ y ₂ - a flat coordinate system for measuring images in the image P ₂ ;

- пространственная система координат с началом в центре проекции снимка Р₁ оси

, которой параллельны соответственно осям o₁x₁ o₁y₁ плоской системы координат снимка Р₁, а ось

является продолжением оптической оси съемочной камеры;

- spatial coordinate system with the beginning in the center of the projection of the image P ₁ axis

, which are parallel to the axes o ₁ x ₁ o ₁ y ₁ respectively _{of the} plane coordinate system of the image P ₁ , and the axis

is a continuation of the optical axis of the camera;

- пространственная система координат с началом в центре проекции снимка Р₂ оси

, которой параллельны соответственно осям o₂x₂ o₂y₂ плоской системы координат снимка Р₂, а ось

является продолжением оптической оси съемочной камеры;

- spatial coordinate system with the beginning in the center of the projection of the image of the P ₂ axis

which are parallel to the axes o ₂ x ₂ o ₂ y ₂ respectively of the planar coordinate system of the image P ₂ , and the axis

is a continuation of the optical axis of the camera;

S ₁ X ₁ Y ₁ Z ₁ - coordinate system with the origin in the center of the projection of the image P ₁ , the axes of which are parallel to the axes of the coordinate system OXYZ;

S ₂ X ₂ Y ₂ Z ₂ —the coordinate system with the origin in the center of the projection of the image P ₂ , the axes of which are parallel to the axes of the OXYZ coordinate system;

- вектор изображения точки I в системе координат

снимка Р₁

;

is the image vector of point I in the coordinate system

snapshot P ₁

;

- вектор изображения точки I в системе координат

снимка Р₂

;

is the image vector of point I in the coordinate system

snapshot P ₂

;

- векторы, определяющие положение точки I соответственно в системе координат S₁X₁Y₁Z₁ и S₂X₂Y₂Z₂ .

- vectors that determine the position of point I, respectively, in the coordinate system S ₁ X ₁ Y ₁ Z ₁ and S ₂ X ₂ Y ₂ Z ₂ .

Figure 2 shows a General view of the position of reference points on the object when constructing topographic plans and solving engineering and geodetic problems. The numbers from 2-1 to 2-9 denote reference points on the terrain, T1 is an electronic total station (theodolite), XYZ is the coordinate system for the object.

Figure 3 shows a General view of the position of reference points on the object (building, structure) when solving applied engineering and geodetic problems. The numbers from 3-1 to 3-9 indicate the reference points on the object, T1, T2 - an electronic total station (theodolite) - is shown at different points in the terrain, XYZ is the coordinate system for the object.

Figure 4 shows a General view of the position of a pair (2) of images (pictures) for the case of satellite imagery, where:

P ₁ - the first (left) picture of a pair of pictures;

P ₂ - the second (right) picture of a pair of pictures;

B is the basis of the survey;

L ₁ - the left projecting beam;

L ₂ - the right projecting beam;

M is a point on the surface of the Earth;

MO - perpendicular to the basis of the survey;

C is the angle of convergence;

And _S is the angle of asymmetry;

V is the angle of inclination.

Figure 5 shows Table 1 with formulas for calculating the coefficients A _i , taking into account the influence of the initial parameters.

Figure 6 shows Table 2 with formulas for calculating the coefficients B _i , taking into account the influence of the initial parameters.

Figure 7 shows Table 3 with formulas for calculating the coefficients E _i , taking into account the influence of the initial parameters.

, κ; Ω, ω, J).Figure 8 shows Table 4 with formulas for calculating the direction cosines for three systems of exterior orientation angles (α, ω, χ; ϕ,

, κ; Ω, ω, J).

для второго снимка пары снимков. Для определения с_tk используются угловые элементы ориентирования и направляющие косинусы а_qs первого снимка, для определения

используются угловые элементы ориентирования и направляющие косинусы а_qs (т.е.

) второго снимка. Figure 9 shows Table 5 with formulas for calculating the coefficients with_tk for the first shot and

 for the second shot of a pair of shots. To determine with_tkused angular orientation elements and guide cosines a_qs first shot to determine

used angular orientation elements and guide cosines a_qs(those.

) second shot.

Figure 10 shows Table 6 with formulas for calculating the values of L _ij , K _ij with j = 1.

Figure 11 shows Table 7 with formulas for calculating the values of L _ij , K _ij with j = 2.

12 shows Table 8 with formulas for calculating the values of L _ij , K _ij at j = 3.

On Fig shows a General view of the position of three randomly located overlapping images, where:

OXYZ - a system of rectangular coordinates in which the spatial of the object under study is determined;

A is the point of the object;

R₁, R₂, R₃- first, second and third shot;

S ₁ - the center of the projection of the image P ₁ ;

S ₂ - the center of the projection of the image P ₂ ;

S ₃ - the center of the projection of the image P ₃ ;

a ₁ , a ₂ , a ₃ - image of point A in the corresponding image P ₁ , P ₂ , P ₃ ;

In ₁ - shooting basis for a pair of pictures P ₁ and P ₂ ;

В ₂ - shooting basis for a pair of images Р ₂ and Р ₃ ;

In ₃ - shooting basis for a pair of pictures P ₁ and P ₃ .

On Fig shows Table 9, Table 10 with the results of the mean square error of determining the coordinates of the point of the object. Aerial photography using the same camera. Table 9 is an ideal shooting case, Table 10 is an arbitrary shooting case.

On Fig shows Table 11 with the results of the mean square error of determining the coordinates of the point of the object. Aerial photography using different shooting cameras. Arbitrary shooting event.

In FIG. Table 12 shows the results of the mean square error of determining the coordinates of an object point. Space imagery using the same camera. Arbitrary shooting event.

In FIG. Figure 17 shows Table 13 with the results of the mean square error of determining the coordinates of the point of the object. Space imagery using different filming cameras. Arbitrary shooting event.

Further, the applicant provides a detailed description of the claimed method.

The initial parameters of the claimed method are:

1. Elements of the interior orientation of the shooting camera (focal length and coordinates of the main point), the mean square error (error) with which they are determined. Elements of internal orientation with the necessary accuracy are determined by calibrating the survey camera (Limonov AN, Gavrilova LA Photogrammetry and remote sensing. -M.: Academic project. 2016. - from 122-123) [4].

2. Elements of the exterior orientation of the shooting camera (three coordinates of the center of the projection of the image, three Euler angles), the error with which they are determined relative to the axes of the spatial coordinate system, in which the coordinates of the points of the object are determined. Elements of the exterior orientation of the camera (images) are determined using on-board navigation equipment (satellite-GPS / GLONASS, inertial-IMU) of the aircraft (camera carrier) or in another way, for example, by the method described in patent No. 2681836 “Method for determining spatial coordinates and angular position of a distant object ”[2].

