Autonomous mining truck summoning system based on three-dimensional reconstruction

Abstract

An autonomous mining truck summoning system based on three-dimensional reconstruction, relating to the technical field of smart mining and comprising a system hardware architecture consisting of a GNSS, a computing unit, a touch screen, and a communication device. According to the autonomous mining truck summoning system based on three-dimensional reconstruction, a three-dimensional model is automatically reconstructed around an excavator in real time and presented to an excavator driver, such that the driver only needs to draw a position and an orientation on the three-dimensional model by gestures when wanting to enable an autonomous mining truck to stop at a certain position for loading. According to such a "what you see is what you get" marking mode, before the mining truck actually arrives at the position, the position where the mining truck needs to stop is visually represented, and the stopping position does not need to be determined by moving the mining truck and an excavator bucket. The marking operation of a driver is facilitated, the operation efficiency of an excavator is improved, and efficient cooperation between the autonomous mining truck and the excavator is guaranteed.

Description

An unmanned mine car summoning system based on 3D reconstruction Technical Field

[0001] The present invention relates to the field of smart mining technology, and in particular to an unmanned mining car summoning system based on three-dimensional reconstruction. Background Art

[0002] In current smart mines, mine carts are unmanned, while excavators or shovels are operated manually or remotely. The excavators / shovels are constantly moving, and operators need to designate a suitable location near the excavator for the unmanned mine cart to dock and load. After receiving the location from the excavator, the unmanned mine cart must autonomously move to that location. To determine the docking location, existing solutions typically install a high-precision positioning system on the excavator. This positioning system determines the excavator's position and orientation, and by adding a certain offset to these positions and orientations, a location near the excavator is determined as the docking location for the unmanned mine cart.

[0003] Its main defects are: 1. Since the offset added to the excavator positioning is a fixed value, the docking position selection of the mine car is not flexible. Sometimes the position calculated by the offset may not be suitable for the site conditions;

[0004] 2. Before starting to load, the driver spends most of his time operating the excavator to sort out the pile. In order to park at the right location, he has to interrupt the pile sorting work and move the excavator to the right location to do so, which reduces work efficiency.

[0005] 3. The docking location cannot be presented to the excavator driver with an intuitive visual representation. Before the unmanned mining truck stops at its location, it is difficult to evaluate whether the location is accurate and reasonable.

[0006] Summary of the Invention

[0007] The purpose of this invention is to provide an unmanned mine cart summoning system based on 3D reconstruction. This system automatically reconstructs a 3D model of the excavator's surroundings in real time and presents it to the excavator driver. To indicate the location where the unmanned mine cart should dock for loading, the driver simply gestures to indicate the location and orientation on the 3D model. This "what you see, what you get" approach intuitively indicates the desired docking location before the cart actually arrives, eliminating the need to move the cart or bucket to determine the docking location. This system facilitates the driver's docking operations, improves the excavator's operating efficiency, and ensures efficient coordination between the unmanned mine cart and the excavator.

[0008] In order to achieve the above objectives, the main technical solutions adopted by the present invention include:

[0009] An unmanned mining car summoning system based on 3D reconstruction, including a system hardware architecture consisting of a GNSS, a computing unit, a touch screen, and a communication device;

[0010] The GNSS is equipped with two antennas, and the computing unit is electrically connected to a camera, a lidar, and an IMU inertial measurement unit;

[0011] The GNSS, the computing unit and the communication device are electrically connected, and the computing unit and the touch screen are electrically connected. The computing unit and the touch screen can be connected by wire, or by wireless or network.

[0012] An unmanned mining car summoning system based on three-dimensional reconstruction includes the following steps:

[0013] S1, SLAM real-time mapping, collects information about the environment around the excavator through the system hardware architecture;

[0014] S2, point cloud image conversion model image, collects information images for conversion, and constructs the model image;

[0015] S3, touch screen presentation, the constructed model diagram is colored and sent to the touch screen, and the driver can view and select it;

[0016] S4, select the docking area and direction. The personnel select the docking location and direction of the mine car through the touch screen;

[0017] S5, sent to the dispatching system, the selected position and orientation information is integrated by the dispatching system and sent to the unmanned mining vehicle;

[0018] S6, the dispatch is sent to the vehicle end. After receiving the information, the unmanned mining vehicle stops according to the instructions.

