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CN112649095B - Large-range accurate temperature measurement system based on affine transformation and optical/infrared double lenses - Google Patents

Large-range accurate temperature measurement system based on affine transformation and optical/infrared double lenses Download PDF

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CN112649095B
CN112649095B CN202011347249.1A CN202011347249A CN112649095B CN 112649095 B CN112649095 B CN 112649095B CN 202011347249 A CN202011347249 A CN 202011347249A CN 112649095 B CN112649095 B CN 112649095B
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田青
张华�
孙昊立
姚锐琳
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Jiangsu Jicui Future City Application Technology Research Institute Co ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01JMEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J5/00Radiation pyrometry, e.g. infrared or optical thermometry
    • G01J5/52Radiation pyrometry, e.g. infrared or optical thermometry using comparison with reference sources, e.g. disappearing-filament pyrometer
    • G01J5/53Reference sources, e.g. standard lamps; Black bodies
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01JMEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J5/00Radiation pyrometry, e.g. infrared or optical thermometry
    • G01J5/80Calibration
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T3/00Geometric image transformations in the plane of the image
    • G06T3/02Affine transformations
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00Image enhancement or restoration
    • G06T5/80Geometric correction
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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    • G06T7/80Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration

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Abstract

A large-range accurate temperature measurement system based on affine transformation and optical/infrared double lenses comprises a background system, terminal equipment and a binocular camera with an optical lens and a thermal imaging lens; image information acquired by the camera is sent to the terminal equipment for processing, and a processing result is sent to the background system; the background system sends control information to the terminal equipment, and the terminal equipment sends a control instruction to the camera; the camera is arranged in the pedestrian passage, and a temperature calibration black body is deployed at the farthest end of the detection range. The technical scheme overcomes the defects of the prior art, can obtain the affine transformation matrix more accurately, effectively solves the problem of position mismatching during pedestrian identification and body temperature detection, and can ensure the accuracy of pedestrian identification and the accuracy and efficiency of measurement of the body surface temperature of pedestrians.