3. The coordinates of the points of the studied object in the images and the error with which they are determined are determined by the results of measurements in the images.

Below, the applicant provides clarifications on the formulas used in the context of the present description used to implement the claimed method.

The claimed method is implemented relative to the center of the projection of the left picture of a pair of pictures (S ₁ ). The method uses the parallactic coefficient N _I , calculated by the formula that takes into account all three components of the survey basis (Mikhailov A.P., Chibunichev A.G. Photogrammetry - M: MIIGAiK Publishing House, 2016. C & 51-53) [3] .

The error with which the spatial coordinates X _I , Y _I , Z _{I of the} point I of the object under study, namely, the root mean square error, is determined by solving the direct problem of the theory of errors. The determination of errors M _X , M _Y , M _Z for point I is carried out according to the basic formulas 2), 3), 4) developed by the applicants:

Where:

A _i , B _i , E _i — coefficients that take into account the influence of model elements, namely, elements of external orientation, elements of internal orientation of shooting cameras and image coordinates on a pair of images, are calculated each for a point measured on a pair of images;

- погрешности определения углов внешнего ориентирования первого и второго снимка пары снимков, а именно углов ориентирования съемочной камеры на момент фотографирования в точке S₁ и S₂;

- errors in determining the external orientation angles of the first and second pictures of a pair of pictures, namely, the orientation angles of the shooting camera at the time of photographing at the point S ₁ and S ₂ ;

- суммарные погрешности линейных элементов внешнего ориентирования для пары снимков, а именно погрешности определения базиса съемки, которые вычисляются по формулам 7):

- total errors of linear elements of exterior orientation for a pair of images, namely, errors in determining the basis of shooting, which are calculated by formulas 7):

where:

- погрешности, с которыми определены элементы внутреннего ориентирования первой и второй съемочной камеры;

- errors with which elements of the internal orientation of the first and second film camera are determined;

- погрешности измерения координат изображений точки на первом и втором снимках пары снимков;

- errors in measuring the coordinates of the images of the point in the first and second pictures of a pair of pictures;

The coefficients A _i , B _i , E _i determine for each point measured on a pair of images. The determination of the coefficients A _i , B _i , E _{i is} performed according to the formulas that are presented in Table 1 - Table 3 in Fig. 5 - Fig. 7. The formulas for determining the coefficients A _i , B _i , E _{i are} compiled for angular elements of exterior orientation (Euler angle systems) used in photogrammetry, namely:

- for the second system of angles α, ω, χ (α is the longitudinal angle of inclination, ω is the transverse angle of inclination, χ is the angle of rotation of the image);

, κ (ϕ - продольный угол наклона,

- поперечный угол наклона, κ - угол поворота плоскости изображения;- for the angle system recommended by the international society of photogrammetry and remote sensing (IOFD) ϕ,

, κ (ϕ is the longitudinal angle of inclination,

- transverse angle of inclination, κ - angle of rotation of the image plane;

- for the system of angles Ω, ω, J used in space photogrammetry.

The claimed method for determining the mean square error, with which the spatial coordinates of the points of the object are determined, from processing images of the object formed by shooting cameras with arbitrary values of the orientation elements, is as follows.

1. Obtain overlapping images of the object using at least two shooting cameras with different technical characteristics and, accordingly, with different elements of internal orientation, namely, focal lengths and coordinates of the main points.

2. Determine the elements of the interior orientation of the shooting camera - focal lengths and coordinates of the main points: x ₀ , y ₀ , f and the errors with which they are determined. Elements of the interior orientation of the camera and their errors are determined by calibrating the camera.

) и втором (

) снимках пары снимков, определяют значения средних квадратических ошибок определения координат изображений точек объекта. Измерения выполняют либо в ручном режиме, либо в автоматическом режиме с использованием специального программного обеспечения, разработанного заявителем, либо в полуавтоматическом режиме, то есть с использованием частично ручного, частично автоматического режима. Программное обеспечение не является объектом патентных притязаний, так как относится к объектам авторского права, поэтому не приводится в контексте настоящего описания.3. Determine the coordinates of the image points i of the investigated object on the first (

) and second (

) images of a pair of images, determine the mean square errors of determining the coordinates of the image points of the object. Measurements are performed either in manual mode or in automatic mode using special software developed by the applicant, or in semi-automatic mode, that is, using partially manual, partially automatic mode. The software is not subject to patent claims, as it relates to copyright, therefore, is not given in the context of the present description.

4. Determine the linear and angular elements of external orientation that have any values in the spatial coordinate system, in which the coordinates of the object’s points are determined by using the on-board navigation equipment (satellite-GPS / GLONASS, inertial-IMU) of the aircraft (shooting camera carrier) or otherwise in a way that does not involve the use of control points at the test object.

5. Take the value of the focal length of at least two survey cameras, the coordinates of the main points of the survey cameras, the mean square errors with which the focal lengths, the coordinates of the main points of the survey cameras, linear and angular elements of the exterior orientation of the survey cameras and the errors with which the linear and angular elements of the exterior orientation of the shooting cameras, the coordinates of the image points on two images of a pair of images, and the error with which each image coordinate is determined for each picture and determine the mean square error of the spatial coordinates of the object points, for which:

приведены в Таблице 4 на Фиг.8;a) in a known manner determine the directional cosines a _tk for the first (left) image and the direction of the cosines for the second (right) image in accordance with the used system of orientation angles, formulas for determining a _tk and

are shown in Table 4 in FIG. 8;

b) in a known manner determine the spatial coordinates of the images of the point of the investigated object:

с началом в центре проекции снимка Р₁ (см. Фиг. 1)- in the spatial coordinate system

with the beginning in the center of the projection of the image P ₁ (see Fig. 1)

с началом в центре проекции снимка Р₂ (см. Фиг. 1)- in the spatial coordinate system

with the beginning in the center of the projection of the image P ₂ (see Fig. 1)

where:

- направляющие косинусы для первого и второго снимков соответственно;

- guide cosines for the first and second pictures, respectively;

- координаты изображения точки соответственно в плоской системе координат o₁x₁y₁ на первом снимке Р₁ и o₂x₂y₂ на втором снимке Р₂ (см. Фиг. 1);

- the coordinates of the image of the point, respectively, in a flat coordinate system o ₁ x ₁ y ₁ in the first picture of P ₁ and o ₂ x ₂ y ₂ in the second picture of P ₂ (see Fig. 1);

- элементы внутреннего ориентирования соответственно первого и второго снимков, в частном случае, а именно при формировании первого и второго изображения одной и той же съемочной камерой следует принять

.

