CN115393311A - Binocular vision distance measurement method based on baseline distance - Google Patents
Binocular vision distance measurement method based on baseline distance Download PDFInfo
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Abstract
The invention relates to the field of binocular computer vision measurement, in particular to a binocular vision distance measurement method based on a baseline distance. The method comprises the following steps: s1, calibrating a binocular camera; s2, image acquisition is carried out by using a binocular camera: s3, calculating the parallax of target points in a left view imaged by the left eye camera and a right view imaged by the right eye camera by using a target recognition and feature point matching algorithm; s4, rightwards offsetting the right view imaged by the right eye camera by a distance C: and S5, adjusting the baseline distance to enable the image parallax to be 0, and obtaining the distance to be measured according to the adjusted baseline distance. When the method is used for ranging, the problem that the measurement precision at two ends is dispersed in the existing parallax method ranging can be effectively solved, so that the effective measurement range is wider and the precision is higher.
Description
Technical Field
The invention relates to the field of binocular computer vision measurement, in particular to a binocular vision distance measurement method based on a baseline distance.
Background
With the development of vision technology, the application of binocular stereo vision in the fields of three-dimensional reconstruction, vehicle auxiliary driving and the like is more and more extensive, and the requirement of converting two-dimensional information acquired by a camera into three-dimensional information with depth is more and more strong. The existing binocular stereo vision adopts a parallax method that a fixed base line distance changes through the imaging parallax of a binocular camera to measure distance, and because the parallax and the distance form an inverse proportion relation, the measurement precision is caused to diverge at two ends, and only the middle section precision is higher. Therefore, in the prior art, the parallax binocular stereo distance measurement is mostly concentrated in a small range.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a binocular vision distance measurement method based on a baseline distance.
The technical scheme of the invention is as follows: a binocular vision distance measuring method based on a baseline distance comprises the following steps:
s1, calibrating a binocular camera;
s2, image acquisition is carried out by using a binocular camera:
respectively imaging the object to be measured in a left eye camera and a right eye camera;
s3, calculating the parallax of target points in a left view imaged by a left eye camera and a right view imaged by a right eye camera by using a target recognition and feature point matching algorithm;
identifying a target to be detected in the left view and the right view imaged by the binocular camera by using a target identification algorithm, externally connecting rectangles to the target to be detected in the images, acquiring the coordinates of the externally connected rectangles of the target to be detected, adopting a feature point matching algorithm in a rectangular area, averaging the abscissa of the successfully matched feature points to be used as the abscissa of a target point, and setting the abscissa value in the left view imaged by the left eye camera as X l The abscissa value in the right view imaged by the right eye camera is X r Then the parallax of the target point in the left and right views is D = X l -X r ；
S4, rightwards offsetting the right view imaged by the right eye camera by a distance C:
in order to ensure that the resolution ratio of an image is unchanged, adding C columns of pixel points with the pixel value of 0 to the left side of an image matrix of a right view imaged by a right-eye camera, deleting C columns of pixel points on the rightmost side of the image matrix of the right view imaged by the right-eye camera, and carrying out offset processing on the position of an original pixel point of the right view imaged by the right-eye camera, wherein D-10 is more than or equal to C and less than or equal to D, and C is selected to ensure that an offset object to be detected is completely displayed in the right view;
s5, adjusting the baseline distance to enable the image parallax to be 0, and obtaining the distance to be measured according to the adjusted baseline distance;
taking the left eye camera as a reference, horizontally translating the right eye camera to ensure that the abscissa of a target point in a right view imaged by the right eye camera is equal to the abscissa of a target point in a left view imaged by the left eye camera, and measuring to obtain an adjusted base line distance T of the binocular camera, wherein the parallax of the target point in the left view and the right view is zero;
at this time, the real parallax value between the left view and the right view is C, the base line distance of the binocular camera is T, and the distance Z to be measured, namely the distance between the object to be measured and the projection center of the camera, is obtained by the following formula:
wherein f is the focal length of the camera, and 1/dx is a proportionality coefficient converted from a pixel unit to a length unit;
s6, changing the distance between the object to be measured and the camera, and repeating the step S5 to obtain the changed distance Z to be measured;
and if the parallax cannot be adjusted to be 0 all the time within the translation adjustment range of the right-eye camera, repeating the steps S2, S3, S4 and S5, and re-determining the offset distance C to obtain the changed distance Z to be measured.