[0019] Furthermore, the step S1 includes the following specific steps:

[0020] S11, pose prediction, pose prediction uses the imu data between two frames of lidar to perform pre-integration and predict the current radar pose;

[0021] S12, point cloud registration, using the predicted pose as the initial value, and then performing registration optimization through the NDT method to obtain the accurate pose;

[0022] S13, overall optimization. Point cloud registration has a relatively accurate pose, but may have accumulated errors after long-term operation or interference. Fusion with RTK can eliminate the accumulated errors and obtain a more accurate pose.

[0023] S14, RGB coloring, by comparing information from the camera and lidar, the image can be colored according to the coordinate information.

[0024] Furthermore, in step S11, the acceleration a of the two frames of imu data at time i and i+1 is set to i , a i+1 , angular velocity w i ,w i+1 , the time interval is t, the acceleration bias is ba, the angular velocity bias is bg, the gravitational acceleration is grav, and the position at time i is P i , the posture at time i is R i , the speed at time i is V i , we can predict the position, attitude, and speed at time i+1: R i+1 =R i *Exp(((w i +w i+1 ) / 2-bg)*t) V i+1 =V i +R i *((a i +a i+1 ) / 2-ba)*t) P i+1 =P i +(V i +V i+1 ) / 2*t

[0025] Furthermore, in the step S12, the initial value is to transform the i+1th frame point cloud to the i-th frame point cloud, and the accurate pose is the accurate pose of the i+1th frame point cloud.

[0026] Furthermore, the NDT method in step S12 is specifically as follows:

[0027] 1. Divide the point cloud of the i-th frame into several m*m*m grids, count all the points in each grid, and count their distribution on the x, y, and z axes respectively, and express them with mean and covariance:

[0028] mean Covariance

[0029] 2. Each grid corresponds to a probability density function:

[0030] 3. Divide the transformed point cloud of the i+1th frame into a grid of size m*m*m. Calculate the probability density value of each point in the grid. The larger the sum of the probability densities, the better the registration of the two point clouds. The sum of the probability densities is the score of the point cloud registration:

[0031] 4. Since the point cloud in the i+1th frame is obtained through transformation, let the transformation be T. Then S can be derived from T to optimize T, and a T that maximizes the S value is obtained, which is the optimal transformation after registration.

[0032] Furthermore, the specific method in step S13 is as follows:

[0033] 1. Radar and RTK have different operating frequencies and timestamps. First, interpolate the RTK to get the RTK pose at the radar time. rtk ,t rtk express,

[0034] 2. The radar and RTK are installed at different positions on the shovel. The two positions are calibrated at the time of installation to obtain the attitude difference R between them. ex and position difference t ex ,

[0035] 3. Transform the RTK pose to the radar position to obtain the RTK pose in radar time and radar coordinates: R′ rtk =R rtk *R ex

[0036] t′ rtk =R rtk *t ex +t rtk

[0037] 4. Let the radar's position be R L ,t L The difference between this pose and the pose represented by RTK is T L :

[0038] 5. Every time the shovel moves a distance L, it will make an overall optimization with RTK, so that T error The value of is optimized to the minimum, thus obtaining a point cloud in the global coordinate system. Let the point cloud PC of the i-th frame be i The global pose after optimization is R i ,t i ,

[0039] 6. Combine the last N frames of point clouds through global pose transformation to form a point cloud map.