- elements of interior orientation, respectively, of the first and second pictures, in a particular case, namely when forming the first and second images with the same shooting camera, you should take

.

C) in a known manner determine the parallactic coefficient of the direct photogrammetric notching method, taking into account the slope of the survey basis relative to all three axes of the spatial coordinate system, in which the coordinates of the points of the object are determined:

where:

X ₀ , Y ₀ , Z ₀ - components of the vector R ₀ , which determines the position of the center of photographing S ₂ relative to the center of photographing S ₁ (see Fig. 1), is determined by the formulas:

d) determine the parameters of the influence of linear and angular elements of the external orientation of the pair of images, the elements of the internal orientation of the shooting cameras, the coordinates of the image points measured on the pair of images, on the accuracy of determining the spatial coordinates of the points of the object under study, using the formulas developed by the applicant, namely:

для первого снимка и коэффициенты

для второго снимка пары снимков в соответствии с используемой системой углов ориентирования. Формулы для определения

и

приведены в Таблице 5 на Фиг.9.- determine the coefficients

for the first shot and the odds

for the second picture, a pair of pictures in accordance with the orientation system used. Formulas for determining

and

are shown in Table 5 in Fig.9.

и

соответственно для первого и второго снимков:- determine the coefficients

and

respectively for the first and second shots:

for the first shot

for the second shot

where:

- направляющие косинусы для первого и второго снимков соответственно;

- guide cosines for the first and second pictures, respectively;

- координаты изображения точки соответственно в плоской системе координат o₁x₁y₁ первого снимка Р₁ и o₂x₂y₂ второго снимка Р₂ (см. Фиг. 1);

- the coordinates of the image of the point, respectively, in a flat coordinate system o ₁ x ₁ y _{1 of the} first picture P ₁ and o ₂ x ₂ y _{2 of the} second picture P ₂ (see Fig. 1);

- элементы внутреннего ориентирования соответственно первого и второго снимков, в частном случае, а именно при формировании первого и второго изображения одной и той же съемочной камерой, следует принять

- elements of internal orientation of the first and second shots, respectively, in the particular case, namely when forming the first and second images with the same shooting camera, you should accept

:- determine the values

:

where:

K _ij , L _ij - determined by the formulas shown in Table 6 - Table 8 in Fig.10 - Fig.12.

- determine the influence parameters, namely, the coefficients A _i , B _i , E _i (see Table 1 - Table 3 in Fig. 5 - Fig. 7).

e) determine the square of the mean square error separately for each element of the external and internal orientation of the shooting cameras, image coordinates measured on a pair of images, taking into account the error that each element of external and internal orientation and each measured coordinate, which are used in formulas 4), 5), 6).

f) determine the total square of the mean square error for each of the three spatial coordinates of the points of the studied object, taking into account the influence of the mean square errors, with which the elements of external and internal orientation and the coordinates of the images measured on a pair of images are determined, according to formulas 4), 5), 6 )

g) determine the mean square error of the spatial coordinates of the points of the investigated object by the formulas

h) when the number of pairs of images is more than one, the mean square errors are determined as the statistical average for the number of pairs of images used to determine the coordinates of the points of the object (see Fig. 13), for example, by the formulas:

where:

n is the number of pairs of pictures,

k is the number of snapshot pairs.

For example, in Fig.13 shows three pictures with which you can make three pairs of pictures (N = 3, k = 1,2,3).

In this case, the applicants note that the above sequence of actions of the claimed method can be changed, for example, in the case of determining errors in the post-processing mode (Post), the determination of elements of the interior orientation of the shooting camera and their errors (paragraph 2 of the sequence of actions) can be performed after determining elements of external orientation (paragraph 4 of the sequence of actions), which does not affect the achievement of the claimed technical result.

It should be noted that a characteristic feature of the claimed technical solution, in contrast to the technical solutions known from the investigated prior art, as of the filing date of this application, is that the claimed technical solution does not require the placement of reference (control) points on the ground.

Thus, the above sequence of actions of the claimed method leads to the achievement of the claimed technical result, namely, to increase the reliability of determining the mean square error (error) of the spatial coordinates of the points of the investigated object from processing intermittent images of the studied object.

Further, the applicants present the results of verification of the claimed method, namely, the results of determining the error of the spatial coordinates of the points of the investigated object when shooting from UAVs and satellites by comparing the error determined by the claimed technical solution and the error of the prototype with the error that results from comparing the coordinates, obtained from processing a pair of images by direct photogrammetric notching, with previously known coordinates of these points.

Example 1. The case of aerial photography from UAVs (see Tables 9, 10 in Fig. 14) using the same camera.

For the case when the survey was performed by two different cameras, the prototype does not allow to determine the mean square error of determining the coordinates of the points of the studied object.

Therefore, in Table 9 and Table 10 in Fig. 14, a comparison is made of the mean square error of determining the spatial coordinates of the points of the studied object obtained (mean square error) using the claimed technical solution and using the prototype for an ideal case and an arbitrary case of aerial photography, namely aerial photography with UAVs using the same camera.

, ϕ, κ) для первого и второго снимков стереопары для произвольного случая составили 50°, 40°, 5° и 40°, 30°, 5° соответственно, а угол наклона базиса съемки относительно горизонта 32°.Flight altitude H = 150 m, longitudinal overlapping of stereo pair images 60%. The focal length of the shooting camera (Sony Alpha A5000) is f = 20 mm, the dimensions of the matrix (along the y and x axis) are 5456 x 3632 pixels, and the pixel size is pix = 4.25 μm. Errors in determining the linear and angular elements of the external orientation of the camera are taken equal to the characteristics of the GNSS-inertial Trimble ARX-15 UA UA solution for the real time mode (RTK) and post-processing mode (Post) [11]. Errors of measurement of image coordinates mx = my = 0.5 pix, longitudinal parallax mp = 0.3 pix. Orientation Angles (

, ϕ, κ) for the first and second pictures of the stereo pair for an arbitrary case were 50 °, 40 °, 5 ° and 40 °, 30 °, 5 °, respectively, and the angle of inclination of the survey basis relative to the horizon was 32 °.

The data shown in Table 9 and Table 10 in Fig. 14 show that for the ideal shooting case (when the orientation angles are practically zero), the mean square error of the coordinate determination obtained in the prototype is unreasonably high (not reflecting the real values) according to compared with the standard error of the square obtained using the claimed solution. The value of the mean square error obtained in the conditions of the prototype is less than the value of the mean square error obtained using the claimed solution, solely due to the fact that in the conditions of the prototype take into account a significantly smaller number of interfering parameters than in the claimed technical solution. As can be seen from formulas 1), 2), 3) (prototype) and 4), 5), 6) (the claimed solution), the claimed solution, in contrast to the prototype, allows you to take into account a larger number of parameters, namely, errors of angular orientation elements , errors of linear orientation elements, errors of elements of internal orientation of the shooting camera.