In the invention, in the step S1, the binocular camera is calibrated to obtain internal parameters of the camera, distortion parameters of the camera are obtained through the calibration of the camera, each frame of image shot by the camera is corrected through the distortion parameters, the deformation of the image caused by lens distortion is corrected, and the binocular camera is aligned to the same observation plane through polar line correction, so that the imaging pixel lines of the binocular camera are aligned.
In the step S1, the binocular vision distance measuring device comprises a left eye camera, a right eye camera, a stepping motor I, a stepping motor ii and a guide rail lead screw sliding table frame body, wherein the left eye camera and the right eye camera are both arranged on the guide rail lead screw sliding table frame body;
an output shaft of the stepping motor II is connected with a screw rod II through a coupler, the other end of the screw rod II is rotatably connected with a baffle, the left eye camera is fixedly arranged on the guide rail sliding table II, the guide rail sliding table II is sleeved on the screw rod II, the screw rod II is in threaded connection with the guide rail sliding table II, and the guide rail sliding table II and the left eye camera reciprocate along the axial direction of the screw rod II during the rotation process of the screw rod II;
the guide rail screw rod sliding table frame body is connected with a triangular support frame below the guide rail screw rod sliding table frame body.
In the above-mentioned step S2, the step of,
and in the process of controlling the stepping motor II to rotate the screw rod II through the computer, the guide rail sliding table II and a left eye camera fixed on the guide rail sliding table II are driven to move, a left view image formed by the left eye camera horizontally moves, and an object to be measured in the left view image is adjusted to the middle of the view image.
In the above-mentioned step S5, the step of,
and taking the left view as a reference, controlling a stepping motor I by the computer to enable the screw rod I to rotate, and simultaneously driving the guide rail sliding table I and a right eye camera fixed on the guide rail sliding table I to move, wherein the right view imaged by the right eye camera horizontally moves, the abscissa value of a target point moved to the right view is consistent with the abscissa value of the target point in the left view, and the parallax of the abscissa of the target point in the left view and the right view is zero.
For ease of calculation, in step S4 described above, C =10n (n =1,2, …).
The invention has the beneficial effects that:
(1) The binocular vision distance measurement method based on the baseline distance provides an operation mode of obtaining zero image parallax by matching offset right view with baseline distance adjustment, and makes the distance Z to be measured and the baseline distance T present a linear relation by fixing the parallax C and changing the baseline distance T;
(2) In the measuring process, the problems that the measuring range of the existing binocular stereo vision distance measurement is small and the precision of two ends is diverged are solved.
Drawings
FIG. 1 is a schematic perspective view of a binocular vision rangefinder;
FIG. 2 is a schematic view of a top view structure of a rail screw sliding table frame in the binocular vision distance measuring device;
fig. 3 is a schematic view of the binocular vision distance measuring apparatus in an operating state;
FIG. 4 is a measurement flow chart of a binocular vision ranging method with variable baseline distance;
FIG. 5 (a) is the original image matrix before the right view is shifted;
FIG. 5 (b) is a new image matrix after right view offset;
fig. 6 (a) is an image of a corrected binocular camera;
FIG. 6 (b) is a schematic diagram of the structure after shifting the right view horizontally by a pixel distance C to the right;
FIG. 6 (c) is a schematic diagram showing the arrangement of the target points in the left and right views after the baseline distance adjustment;
in the figure: 1, a computer; 2, a stepping motor I;3, a screw mandrel I;4, a right eye camera; 5, a guide rail sliding table I;6, a screw mandrel II;7 left eye camera; 8, a guide rail sliding table II;9, a step motor II; 10 guide rail screw rod sliding table frame bodies; 11, a coupler; 12 a triangular support frame; the plate is calibrated 13.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, specific details are set forth in order to provide a thorough understanding of the present invention. The invention can be implemented in a number of ways different from those described herein and similar generalizations can be made by those skilled in the art without departing from the spirit of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.