[0040] Furthermore, the specific method in step S14 is as follows:

[0041] 1. The camera and the lidar are not completely aligned. There is a rotation R between them after installation. c2L ,t c2LAt the same time, the radar and the camera do not have the same frequency and have different timestamps. First, interpolate the pose on the camera timestamp to get R ci ,t ci , we can know the pose difference between the camera and the radar:

[0042] 2. The point cloud PC under the camera pose i for:

[0043] PC′ i =T diff *PC i

[0044] 3. PC' i Each point in the PC i The points in the table correspond to PC' i The point is projected onto the camera image, and the RGB color can be queried, that is, PC i The points in the PC are also colored. i The points in are 3-dimensional points, while the points on the image are 2-dimensional points. The method of projecting 3-dimensional points to 2-dimensional points is:

[0045] 4. Assume that after the camera is calibrated, the internal parameters are fx, fy, cx, cy, and the distortion parameters are k1, k2, k3, p1, p2. Let the 3D point be X, Y, Z. The point on the image plane at z = 1 is: xo = X / Z yo = Y / Z

[0046] The distance r between (xo, yo) and the camera origin is

[0047] 5. The point after dedistortion is: xd=xo(1+k1r 2 +k2r 4 +k3r 6 )+2p1xoyo+p2(r 2 +2xo 2 ) yd=yo(1+k1r 2 +k2r 4 +k3r 6 )+2p2xoyo+p1(r 2 +2yo 2 )

[0048] 6. Projecting the internal reference onto the image is: u=f x xd+c x v=f y yd+c y

[0049] The RGB color of the image can be queried through the coordinates (u, v). Beneficial effects

[0050] The present invention provides an unmanned mining car summoning system based on 3D reconstruction. Compared with the existing technology, it has the following advantages:

[0051] This unmanned mining truck summoning system, based on 3D reconstruction, automatically reconstructs a 3D model of the excavator's surroundings in real time and presents it to the excavator driver. To indicate the location where the unmanned mining truck should dock for loading, the driver simply gestures on the 3D model to indicate the desired docking position and orientation. This intuitive, what-you-see-what-you-get approach intuitively indicates the docking location before the truck actually arrives, eliminating the need to move the truck or bucket to determine the docking location. This facilitates the driver's docking operation, improves excavator operating efficiency, and ensures efficient coordination between the unmanned mining truck and the excavator. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] FIG1 is a schematic diagram of the hardware architecture structure of the present invention;

[0053] FIG2 is a flowchart of the parking position marking of the present invention;

[0054] FIG3 is a schematic diagram of the SLAM real-time mapping principle of the present invention.

[0055] In the figure: 1. Ground anchor seat; 2. Ground anchor rod; 3. Fixed seat; 4. Fixed ring; 5. Limiting assembly; 51. Connecting rod; 52. Gripping seat; 53. Nail seat; 6. Drill bit; 7. Transmission rod; 71. Transmission plate; 8. Adjusting handle; 9. Movable slot; 10. Positioning rod; 11. Extension plate; 111. Positioning slot. DETAILED DESCRIPTION

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0057] Example 1:

[0058] FIG1 shows an embodiment of an unmanned mine car calling system based on 3D reconstruction according to the present invention. An unmanned mine car calling system based on 3D reconstruction includes a system hardware architecture consisting of a GNSS, a computing unit, a touch screen, and a communication device;

[0059] The GNSS is equipped with two antennas, and the computing unit is electrically connected to a camera, a lidar, and an IMU inertial measurement unit;

[0060] The GNSS, the computing unit and the communication device are electrically connected, and the computing unit and the touch screen are electrically connected. The computing unit and the touch screen can be connected by wire, or by wireless or network.

[0061] Example 2:

[0062] FIG2 shows an embodiment of an unmanned mine car calling system based on 3D reconstruction according to the present invention. An unmanned mine car calling system based on 3D reconstruction includes the following steps:

[0063] S1, SLAM real-time mapping, collects information about the environment around the excavator through the system hardware architecture;

[0064] S2, point cloud image conversion model image, collects information images for conversion, and constructs the model image;

[0065] S3, touch screen presentation, the constructed model diagram is colored and sent to the touch screen, and the driver can view and select it;

[0066] S4, select the docking area and direction. The personnel select the docking location and direction of the mine car through the touch screen;

[0067] S5, sent to the dispatching system, the selected position and orientation information is integrated by the dispatching system and sent to the unmanned mining vehicle;

[0068] S6, the dispatch is sent to the vehicle end. After receiving the information, the unmanned mining vehicle stops according to the instructions.