In the case of arbitrary shooting, taking into account all possible errors leads to even more significant differences in comparison with the prototype - see Table 10 in Fig. 14. The prototype gives unreasonably high accuracy solely due to the fact that in the conditions of the prototype take into account a significantly smaller number of interfering parameters than in the claimed technical solution. The use of the prototype in this case may not be justified, and in this case, to determine the mean square error of the spatial coordinates of the points of the object under study, it will be necessary to create a system of control points on the object, which will lead to additional time and material costs.

Example 2. The case of aerial photography from UAVs (see Table 11 in Fig. 15) using different shooting cameras.

For the case when the survey was performed by two different cameras, the prototype does not allow to determine the mean square error of determining the coordinates of the points of the studied object.

Table 11 in Fig. 15 shows the mean square errors of determining the coordinates of the point of the studied object, obtained using the claimed technical solution, for a pair of images obtained by different shooting cameras.

).The flight (shooting) altitude of the first UAV N = 130.0m. The flight (survey) altitude of the second UAV N = 165.0m, the slope of the survey basis relative to the axes of the coordinate system, in which the coordinates of the point of the object under study are determined, 32 °. Orientation system (

)

In order to determine the mean square error of the coordinates of the point of the object under study:

- receive overlapping images of the object using different shooting cameras;

- determine the focal length of different shooting cameras as an element of interior orientation: f ₁ = 20.0 mm, pixel size pix = 4.25 microns; f ₂ = 25.0 mm, pixel size pix = 5.6 μm; matrix dimensions (along the y and x axis) 5456x3632 pix (pixels), the origin of the coordinate system of the image in the geometric center of the image;

- the spatial coordinates of the points of the investigated object are determined by one or more pairs of images obtained by different shooting cameras (in the example used, two images);

- get the mean square error of determining the coordinates of the images of the points of the investigated object: mx ₁ = 1.0 pix, mu ₁ = 1.0 pix, mx ₂ = 0.5 pix, mu ₂ = 0.5 pix;

- determine the linear and angular elements of the external orientation of different survey cameras having any values in the spatial coordinate system in which the coordinates of the points of the object under study are determined: X _S1 = 1050.0 m, Y _S1 = 1028.868 m, Z _S1 = 130.0 m; X _S2 = 1090.0 m, Y _S2 = 1058.868.1 m, Z _S2 = 168.0 m;

- to determine the mean square errors of the spatial coordinates of the points of the studied object, take the value of the focal length of at least two shooting cameras and the coordinates of the images of the points in two images: f ₁ = 20.0 mm, f ₂ = 25.0 mm; x ₁ = 1047.3 pix, y ₁ = 1036.7 pix; x ₂ = -0526.8 pix, y ₂ = -0895.0 pix;

- then take the mean square errors for the coordinates of the images of the points of the studied object in the images: mx ₁ = 1.0 pix, mu ₁ = 0.5 pix, mx ₂ = -0.5 pix, mu ₂ = 0.5 pix;

- in addition to the focal length of the shooting cameras, the coordinates of the main points of at least two shooting cameras are used: (x ₀₁ = 2.0 pix, y ₀₁ = 1.0 pix; x ₀₂ = 1.0 pix, y ₀₂ = 1.0 pix), mean square errors with which the focal lengths (mf ₀₁ = 1.0 pix, mf ₀₂ = 0.5 pix) and the coordinates of the main points of the shooting cameras (mx ₀₁ = 0.5 pix, mу ₀₁ = 1.0 pix; mx ₀₂ = 0.5 pix, mu ₀₂ = 0.5 pix) were determined;

- when determining the mean square error of the points of the studied object, linear and angular elements of the exterior orientation of the survey cameras and the mean square errors with which the linear and angular elements of the exterior orientation of the survey cameras are determined are used: mX _S1 = 0.02 m, mY _S1 = 0.02 m, mZ _S1 = 0.05 m; m _ω1 = 0.03 °, mϕ ₁ = 0.03, mκ ₁ = 0.18 °; mX _S1 = 0.02 m, mY _S1 = 0.02 m, mZ _S1 = 0.05 m; m _ω2 = 0.03 °, m _ϕ2 = 0.03 °, m _κ2 = 0.18 °;

- when determining the mean square error of the spatial coordinates of the points of the studied object, use the coordinates of the images of the points in each image and the average square error with which each image coordinate of the points of the studied object in each image is determined: x ₁ = 1047.3 pix, y ₁ = 1036.7 pix; x ₂ = -0526.8 pix, y ₂ = -0895.0 pix; mx ₁ = 1.0 pix, mu ₁ = 0.5 pix, mx ₂ = -0.5 pix, mu ₂ = 0.5 pix;

- determine the parallactic coefficient N of the direct photogrammetric notching method, taking into account the slope of the survey basis relative to all three axes of the spatial coordinate system, in which the coordinates of the points of the object under study are determined: N = 3277.326464;

- determine the influence parameters (A, B, E) of linear and angular elements of the external orientation of the pair of images, the elements of the internal orientation of the shooting cameras, the coordinates of the image points of the object under study, measured on a pair of images, on the accuracy of determining the spatial coordinates of the points of the object under study

(influence parameters A, B, E have the same values for real-time mode (RTK) and post-processing mode (Post)):

A ₁ = 7395.27, A ₂ = -70685.86, A ₃ = -14911.72, A ₄ = -12735.29, A ₅ = 7082.56, A ₆ = -1883.58, A ₇ = -0.05, A ₈ = -0.19, A ₉ = - 0.03, A ₁₀ = -3401.57, A ₁₁ = 170.85, A ₁₂ = -396.89,

A ₁₃ = -573.11, A ₁₄ = -1877.93, A _{15 =} 251.41, A ₁₆ = -635.57, A ₁₇ = -1126.76, A ₁₈ = 150.85,

A ₁₉ = -381.34;

B ₁ = -15208.77, B ₂ = 20291.58, B ₃ = 1664.98, B ₄ = 77853.36, B ₅ = - 43297.14, B ₆ = 11514.72,

B₇= 0.31, B₈= 1.14, B₉= 0.18, B₁₀= -1000.43, B_eleven= -661.53, B₁₂= 2426.27, B_thirteen= 3503.51, B₁₄= -1425.84, B_fifteen= -2841.99, B₁₆= 1723.39, B₁₇= -3004.68, B₁₈= -2841.99, B₁₉= 1723.39;