The binocular vision distance measuring method based on the baseline distance comprises the following specific steps.
Firstly, connecting the binocular vision distance measuring device with a computer to calibrate a binocular camera.
As shown in fig. 1 to 3, the binocular vision distance measuring device comprises a left eye camera 7, a right eye camera 4, a guide rail lead screw sliding table frame body 10, a stepping motor I2, a stepping motor II9, a lead screw I3, a lead screw II6, a guide rail sliding table I5 and a guide rail sliding table II8. The left eye camera 7 and the right eye camera 4 are both arranged on the guide rail screw rod sliding table frame body 10, a baffle is arranged between the left eye camera 7 and the right eye camera 4, and the baffle is fixedly arranged on the guide rail screw rod sliding table frame body 10.
Both ends are fixed mounting respectively about guide rail lead screw slip table support body 10 has step motor II9 and step motor I2, and step motor II 9's output shaft passes through shaft coupling 11 to be connected with lead screw II6, and the other end and the baffle of lead screw II6 rotate to be connected. An output shaft of the stepping motor I2 is connected with a screw rod I3 through a coupler, and the other end of the screw rod I3 is rotatably connected with a baffle. The screw II6 and the screw I3 can rotate along with the rotation of the stepping motor II9 and the stepping motor I2.
The right eye camera 4 is fixedly arranged on the guide rail sliding table I5, the guide rail sliding table I5 is sleeved on the outer side of the screw rod I3, and the screw rod I3 is in threaded connection with the guide rail sliding table I5. The left eye camera 7 is fixedly arranged on the guide rail sliding table II8, the guide rail sliding table II8 is sleeved on the outer side of the screw rod II6, and the screw rod II6 is in threaded connection with the guide rail sliding table II8. Guide rail slip table II8 and guide rail slip table I5 can be followed lead screw II6 and lead screw I3's rotation and removed, install left eye camera 7 and right eye camera 4 on guide rail slip table II8 and the guide rail slip table I5 respectively to the realization is through step motor II9 and step motor I2 adjustment left eye camera 7 and right eye camera 4 position, changes the base line distance of two mesh cameras then. The guide rail screw rod sliding table frame body 10 is connected with a triangular support frame 12 below the guide rail screw rod sliding table frame body;
a binocular camera consisting of a left eye camera 7 and a right eye camera 4, a stepping motor I2 and a stepping motor II9 are respectively connected with a computer 1, the binocular camera is calibrated by adopting a Zhang Zhengyou calibration method, distortion parameters of the camera are obtained through camera calibration, each frame of image shot by the camera is corrected through the distortion parameters, the deformation of the image caused by lens distortion is corrected, the binocular camera is aligned to the same observation plane through polar line correction, and imaging pixel lines of the binocular camera are aligned.
And secondly, acquiring images by using a binocular camera.
And respectively carrying out image acquisition on the object to be measured 13 by using the left eye camera 7 and the right eye camera 4. The object to be measured 13 is imaged in the left eye camera 7 and the right eye camera 4 respectively, the computer 1 controls the stepping motor II9, the stepping motor II9 drives the guide rail sliding table II8 to move horizontally, the left eye camera 7 fixed on the guide rail sliding table II8 moves along with the horizontal movement, and an imaging picture of the object to be measured 13 in a left view imaged in the left eye camera 7 is moved to the middle of the view to be used as a measuring reference.
In the present embodiment, as shown in fig. 6 (a), since the camera marking and epipolar line constraining operation is performed in the first step, each corresponding point in the left and right views is horizontally aligned.
And thirdly, calculating the parallax of the target point in the left view imaged by the left eye camera and the right view imaged by the right eye camera by using a target recognition and feature point matching algorithm.
Due to the base line distance of the binocular camera, a point P in the space is in the abscissa value X of the left view imaged by the left eye camera l Abscissa value X in right view imaged with right eye camera r Is different from, and X l Always ratio X r Is large.