[0069] Example 3;

[0070] As shown in Figures 1 to 3, an unmanned mining car summoning system based on 3D reconstruction includes the following specific steps:

[0071] Since the environment around the excavator is constantly changing, the map needs to be updated in real time. The update frequency can be set in the software parameters. One setting is to update based on time, which is every N minutes. The other setting is to update based on tasks, which is updated every time a truck is loaded. It can be set according to the actual situation on site.

[0072] 1. Pose Prediction

[0073] The pose prediction uses the imu data between two frames of lidar to perform pre-integration and predict the current pose of the lidar.

[0074] Suppose the acceleration a of two frames of imu data at time i and i+1 is i , a i+1 , angular velocity w i ,w i+1, the time interval is t, the acceleration bias is ba, the angular velocity bias is bg, the gravity acceleration is grav, and the position at time i is P i , the posture at time i is R i , the speed at time i is V i , we can predict the position, attitude, and speed at time i+1: R i+1 =R i *Exp(((w i +w i+1 ) / 2-bg)*t) V i+1 =V i +R i *((a i +a i+1 ) / 2-ba)*t) P i+1 =P i +(V i +V i+1 ) / 2*t

[0075] 2. Point Cloud Registration

[0076] Using the predicted pose as the initial value, transform the i+1th frame point cloud to the i-th frame point cloud, and then perform registration optimization using the following NDT (Normal Distribution Transform) method to obtain the accurate pose of the i+1th frame point cloud:

[0077] 1) Divide the point cloud of the i-th frame into several m*m*m grids, count all the points in each grid, and calculate their distribution on the x, y, and z axes respectively, and express them with mean and covariance:

[0078] mean Covariance

[0079] 2) Each grid corresponds to a probability density function:

[0080] 3) The transformed point cloud of the i+1th frame is also divided into a grid of size m*m*m. The probability density value of each point in the grid is calculated. The larger the sum of the probability densities, the better the registration of the two frame point clouds. The sum of the probability densities is the point cloud registration score:

[0081] 4) Since the point cloud in the i+1th frame is obtained through transformation, let the transformation be T. Then S can be derived from T to optimize T, and a T that maximizes the S value is obtained, which is the optimal transformation after registration.

[0082] 3. Overall optimization

[0083] Point cloud registration provides relatively accurate poses, but may accumulate errors after long periods of operation or interference. Fusion with RTK can eliminate these accumulated errors, resulting in a more accurate pose.

[0084] 1) Radar and RTK have different operating frequencies and timestamps. First, interpolate the RTK to get the RTK pose at the radar time. rtk ,t rtk express,

[0085] 2) The radar and RTK are installed at different positions on the shovel. The two positions are calibrated at the time of installation to obtain the attitude difference R between them. ex and position difference t ex ,

[0086] 3) Transform the RTK pose to the radar position to obtain the RTK pose in radar time and radar coordinates: R′ rtk =R rtk *R ex t′ rtk =R rtk *t ex +t rtk

[0087] 4) Let the radar pose be R L ,t L The difference between this pose and the pose represented by RTK is T L :

[0088] 5) Every time the shovel moves a distance L, it performs an overall optimization with RTK, letting T error The value of is optimized to the minimum, thus obtaining a point cloud in the global coordinate system. Let the point cloud PC of the i-th frame be i The global pose after optimization is R i ,t i ;

[0089] 6) The point clouds of the last N frames are transformed through the global pose and combined together to form a point cloud map.

[0090] 4. RGB coloring

[0091] The camera and the laser radar are not completely aligned. After installation, there is a rotation R between them. c2L ,t c2L At the same time, the radar and the camera do not have the same frequency and have different timestamps. First, interpolate the pose on the camera timestamp to get R ci ,t ci , we can know the pose difference between the camera and the radar:

[0092] Then the point cloud PC under the camera pose is i for:

[0093] PC′ i =T diff *PC i

[0094] PC' i Each point in the PC i The points in the table correspond to PC' i The point is projected onto the camera image, and the RGB color can be queried, that is, PC i The points in the PC are also colored. i The points in are 3-dimensional points, while the points on the image are 2-dimensional points. The method of projecting 3-dimensional points to 2-dimensional points is:

[0095] Assume that after the camera is calibrated, the internal parameters are fx, fy, cx, cy, and the distortion parameters are k1, k2, k3, p1, p2. Let the 3D point be X, Y, Z. The point on the image plane at z = 1 is: xo = X / Z yo = Y / Z

[0096] The distance r between (xo, yo) and the camera origin is

[0097] The point after dedistortion is: xd=xo(1+k1r 2 +k2r 4 +k3r 6 )+2p1xoyo+p2(r 2 +2xo 2 ) yd=yo(1+k1r 2 +k2r 4 +k3r 6 )+2p2xoyo+p1(r 2 +2yo 2 )

[0098] Projecting the internal parameters onto the image gives: u=f x xd+c x v=f y yd+c y

[0099] The RGB color of the image can be queried through the coordinates (u, v).

[0100] 4. Select the docking position and direction

[0101] 1. Data format

[0102] 2. Select operation

[0103] You can use 2 or 3 fingers to operate on the touch screen.

[0104] When using two fingers, press and hold the first finger, then move the second finger to select the desired orientation. A line with an arrow drawn from the first finger to the second finger displays the orientation in real time. Once the arrow appears, the first finger can be moved to adjust the docking position. Both fingers can also be lifted off the screen at any time; the arrow's position and orientation before leaving the screen will represent the docking position and orientation.

[0105] When operating with three fingers, press and hold the first finger first, then press the second and third fingers in sequence. Arrows from the first finger to the second finger and from the first finger to the third finger will be drawn on the screen in real time, indicating that the vehicle can be parked between these two arrows; the first finger can also be moved to adjust the parking position; the three fingers can also leave the screen at any time, and the position and direction of the arrow before leaving represent the position and direction of the parking space.

[0106] 5. Send to the dispatch system and vehicle end

[0107] The selected stop position and direction are transmitted to the dispatching system and the vehicle end via UDP or MQTT message format.

[0108] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. An unmanned mine car calling system based on three-dimensional reconstruction, characterized in that: Including system hardware architecture consisting of GNSS, computing unit, touch screen and communication equipment; The GNSS is equipped with two antennas, and the computing unit is electrically connected to a camera, a laser radar, and an IMU inertial measurement unit; The GNSS, the computing unit and the communication device are electrically connected, the computing unit and the touch screen are electrically connected, and the computing unit and the touch screen may be connected by wire, or by wireless or network.

2. An unmanned mine car calling system based on three-dimensional reconstruction, characterized in that The steps include: S1, SLAM real-time mapping, collects information about the environment around the excavator through the system hardware architecture; S2, point cloud image conversion model image, collects information images for conversion, and constructs a model image; S3, touch screen presentation, the constructed model diagram is colored and sent to the touch screen, and the driver can view and select; S4, select the docking area and direction. The personnel select the docking position and direction of the mine car through the touch screen; S5, sent to the dispatching system, the selected position and orientation information is integrated by the dispatching system and sent to the unmanned mining vehicle; S6, the dispatch is sent to the vehicle end. After receiving the information, the unmanned mining vehicle stops according to the instructions.

3. According to the unmanned mining car calling system based on three-dimensional reconstruction according to claims 1-2, it is characterized in that: The step S1 comprises the following specific steps: S11, posture prediction, posture prediction uses the imu data between two frames of lidar to perform pre-integration and predict the current radar posture; S12, point cloud registration, using the predicted pose as the initial value, and then performing registration optimization through the NDT method to obtain the accurate pose; S13, overall optimization, point cloud registration has relatively accurate posture, but there may be cumulative errors after long-term operation or interference. The cumulative errors can be eliminated by fusion with RTK, thus Get more accurate pose; S14, RGB coloring, by comparing the information of the camera and the lidar, the image can be colored according to the coordinate information.