E ₁ = 83,317.82, E ₂ = -7289.34, E ₃ = 14963.95, E ₄ = -38205.86, E ₅ = 21247.70, E ₆ = 5650.75,

E ₇ = -0.16, E ₈ = 0.56, E ₉ = -0.09, E ₁₀ = 501.89, E ₁₁ = 3881.61, E ₁₂ = -1190.67, E ₁₃ = -1719.32,

E ₁₄ = 344.40, E ₁₅ = -1081.14, E ₁₆ = -833.79, E ₁₇ = 430.50, E ₁₈ = -1351.43, E ₁₉ = -1042.23;

- determine the square of the mean square error separately for each element of the external and internal orientation of the shooting cameras, for each coordinate of the images of the points of the studied object, measured on a pair of images, taking into account the error that each element of external and internal orientation and each measured coordinate introduce:

real time (RTK)

(A₁m_ω1)² = 18.14, (A₂m_ϕ1)²= 1657.48, (A₃m_κ1)²= 2268.36, (A₄m_ω2)² = 53.80, (A₅m_ϕ2)²= 16.64, (A₆m_κ2)²= 36.19, (A₇m_X0)² = 6.36, (A₈m_Y0)²= 86.79, (A₉m_Z0)²= 2.18, (A₁₀m_x1)² = 209.00, (A_elevenm_y1)²= 0.53, (A₁₂m_x2)²= 1.24, (A_thirteenm_y2)² = 2.58, (A₁₄m_x01)²= 15.55, (A_fifteenm_y01)²= 1.14, (A₁₆m_f1)²= 7.30, (A₁₇m_x02)²= 9.95, (A₁₈m_y02)²= 0.18, (A₁₉m_f2)²= 1.14;

(B₁m_ω1)²= 63.41, (B₂m_ϕ1)²= 112.88, (B₃m_κ1)²= 27.36, (B₄m_ω2)² = 1661.70, (B₅m_ϕ2)²= 513.94, (B₆m_κ2)²= 1308.60, (B₇m_X0)² = 237.72, (B₈m_Y0)²= 3243.56, (B₉m_Z0)²= 81.50, (B₁₀m_x1)² = 18.08, (B_elevenm_y1)²= 7.90, (B₁₂m_x2)²= 46.15, (B_thirteenm_y2)² = 96.23, (B₁₄m_x01)²= 8.97, (B_fifteenm_y01)²= 145.89, (B₁₆m_f1)²= 53.65, (B₁₇m_x02)²= 70.78, (B₁₈m_y02)²= 63.32, (B₁₉m_f2)²= 23.29;

(E₁m_ω1)²= 1903.15, (E₂m_ϕ1)²= 14.57, (E₃m_κ1)²= 2210.00, (E₄m_ω2)² = 400.18, (E₅m_ϕ2)²= 123.77, (E₆m_κ2)²= 315.15, (E₇m_X0)² = 57.25, (E₈m_Y0)²= 781.14, (E₉m_Z0)²= 19.63, (E₁₀m_x1)² = 4.55, (E_elevenm_y1)²= 272.15, (E₁₂m_x2)²= 11.11, (E_thirteenm_y2)² = 23.18, (E₁₄m_x01)²= 0.52, (E_fifteenm_y01)²= 21.11, (E₁₆m_f1)²= 12.56, (E₁₇m_x02)²= 1.45, (E₁₈m_y02)²= 14.32, (E₁₉m_f2)²= 8.52;

post processing mode (Post)

(A₁m_ω1)² = 10.41, (A₂m_ϕ1)²= 951.26, (A₃m_κ1)²= 2194.60, (A₄m_ω2)² = 303.88, (A₅m_ϕ2)²= 9.55, (A₆m_κ2)²= 35.02, (A₇m_X0)² = 6.36, (A₈m_Y0)²= 86.79, (A₉m_Z0)²= 2.18, (A₁₀m_x1)² = 209.00, (A_elevenm_y1)²= 0.53, (A₁₂m_x2)²= 1.24, (A_thirteenm_y2)² = 2.58, (A₁₄m_x01)²= 15.55, (A_fifteenm_y01)²= 1.14, (A₁₆m_f1)²= 7.30, (A₁₇m_x02)²= 9.95, (A₁₈m_y02)²= 0.18, (A₁₉m_f2)²= 1.14;

(B₁m_ω1)²= 44.04, (B₂m_ϕ1)²= 78.39, (B₃m_κ1)²= 27.36, (B₄m_ω2)² = 1153.96, (B₅m_ϕ2)²= 356.91, (B₆m_κ2)²= 1308.60, (B₇m_X0)² = 237.72, (B₈m_Y0)²= 3243.56, (B₉m_Z0)²= 81.50, (B₁₀m_x1)² = 18.08, (B_elevenm_y1)²= 7.90, (B₁₂m_x2)²= 46.15, (B_thirteenm_y2)² = 96.23, (B₁₄m_x01)²= 8.97, (B_fifteenm_y01)²= 145.89, (B₁₆m_f1)²= 53.65, (B₁₇m_x02)²= 70.78, (B₁₈m_y02)²= 63.32, (B₁₉m_f2)²= 23.29;

(E₁m_ω1)² = 1321.63, (E₂m_ϕ1)²= 10.12, (E₃m_κ1)²= 2210.00, (E₄m_ω2)² = 277.90, (E₅m_ϕ2)²= 85.95, (E₆m_κ2)²= 315.15, (E₇m_X0)² = 57.25, (E₈m_Y0)²= 781.14, (E₉m_Z0)²= 19.63, (E₁₀m_x1)² = 4.55, (E_elevenm_y1)²= 272.15, (E₁₂m_x2)²= 11.11, (E_thirteenm_y2)² = 23.18, (E₁₄m_x01)²= 0.52, (E_fifteenm_y01)²= 21.11, (E₁₆m_f1)²= 12.56, (E₁₇m_x02)²= 1.45, (E₁₈m_y02)²= 14.32, (E₁₉m_f2)²= 8.52;

- determine the total square of the mean square error for each of the three spatial coordinates of the points of the investigated object, taking into account the influence of the mean square errors with which the elements of external and internal orientation and image coordinates of the points of the studied object are measured, measured on a pair of images:

real time (RTK)

M _X ² = 4394.55 mm ² , M _Y ² = 7784.93 mm ² , M _Z ² = 6194.30 mm ² ;

post processing mode (Post)

M _X ² = 3575.65 mm ² , M _Y ² = 7066.29 mm ² , M _Z ² = 5448.23 mm ² ;

- determine the mean square error of the spatial coordinates of the points of the investigated object (see Table 11 in Fig. 15).