And identifying the target to be detected in the left view and the right view imaged by the binocular camera by using a target identification algorithm, and externally connecting rectangles to the target to be detected in the images to obtain the coordinates of the externally connected rectangles of the target to be detected. In order to guarantee the accuracy of the parallax value, the characteristic point matching algorithm is adopted, the mean value of the abscissa of the successfully matched characteristic points in the rectangle is used as the abscissa of a target point, and the abscissa value in the left view imaged by the left eye camera is set as X l The abscissa value in the right view imaged by the right eye camera is X r If the parallax of the target point in the left and right views is X l -X r 。
In this embodiment, an optical calibration plate with 8 × 11 angular points and a rectangular side length of 25 (mm) is used as the object to be measured 13. In order to ensure the accuracy of the parallax value, the horizontal coordinate of the target point is obtained by adopting a mode of averaging multiple characteristic points. Firstly, 8 × 11 corner points of the object to be measured 13 in the left view and the right view are detected by using a corner point detection algorithm. Taking the left view as an example, calculating the mean value of the coordinates of 8-11 angular points of the object to be measured 13 as the coordinates of a target point, and taking the abscissa of the target point as X l In the same way, the abscissa of the target point in the right view can be taken as X r Thereby obtaining a target point disparity of D (px) = X in both views l -X r 。
In this example, X l ＝969.3(px)，X r =763.9 (px), when D = X l -X r ＝969.3-763.9＝205.4(px)。
Fourth, the right view imaged by the right eye camera is shifted to the right by a distance C (px).
In order to ensure that the resolution ratio of the image is unchanged, C columns of pixel points with the pixel value of 0 are added to the left side of an image matrix of a right view imaged by a right-eye camera, meanwhile, C columns of pixel points on the rightmost side of the image matrix of the right view imaged by the right-eye camera are deleted, the original pixel point position of the right view imaged by the right-eye camera is subjected to offset processing, wherein D-10 is more than or equal to C, and C is selected to enable an object to be detected after offset to be completely displayed in the right view. In the present embodiment, for convenience of calculation, C =10n (n =1,2, …).
In this embodiment, the meaning of right view shift to the right is explained by distance. As shown in fig. 5 (a) and 5 (b), the 8*8 image is shifted to the right by 2 (px). That is, two rows of pixel points with pixel values of 0 are added to the left side of the original image matrix, and two rows of pixel points on the rightmost side of the original image are deleted, so that the resolution of the image is kept unchanged, and the original pixel point position of the image is subjected to offset processing, for example, the pixel point coordinate with pixel value of 123 in the original image is (0,0), the coordinate after offset is (2,0), and the horizontal coordinate is changed from 0 to 0+2.
As can be seen from the above, the right view imaged by the right-eye camera is shifted to the right by the distance C, that is, C columns of pixel points with a pixel value of 0 are added to the left side of the original image, and the C columns of pixel points on the right side of the original image are deleted. Thus, the positions of the remaining pixel points in the original image are integrally moved rightwards by C.
In this embodiment, the right view imaged by the right eye camera is shifted to the right by a distance of 200 (px) with reference to the left view imaged by the left eye camera, as shown in fig. 6 (b). Comparing the abscissa of the target point in the right view before the offset in FIG. 6 (a), the abscissa X of the target point in the right view after the offset in FIG. 6 (b) r It becomes 763.9+200=963.9 (px).
And fifthly, adjusting the baseline distance to enable the image parallax to be 0, and obtaining the distance to be measured according to the measured baseline distance.
And (3) performing horizontal translation on the right eye camera 4 by taking the left eye camera 7 as a reference, wherein the abscissa of a target point in the right view imaged by the right eye camera changes in real time in the translation process, when the abscissa of the target point in the right view imaged by the right eye camera is equal to the abscissa of the target point in the left view imaged by the left eye camera, the parallax of the target point in the left view and the right view is zero, the right eye camera 4 stops moving, the adjusted base line distance T of the binocular camera is measured, and the real parallax value of the left view and the right view is C.