4. The unmanned mine car calling system based on three-dimensional reconstruction according to claim 3 is characterized in that: In step S11, the acceleration a of two frames of imu data at time i and i+1 is assumed to be i , a i+1 , angular velocity w i ,w i+1 , the time interval is t, the acceleration bias is ba, the angular velocity bias is bg, the gravity acceleration is grav, and the position at time i is P i , the posture at time i is R i , the speed at time i is V i , we can predict the position, attitude, and speed at time i+1: R i+1 =R i *Exp(((w i +w i+1 ) / 2-bg)*t) V i+1 =V i +R i *((a i +a i+1 ) / 2-ba)*t) P i+1 =P i +(V i +V i+1 ) / 2*t 5. The unmanned mine car calling system based on three-dimensional reconstruction according to claim 4 is characterized in that: In the step S12, the initial value is to transform the i+1th frame point cloud to the i-th frame point cloud, and the accurate pose is the accurate pose of the i+1th frame point cloud.

6. The unmanned mining car calling system based on three-dimensional reconstruction according to claim 3 is characterized in that: The NDT method in step S12 is specifically as follows:

1. Divide the point cloud of the i-th frame into several m*m*m grids, count all the points in each grid, and count their distribution on the x, y, and z axes respectively, and express them with mean and covariance: Mean Covariance 2. Each grid corresponds to a probability density function:

3. Divide the transformed i+1th frame point cloud into a grid of m*m*m size, and calculate the probability density value of each point in the grid. The larger the sum of the probability density, the better the registration of the two frames of point clouds. The sum of the probability density is the score of the point cloud registration:

4. Since the point cloud in the i+1th frame is obtained through transformation, let the transformation be T. Then S can be derived from T to optimize T and obtain a T that maximizes the S value, which is the optimal transformation after registration.

7. The unmanned mine car calling system based on three-dimensional reconstruction according to claim 3 is characterized in that: The specific method in step S13 is as follows:

1. Radar and RTK have different operating frequencies and timestamps. First, interpolate the RTK to get the RTK pose at the radar time. rtk ,t rtk express, 2. The radar and RTK are installed at different positions on the shovel. The two positions are calibrated at the time of installation to obtain the attitude difference R between them. ex and position difference t ex , 3. Transform the RTK pose to the radar position to obtain the pose represented by RTK in radar time and radar coordinates: R′ rtk =R rtk *R ex t′ rtk =R rtk *t ex +t rtk 4. Assume the radar position is R L ,t L The difference between this pose and the pose represented by RTK is T L :

5. Every time the shovel moves a distance L, it will make an overall optimization with RTK, so that T error The value of is optimized to the minimum, thus obtaining a point cloud in the global coordinate system. Let the i-th frame point cloud PC i The global pose after optimization is R i ,t i , 6. Combine the point clouds of the most recent N frames through global pose transformation to form a point cloud map.

8. The unmanned mining car calling system based on three-dimensional reconstruction according to claim 3 is characterized in that: The specific method in the step S14 is as follows:

1. The camera and the laser radar are not completely overlapped. After installation, there is a rotation R between them. c2L ,t c2L At the same time, the radar and the camera do not have the same frequency and have different timestamps. First, interpolate the pose at the camera timestamp to get R ci ,t ci , we can know the difference between the camera and the radar:

2. The point cloud PC' under the camera pose i for: PC′ i =T diff *PC i 3. PC' i Each point in the PC i The points in the table correspond to PC' i The point is projected onto the camera image, and the RGB color can be queried, that is, PC i The points in the PC also get colors. i The points in are 3D points, while the points on the image are 2D points. The method of projecting 3D to 2D is:

4. Assume that after the camera is calibrated, the internal parameters are fx, fy, cx, cy, and the distortion parameters are k1, k2, k3, p1, p2. Let the 3D point be X, Y, Z. The point of the 3D point on the image plane at z = 1 is: xo=X / Z yo=Y / Z The distance r between (xo, yo) and the camera origin is 5. The points after dedistortion are: <h2 style=";text-align:left;direction:ltr">xd = xo(1 + k1r<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +k2r<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +k3r<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> )+2p1xoyo+p2(r<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2xo<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> ) <h2 style=";text-align:left;direction:ltr">yd=yo(1+k1r<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +k2r<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +k3r<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> )+2p2xoyo+p1(r<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2yo<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> ) 6. Projecting the internal reference onto the image is: u=f x xd+c x v=f y yd+c y 7. The RGB color of the image can be queried through the coordinates (u, v).

Images