From the data shown in Table 11 in Fig. 15, we can conclude that the claimed method determines the mean square error of determining the coordinates of the point of an object using different shooting cameras, which is unattainable in the conditions of the prototype.

Example 3. The case of satellite imagery (see Table 12 in Fig. 16) using the same camera.

); угол конвергенции 35°; широта объекта съемки 50°.Table 12 in Fig. 16 shows the mean square error of determining the coordinates obtained using the claimed technical solution and using the prototype for the case of satellite imagery performed by one satellite: orbit (survey) height N = 450 km; 98 ° orbital inclination; focal length of the camera f = 8800 mm; pixel size pix = 12.0 μm; orientation system (

); angle of convergence 35 °; latitude of the subject 50 °.

The mean square errors determined by the claimed technical solution actually characterize the accuracy in the coordinate system in which the coordinates of a point on the Earth’s surface are determined, namely in a rectangular spatial coordinate system (Urmaev M.S. Space Cosmic Photogrammetry - M .: Nedra, 1989, p. 52-57) [12]. The data shown in Table 12 in Fig. 16 show that in the case of satellite imagery, as well as for aerial photography, with a significant slope of the survey basis, large angles of inclination of the images, the mean square error in determining the coordinates obtained under the conditions of the prototype is overestimated in comparison with the mean square error obtained using the claimed technical solution, solely due to the fact that in the conditions of the prototype take into account a significantly smaller number of interfering parameters than in the claimed technical om solution. Those. the mean square error obtained using the prototype is unreasonably less than the mean square error obtained using the claimed technical solution. At the same time, the applicant believes that the mean square error values obtained using the claimed technical solution are much more relevant to reality due to the fact that the claimed technical solution takes into account a larger number of parameters, namely, errors of angular orientation elements, errors of linear orientation elements, errors of elements of the interior orientation of the shooting camera.

Example 4. The case of satellite imagery (see Table 13 in Fig. 17) using different shooting cameras.

For the case when the survey was performed by two different cameras, the prototype does not allow to determine the mean square error of determining the coordinates of the points of the studied object.

Table 13 in Fig. 17 shows the mean square errors of determining the coordinates of the point of the studied object, obtained using the claimed technical solution, for a pair of images obtained by different shooting cameras.

).The height of the orbit (survey) of the first satellite N = 450 km; 98 ° orbital inclination. The height of the orbit (survey) of the second satellite N = 617 km, the inclination of the orbit 98 °. Latitude, longitude of the studied object 50 °, 45 °. Convergence angle of at least 35 °. Orientation system (

)

In order to determine the mean square error of the coordinates of the point of the object under study:

- receive overlapping images of the object using different shooting cameras;

- determine the focal length of different shooting cameras as an element of interior orientation (f ₁ = 8800.0 mm, pixel size pix = 12.0 μm; f ₂ = 13300.0 mm, pixel size pix = 6.6 μm; the origin of the coordinate system of the image in the geometric center of the image);

- the spatial coordinates of the points of the investigated object are determined by one or more pairs of images obtained by different shooting cameras (in the example used, two images);

- get the mean square errors of determining the coordinates of the images of the points of the object under study: mx ₁ = 0.5 pix, mu ₁ = 0.3 pix, mx ₂ = 0.4 pix, mu ₂ = 0.5 pix;

;

;- determine the linear and angular elements of the external orientation of different survey cameras having any values in the spatial coordinate system in which the coordinates of the points of the object under study are determined: (X _S1 = 4384648.4 m, Y _S1 = 3100414.6 m, Z _S1 = 5225420.5 m; X _S2 = 4187216.4 m, Y _S2 = 2960809.1 m, Z _S2 = 5594960.5 m;

;

;

- to determine the mean square errors of the spatial coordinates of the points of the studied object, take the value of the focal length of at least two shooting cameras and the coordinates of the images of the points in two images (f ₁ = 8800 mm, f ₂ = 13300 mm; x ₁ = 12605.7 pix, y ₁ = --33311.9 pix; x ₂ = 29829.5 pix, y ₂ = 21143.3 pix);

- then take the mean square errors for the coordinates of the images of the points of the studied object in the pictures: mx ₁ = 0.5 pix, mu ₁ = 0.5 pix, mx ₂ = 1.0 pix, mu ₂ = 1.0 pix;

- in addition to the focal length of the shooting cameras, the coordinates of the main points of at least two shooting cameras are used: x ₀₁ = 1.0 pix, y ₀₁ = 2.0 pix; x ₀₂ = 1.0 pix, y ₀₂ = 1.0 pix and the mean square errors with which the focal lengths were determined: mf ₀₁ = 1.0 pix, mf ₀₂ = 0.5 pix and the coordinates of the main points of the shooting cameras: mx ₀₁ = 0.5 pix, mу ₀₁ = 1.0 pix; mx ₀₂ = 0.5 pix, mu ₀₂ = 0.5 pix;

- when determining the mean square error of the points of the studied object, linear and angular elements of the exterior orientation of the survey cameras and the mean square errors with which the linear and angular elements of the exterior orientation of the survey cameras are used (mX _S1 = 0.2 m, mY _S1 = 0.2 m, mZ _S1 = 0.4 m; m _ω1 = 2′.0, m _ϕ1 = 2′.0, m _κ1 = 2′.0; mX _S1 = 0.2 m, mY _S1 = 0.2 m, mZ _S1 = 0.4 m; m _ω2 = 1 ′ .9, m _ϕ2 = 1′.9, m _κ2 = 1′.8);

- when determining the mean square error of the spatial coordinates of the points of the studied object, use the coordinates of the images of the points in each image and the average square error with which each coordinate of the image of the points of the studied object in each image is determined: x ₁ = 12605.7 pix, y ₁ = -33311.9 pix; x ₂ = 29829.5 pix, y ₂ = 21143.3 pix; mx ₁ = 0.5 pix, mu ₁ = 0.3 pix; mx ₂ = 0.4 pix, mu ₂ = 0.5 pix;

- determine the parallactic coefficient N of the direct photogrammetric notching method, taking into account the slope of the survey basis relative to all three axes of the spatial coordinate system, in which the coordinates of the points of the object under study are determined: N = 54114.03856;

- determine the influence (A, B, E) of the linear and angular elements of the external orientation of the pair of images, the elements of the internal orientation of the shooting cameras, the coordinates of the image points of the object under study, measured on a pair of images, on the accuracy of determining the spatial coordinates of the points of the object under study:

A ₁ = -135472624.1, A ₂ = 111685440.5, A ₃ = -9037461.9, A ₄ = 252377236.7, A ₅ = -771806617.2, A ₆ = -4152332.9, A ₇ = 1.1, A ₈ = 0.4, A ₉ = -0.3, A ₁₀ = -12708.2, A ₁₁ = -26161.8, A ₁₂ = 87681.3,

A ₁₃ = 30273.54, A ₁₄ = -37486.59, A _{15 =} -2055.8, A ₁₆ = -1292.7, A ₁₇ = -56655.8, A ₁₈ = -3107.1, A ₁₉ = -1953.7;

B ₁ = 233797484.3, B ₂ = 157169155.8, B ₃ = 101165.8, B ₄ = 49948032.2, B ₅ = - -152748410.7,

B₆= -821789.1, B₇= 0.22, B₈= 0.09, B₉= 0.06, B₁₀= -17817.5, B_eleven= 47753.8, B₁₂= 17353.0, B_thirteen= 5991.4, B₁₄232.2, B_fifteen= -26872.6, B₁₆= 1077.9, B₁₇= 351.0, B₁₈= -40614.3, B₁₉= 1629.1;

E₁= -167657141.3, E₂= 637750551.8, E₃= -33305740.5, E₄= 167940303.1, E₅= -513586086.1, E₆= -2763102.0, E₇= 0.74, E₈= 0.29, E₉= -0.20, E₁₀= -72472.6, E_eleven= -28659.9, E₁₂= 58346.1, E_thirteen= 20145.0, E₁₄= 7063.2, E_fifteen= 4257.4, E₁₆= -565.6, E₁₇= 10675.1, E₁₈= 6434.5,

E ₁₉ = -854.7;

- determine the square of the mean square error separately for each element of the external and internal orientation of the shooting cameras, for each coordinate of the images of the points of the studied object, measured on a pair of images, taking into account the error that each element of external and internal orientation and each measured coordinate introduce:

(A₁m_ω1)² = 6199351887.7, (A₂m_ϕ1)²= 4213435261.8, (A₃m_κ1)²= 27094152.9,

(A₄m_ω2)² = 21515109672.6, (A₅m_ϕ2)²= 201214928085.6, (A₆m_κ2)²= 5719617.1,

(A₇m_X0)² = 49763.6, (A₈m_Y0)²= 7403.0, (A₉m_Z0)²= 3632.5, (A₁₀m_x1)² = 5813.9,

(A_elevenm_γ1)²= 24639.9, (A₁₂m_κ2)²= 334890.3, (A_thirteenm_γ2)²= 39922.1, (A₁₄m_κ01)²= 50588.8,

(A_fifteenm_γ01)²= 608.6, (A₁₆m_f1)²= 240.6, (A₁₇m_κ02)²= 34955.6, (A₁₈m_γ02)²= 105.1, (A₁₉m_f2)²= 41.5;

(B₁m_ω1)²= 18463875786.8, (B₂m_ϕ1)²= 8344068166.8, (B₃m_κ1)²= 3395.1, (B₄m_ω2)² = 842713535.6, (B₅m_ϕ2)²= 7881277207.5, (B₆m_κ2)²= 224028.5, (B₇m_X0)² = 1949.1, (B₈m_Y0)²= 289.9,

(B ₉ m _Z0 ) ² = 142.2, (B ₁₀ m _x1 ) ² = 11428.7, (B ₁₁ m _y1 ) ² = 82095.3, (B ₁₂ m _x2 ) ² = 13117.1, (B ₁₃ m _y2 ) ² = 1563.6, (B ₁₄ m _x01 ) ² = 1.9, (B ₁₅ m _y01 ) ² = 103987.9, (B ₁₆ m _f1 ) ² = 167.3, (B ₁₇ m _x02 ) ² = 1.3, (B ₁₈ m _y02 ) ² = 17963.3, (B ₁₉ m _f2 ) ² = 28.9;

(E₁m_ω1)² = 9494832674.6, (E₂m_ϕ1)²= 137386762087.3, (E₃m_κ1)²= 367977105.6,

(E₄m_ω2)² = 9526932051.0, (E₅m_ϕ2)²= 89098358162.8, (E₆m_κ2)²= 2532657.5,

(E₇m_X0)²= 22035.4, (E₈m_Y0)²= 3278.0, (E₉m_Z0)²= 1608.4, (E₁₀m_x1)²= 189082.1, (E_elevenm_y1)²= 29570.1, (E₁₂m_x2)²= 148290.1, (E_thirteenm_y2)² = 17677.6, (E₁₄m_x01)²= 1796.0, (E_fifteenm_y01)²= 2610.1,

(E ₁₆ m _f1 ) ² = 46.1, (E ₁₇ m _x02 ) ² = 1241., 0, (E ₁₈ m _y02 ) ² = 450.9, (E ₁₉ m _f2 ) ² = 8.0;

- determine the total square of the mean square error for each of the three spatial coordinates of the points of the investigated object, taking into account the influence of the mean square errors with which the elements of external and internal orientation and image coordinates of the points of the studied object are determined, measured on a pair of images M _X ² = 233176191284.0 mm ² , M _Y ² = 35532394857.5 mm ² , M _Z ² = 245877812432.7 mm ² ;

- determine the mean square error of the spatial coordinates of the points of the investigated object (see Table 13 in Fig. 17).

From the data shown in Table 13 in Fig.17, we can conclude that the claimed method determines the mean square error of determining the coordinates of the point of the object using different shooting cameras, which is unattainable in the conditions of the prototype.

The applicant explains that the determination of the mean square error is made using the computer program developed by the applicant, which is not the subject of patent claims.

However, the applicant explains the following. When determining the spatial coordinates of the points of the object under study using other exterior orientation angles (Euler angle systems) formulas 4), 5), 6) do not change. In this case, the formulas for determining certain coefficients are changed, for example, for A _i , B _i , E _i as it can be seen from Tables 1 - 3 in Fig. 5 - Fig. 7, and for K _ij , L _ij as can be seen from Tables 7 - 8 in FIG. 11 - FIG. 12. The applicant can obtain formulas for these coefficients and for other systems of Euler angles, but in view of the large number of systems of Euler angles, the applicant does not consider it necessary to give these formulas in the present description. In the present description, formulas are given only for the most common systems of Euler angles used in photogrammetry, which, according to the applicant, is sufficient to prove the achievement of the claimed technical result.