In this embodiment, the left eye camera 7 is used as a reference, and the computer 1 controls the stepping motor I2 to drive the rail sliding table I5 and the right eye camera 4 fixed on the rail sliding table I5 to horizontally move to the abscissa value X of the target point in the right eye camera 4 r ＝X l . As shown in fig. 6 (c), after the right eye camera 4 is horizontally translated, the abscissa of the target point in the left view imaged by the left eye camera is X l =969.3 (px), and the abscissa of the target point in the right view imaged by the right eye camera is X r =969.3 (px), when the target point disparity value in the left and right views acquired by the image is zero.
Since the image target point disparity of zero is obtained after the right view is shifted to the right by a distance of C =200 pixels, the true disparity value between the left view and the right view at this time is C =200 (px). The distance between the left eye camera 7 and the right eye camera 4 is measured, and the base line distance T =113.2mm of the adjusted binocular camera is obtained.
Substituting the baseline distance T and the real parallax value C measured in the above steps into the following relational expression to obtain the distance Z to be measured:
wherein f is the focal length of the camera, 1/dx is the proportionality coefficient of pixel unit converted to length unit, f/dx is the product of the focal length f of the camera and the proportionality coefficient 1/dx of pixel unit converted to length unit, and f/dx is the internal parameter of the camera. While the true disparity value C is also a known number, then
Is a constant. Therefore, the above formula shows that the distance Z to be measured is proportional to the baseline distance T.
In this example, f/dx =2742.6, c =200 (px), and T =113.2 (mm). The distance Z between the object to be measured 13 and the projection center of the binocular camera is as follows: 1552.3 (mm).
And sixthly, changing the distance between the object to be measured and the camera, and repeating the fifth step to obtain the changed distance Z to be measured.
If the parallax of the right-eye camera 4 cannot be adjusted to 0 all the time within the translational adjustment range due to the limitation of the length of the guide rail screw rod sliding table frame body 10, repeating the second step, the third step, the fourth step and the fifth step, and reselecting the offset distance C to obtain the changed distance Z to be measured.
Therefore, when the binocular vision distance measurement method based on the baseline distance is used for distance measurement, the distance to be measured can be simply and accurately obtained according to the method provided by the invention only by determining the C value.
The binocular vision distance measuring method based on the baseline distance provided by the invention is described in detail above. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention. The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (6)
1. A binocular vision distance measuring method based on a baseline distance is characterized by comprising the following steps:
s1, calibrating a binocular camera;
s2, image acquisition is carried out by using a binocular camera:
respectively imaging the object to be measured in a left eye camera and a right eye camera;
s3, calculating the parallax of target points in a left view imaged by a left eye camera and a right view imaged by a right eye camera by using a target recognition and feature point matching algorithm;
identifying a target to be detected in the left view and the right view imaged by the binocular camera by using a target identification algorithm, externally connecting rectangles to the target to be detected in the images, acquiring the coordinates of the externally connected rectangles of the target to be detected, adopting a feature point matching algorithm in a rectangular area, averaging the abscissa of the successfully matched feature points to be used as the abscissa of a target point, and setting the abscissa value in the left view imaged by the left eye camera as X l The abscissa value in the right view imaged by the right eye camera is X r Then the parallax of the target point in the left and right views is D = X l -X r ；
S4, rightwards offsetting the right view imaged by the right eye camera by a distance C:
in order to ensure that the resolution ratio of an image is unchanged, C columns of pixel points with the pixel value of 0 are added to the left side of an image matrix of a right view imaged by a right-eye camera, the C columns of pixel points on the rightmost side of the image matrix of the right view imaged by the right-eye camera are deleted, the original pixel point position of the right view imaged by the right-eye camera is subjected to offset processing, wherein D-10 is more than C and less than or equal to D, and C is selected to enable an object to be detected after offset to be completely displayed in the right view;
s5, adjusting the baseline distance to enable the image parallax to be 0, and obtaining the distance to be measured according to the adjusted baseline distance;
taking the left eye camera as a reference, horizontally translating the right eye camera to ensure that the abscissa of a target point in a right view imaged by the right eye camera is equal to the abscissa of a target point in a left view imaged by the left eye camera, and measuring to obtain an adjusted base line distance T of the binocular camera, wherein the parallax of the target point in the left view and the right view is zero;
at this time, the real parallax value between the left view and the right view is C, the base line distance of the binocular camera is T, and the distance Z to be measured, namely the distance between the object to be measured and the projection center of the camera, is obtained by the following formula:
wherein f is the focal length of the camera, and 1/dx is a proportionality coefficient converted from a pixel unit to a length unit;
s6, changing the distance between the object to be measured and the camera, and repeating the step S5 to obtain the changed distance Z to be measured;
and if the parallax cannot be adjusted to be 0 all the time within the translation adjustment range of the right-eye camera, repeating the steps S2, S3, S4 and S5, and re-determining the offset distance C to obtain the changed distance Z to be measured.