From the above it can be concluded that the applicant has reached the set goals and the claimed technical result, namely, the reliability of determining the mean square error (error) of the spatial coordinates of the points of the object under study from image processing has been increased, while:

- Images obtained by different shooting cameras;

- linear and angular elements of exterior orientation have been taken into account, having any values in the spatial coordinate system in which the coordinates of the points of the object are determined;

- the values of the focal length of different shooting cameras and the coordinates of the image points on two pictures of the stereo pair are taken into account;

- the errors of measuring the coordinates of the image points on the pair of images of a stereo pair are taken into account;

- the errors of linear and angular elements of the external orientation of different survey cameras and the errors with which the linear and angular elements of the external orientation of the survey cameras are taken into account;

- the errors of elements of the interior orientation of the shooting cameras were taken into account - the mean square errors with which the focal lengths and coordinates of the main points of the shooting cameras were determined;

- the slope of the survey basis with respect to all three axes of the spatial coordinate system is taken into account, in which the coordinates of the points of the object under study are determined, i.e. the angular position of the survey basis with respect to the axes of a rectangular coordinate system is taken into account.

The claimed technical solution meets the criterion of "novelty" presented to the invention, because from the prior art investigated by the applicant, the totality of the characteristics given in the independent paragraphs of the claimed technical solution is not revealed.

The claimed technical solution meets the criterion of "inventive step" for inventions, because from the prior art examined by the applicant, technical solutions with the claimed combination of essential features specified in the independent clauses of the claimed technical solution have not been identified, and technical results realized through the application of the indicated features have not been identified. In addition to the indicated, the claimed technical solution is not obvious to the specialist by virtue of the fact that it allows to obtain errors with which the spatial coordinates of any point located in the overlapping zone of a pair of images (stereo pairs) obtained by different shooting cameras having any values of exterior orientation relative to the axes are obtained spatial rectangular coordinate system in which the coordinates of the points of the investigated object are determined, which is the date of submission of the claimed materials n Based on the analysis of the prior art it was not possible to realize in practice.

The claimed technical solution meets the criterion of "industrial applicability" to the invention, because tested in the field and received confirmation of the ability to realize all the stated goals and technical result.

Used sources:

1. Order of the Ministry of Economic Development of Russia dated 01.03.2016 No. 90 "On approval of requirements for accuracy and methods for determining the coordinates of the characteristic points of the boundaries of the land plot, requirements for accuracy and methods for determining the coordinates of the characteristic points of the contour of a building, structure or construction in progress on a land plot, as well as requirements for determining the area of a building, structure and premises "(Registered in the Ministry of Justice of Russia on 08.04.2016 N 41712).

2. Patent for invention No. 2 681836. A method for determining the spatial coordinates and angular position of a remote object. Priority of invention February 13, 2018 Date of state registration in the register of inventions of the Russian Federation March 13, 2 019

3. Mikhailov A.P., Chibunichev A.G. Photogrammetry - M.: MIIGAiK Publishing House, 2016 .-- 294 p. (10).

4. Nazarov A.S. Photogrammetry. - Minsk: TerraSystems, 2010 .-- 400 p. (3).

5 Limonov A.N., Gavrilova L.A. Photogrammetry and remote sensing. - M.: Academic project. 2016 .-- 296 p.

6. Phototopography. Terms and Definitions. GOST R 52369-2005.

7. A guide to photogrammetry, under. Red V.I. Korableva. - M .: Subsoil. 1970 .-- 183 p.

8. Krasnopevtsev B.V. Photogrammetry. - M .: UPP "Reprography" MIIGAiK, 2008. - 160 p.

9. Instructions for photogrammetric work when creating digital topographic maps and plans. - M .: TsNIIGAiK, 2002 .-- 100 p.

10. Zharova N.E., Chibunichev A.G. Analysis of the accuracy of determining the coordinates of terrain points when using "random" stereo pairs of satellite images. News of higher educational institutions. Geodesy and aerial photography, No. 5, 2017.- 128 p.

12. URL https://www.applanix.com/downloads/products/specs/APX15_UAV.pdf. (Date of treatment 23.10.18).

13. Urmaev MS Cosmic photogrammetry - M .: Nedra, 1989, - 279 p.

Claims (1)

The method for determining the mean square error of the spatial coordinates of the points of the object under study from processing intermittent images obtained by different shooting cameras with arbitrary values of the elements of external and internal orientation, which consists in the fact that receive overlapping images of the object; determine the focal length of the camera as an element of interior orientation; determine the coordinates of the images of the points of the investigated object, get the mean square errors of determining the coordinates of the images of the points of the studied object; then determine the mean square error of the spatial coordinates of the points of the object under study, for which they take the value of the focal length of the camera and the coordinates of the images of the points in the picture; then take the mean square errors for the coordinates of the image points of the investigated object in the picture, characterized in that the overlapping image of the object is obtained using different shooting cameras; determine the focal length of different shooting cameras; the spatial coordinates of the points of the investigated object are determined by one or more pairs of images obtained by different shooting cameras; determine linear and angular elements of the external orientation of different survey cameras having any values in the spatial coordinate system in which the coordinates of the points of the object under study are determined; to determine the mean square errors of the spatial coordinates of the points of the object under study, take the value of the focal length of at least two survey cameras and the coordinates of the images of the points in two images; in addition to the focal length of the shooting cameras, the coordinates of the main points of at least two shooting cameras and the mean square errors with which the focal lengths and coordinates of the main points of the shooting cameras are used; when determining the mean square error of the points of the investigated object, linear and angular elements of the exterior orientation of the survey cameras and the mean square errors with which the linear and angular elements of the exterior orientation of the survey cameras are used are used; when determining the mean square error of the spatial coordinates of the points of the object under study, use the coordinates of the images of the points in each image and the mean square error with which each image coordinate of the points of the object under study in each image is determined; determine the parallactic coefficient of the direct photogrammetric notching method, taking into account the slope of the survey basis relative to all three axes of the spatial coordinate system, in which the coordinates of the points of the object under study are determined; determine the parameters of the influence of linear and angular elements of the external orientation of the pair of images, the elements of the internal orientation of the shooting cameras, the coordinates of the images of the points of the investigated object, measured on a pair of images, on the accuracy of determining the spatial coordinates of the points of the studied object; determine the square of the mean square error separately for each element of the external and internal orientation of the shooting cameras, for each coordinate of the images of the points of the investigated object, measured on a pair of images, taking into account the error that each element of external and internal orientation and each measured coordinate makes; determining the total square of the mean square error for each of the three spatial coordinates of the points of the object under study, taking into account the influence of the mean square errors with which the elements of external and internal orientation and image coordinates of the points of the object under study, measured on a pair of images, are determined; determine the mean square error of the spatial coordinates of the points of the investigated object; when the number of pairs of images is more than one, the mean square errors of the points of the investigated object are determined as the statistical average for the number of pairs of images used to determine the coordinates of the points of the studied object.

Images