2. The method according to claim 1, wherein in step S1, calibrating the binocular camera to obtain internal parameters of the camera, obtaining distortion parameters of the camera through the camera calibration, correcting each frame of image taken by the camera through the distortion parameters, correcting distortion of the image caused by lens distortion, and aligning the binocular camera to the same viewing plane through epipolar line correction to align the rows of imaging pixels of the binocular camera.
3. The method according to claim 1, wherein in step S1, the binocular vision distance measuring device comprises a left eye camera, a right eye camera, a stepping motor I, a stepping motor ii, and a guide rail screw rod slipway frame body, wherein the left eye camera and the right eye camera are both arranged on the guide rail screw rod slipway frame body, a baffle is arranged between the left eye camera and the right eye camera, the baffle is fixed on the guide rail screw rod slipway frame body, the stepping motor I is fixed at one end of the guide rail screw rod slipway frame body, the stepping motor ii is fixed at the other end of the guide rail screw rod slipway frame body, an output shaft of the stepping motor I is connected with the screw rod I through a coupler, the other end of the screw rod I is rotatably connected with the baffle, the right eye camera is fixedly arranged on the guide rail slipway I, the guide rail slipway I is sleeved on the screw rod I, the screw rod I is in threaded connection with the guide rail slipway I, and the guide rail slipway I and the right eye camera reciprocate along the axial direction of the screw rod I during the rotation process of the screw rod I;
an output shaft of the stepping motor II is connected with a screw rod II through a coupler, the other end of the screw rod II is rotatably connected with a baffle, the left eye camera is fixedly arranged on the guide rail sliding table II, the guide rail sliding table II is sleeved on the screw rod II, the screw rod II is in threaded connection with the guide rail sliding table II, and the guide rail sliding table II and the left eye camera reciprocate along the axial direction of the screw rod II during the rotation process of the screw rod II;
the guide rail screw rod sliding table frame body is connected with a triangular support frame below the guide rail screw rod sliding table frame body.
4. The method according to claim 3, wherein in the step S2,
and the stepping motor II is controlled by the computer to drive the guide rail sliding table II and a left eye camera fixed on the guide rail sliding table II to move in the process of rotating the screw rod II, so that the left view imaged by the left eye camera horizontally moves, and an object to be detected in the left view is adjusted to the middle of the view.
5. The method according to claim 3, wherein in the step S5,
and taking the left view as a reference, controlling a stepping motor I by the computer to enable the screw rod I to rotate, and simultaneously driving the guide rail sliding table I and a right eye camera fixed on the guide rail sliding table I to move, wherein the right view imaged by the right eye camera horizontally moves, the abscissa value of a target point moved to the right view is consistent with the abscissa value of the target point in the left view, and the parallax of the abscissa of the target point in the left view and the right view is zero.
6. The method of claim 1, wherein in step S4, C =10n (n =1,2, …).
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| CN116295278A (en) * | 2022-12-09 | 2023-06-23 | 中国科学院上海技术物理研究所 | Three-dimensional vision measurement system of dynamic binocular vision camera baseline |
| CN116819229A (en) * | 2023-06-26 | 2023-09-29 | 广东电网有限责任公司 | Distance measurement method, device, equipment and storage medium for power transmission line |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116295278A (en) * | 2022-12-09 | 2023-06-23 | 中国科学院上海技术物理研究所 | Three-dimensional vision measurement system of dynamic binocular vision camera baseline |
| CN116819229A (en) * | 2023-06-26 | 2023-09-29 | 广东电网有限责任公司 | Distance measurement method, device, equipment and storage medium for power transmission line |
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