Description

Large-range accurate temperature measurement system based on affine transformation and optical/infrared double lenses
Technical Field
The invention relates to a pedestrian body temperature accurate detection technology, in particular to a large-range pedestrian body temperature accurate detection system based on image pixel point matching, which adopts a binocular camera of an optical lens/thermal imaging lens to acquire images.
Background
The modern pedestrian detection method not only needs to obtain the position information of the pedestrian, but also more importantly obtains the body surface temperature of the pedestrian so as to provide technical support for the whole epidemic situation prevention and control system. However, the traditional method of using a monocular thermal imaging camera to detect the temperature of the pedestrian often leads to inaccurate body temperature detection and poor detection effect. If the pedestrian detection by the body temperature gun and the optical lens is adopted, the body temperature detection efficiency is reduced, and great pressure is brought to traffic.
Disclosure of Invention
In order to solve the above technical problem, the present technical solution provides a new pedestrian temperature detection system, which specifically comprises:
a large-range accurate temperature measurement system based on affine transformation and optical/infrared double lenses comprises a background system, terminal equipment and a binocular camera with an optical lens and a thermal imaging lens; image information acquired by the camera is sent to the terminal equipment for processing, and a processing result is sent to the background system; the background system sends control information to the terminal equipment, and the terminal equipment sends a control instruction to the camera; the camera is arranged in the pedestrian passage, and a temperature calibration black body is deployed at the farthest end of the detection range;
a lens mounting height H ═ H + tan α × D of the camera, in which: d is the monitoring distance, h is the height below the human head, and alpha is the overlooking angle of the lens axis;
the matching step of the double-lens image pixel points of the optical lens and the thermal imaging lens comprises the following steps:
1) taking a camera and a chessboard calibration plate, and fixing the relative positions of the camera and the chessboard;
the camera respectively adopts an optical lens and a thermal imaging lens to shoot the chessboard calibration plate, and respectively records the position of the central point of each black grid in the chessboard calibration plate; obtaining an internal reference matrix of the thermal imaging lens, and correcting the distortion of the thermal imaging lens by adopting the internal reference matrix of the thermal imaging lens; the method of correction comprises the steps of:
1.1) converting a source image pixel coordinate system into a camera coordinate system through an internal reference matrix, and correcting camera coordinates of an image through a distortion coefficient;
1.2) converting the corrected camera coordinate system into an image pixel coordinate system through an internal reference matrix, and assigning a new image coordinate according to the pixel of the source image coordinate;
2) the camera shoots the chessboard calibration plate by adopting an optical lens and records the angular point position of the chessboard calibration plate; obtaining an internal reference matrix of the optical lens, and correcting the distortion of the optical lens by adopting the internal reference matrix of the optical lens;
the correction method is the same as the steps 1.1) to 1.2);
3) fixing an optical lens and a thermal imaging lens; sequentially electrifying each resistance wire of the chessboard calibration plate at the position d to obtain the optical coordinates and the infrared coordinates of the central point of each black lattice at the position and obtain an affine transformation matrix G;
4) the positions of the chessboard are changed to d 1 、d 2 ,...d n Obtaining an affine transformation matrix G between the images obtained by the optical lens and the thermal imaging lens at the corresponding positions by adopting the method in the step 3) 1 、G 2 ,...G n
5) And 4) performing least square fitting on each element in the affine transformation matrix obtained in the step 4) to obtain an affine transformation matrix G' corresponding to the picture pixel at each position.
The principle that this scheme realizes detecting on a large scale does:
the prior art has the following problems: the traditional temperature measuring gun and temperature measuring door scheme has limited coverage and needs special personnel to watch, and the efficiency is lower.
Problem two that prior art exists: visible light and infrared image information acquired by the camera are sent to the terminal equipment for processing, and a processing result (temperature information of a detected target is obtained according to the image information of the detected target) is sent to the background system; the background system sends control information to the terminal equipment, and the terminal equipment sends a control instruction to the camera, so that the technology used in the process is mature. However, the matching of the pixel points of the optical lens and the infrared lens is also a technical point. Raw images are the source of data processed by a terminal device (e.g., a computer, etc.). If the original image information is more accurate, system resources required in the processing process are less, and the result is more accurate.
The camera is arranged in the pedestrian passageway, and the temperature calibration black body is arranged at the farthest end of the detection range, which is also a necessary technology of the thermal imaging camera. The calibration black body is fixed, so that the instantaneity and timeliness of calibration are facilitated.
In the prior art, a deployment mode of an optical lens and an infrared lens is used for realizing large-range multi-target detection, a person target and a position (such as a forehead) needing temperature measurement in a coverage range can be detected through the optical lens, temperature information of an object in the coverage range can be obtained through the infrared lens, and the body temperature of each person target can be obtained through matching of pixel points of an image of the optical lens and an image of the infrared lens. However, the matching of the pixel points of the optical lens and the infrared lens is a technical difficulty.
The calibration and pixel point matching method for the optical lens and the infrared lens provided by the invention solves the technical difficulty, and the optical lens image and the infrared lens image can be matched through an affine transformation matrix G':
Figure BDA0002800292300000021
the matching and the deployment scheme are combined to realize large-range multi-target accurate temperature measurement with the width of more than 5 meters.
Drawings
FIG. 1 is a schematic deployment view of the present detection system;
FIG. 2 is a schematic view of the camera mounting height H calculation;
FIG. 3 is a schematic diagram of the camera coverage width W calculation;
FIG. 4 is a schematic view of a calibration aid;
fig. 5 is a schematic diagram of a process for matching pixel points of a dual-lens image of an optical lens and a thermal imaging lens.
Detailed Description
The following explains the technical scheme of the invention by taking an accurate detection system for the body temperature of a certain pedestrian as an example:
in the system construction of the camera adopting the thermal imaging lens, due to the particularity of the thermal imaging lens, firstly, the lens of the camera is calibrated, and then an imaging affine transformation matrix of the camera is obtained, so that the problem of position mismatching during pedestrian identification and body temperature detection is effectively solved, and the accuracy of pedestrian identification and the accuracy and efficiency of measurement of the body surface temperature of pedestrians are ensured.
The equipment used for the construction of the system mainly comprises a calibration plate shifting device used in the process of calibrating the lens. The device adopts seven degree of freedom arms to connect the calibration board, and moves the checkerboard to the designated position through the mechanical arms in sequence according to the checkerboard position requirement. The position of the checkerboard is determined by three-dimensional coordinates d (x, y, z) by taking the coordinate of the central point of the checkerboard as a standard, and the origin of the coordinate is the central point of the root plane of the mechanical arm.
The system mainly comprises the following steps:
firstly, calibrating an optical lens and a thermal imaging lens:
1. an 8X 8 chessboard calibration plate made of optical glass is selected, black grids and white grids are arranged on the surface of the chessboard, and a round hole is arranged in the center of each black grid for placing a resistance wire.
2. The optical camera is fixed, the calibration plate is positioned by the aid of the calibration plate shifting device, each resistance wire is electrified in sequence, and the position of each point is recorded. And after the recording is finished, the lens is changed into a thermal imaging lens, and the previous operation is repeated. At the moment, the position (x) of the central pixel coordinate point of the black grid where the resistance wire is located can be obtained by the optical lens and the infrared lens respectively g ,y g ) And (x) i ,y i )。
3. Calibrating the coordinate points obtained in the step 2 to obtain an internal parameter matrix K of the thermal imaging lens 1
4. Shooting a standard 8 multiplied by 8 checkerboard through an optical lens to obtain the position of each angular point, and obtaining an internal reference matrix K of the optical lens through calibration 2
The camera internal reference reflects the projection relationship between the camera coordinate system and the image coordinate system. The calibration of the internal parameter of the camera is to obtain the internal parameter f of the camera by shooting checkerboard images at different angles x ,f y ,c x ,c y And a distortion coefficient [ k ] 1 ,k 2 ,p 1 ,p 2 ,k 3 ]And the like.
The distortion problem of the lens can be corrected through the internal reference matrix of the thermal imaging lens and the internal reference matrix of the optical lens.
Matching image pixel points of optical lens and thermal imaging lens
1. The positions of the optical lens and the thermal imaging lens are fixed through the calibration plate shifting device, and each resistance wire is electrified in sequence, so that optical coordinates and infrared coordinates of 32 points below the position can be obtained, and an affine transformation matrix G can be obtained at the moment.
2. Moving the grid position to d by means of a scale plate displacement device 1 、d 2 ,...d n Affine transformation matrix sequence G between two lens images at different positions can be obtained 1 、G 2 ,...G n
3. And (5) performing least square fitting (without constraint conditions) on each element in the affine transformation matrix obtained in the sixth step to obtain affine transformation matrices corresponding to the picture pixels at multiple positions.
The above-mentioned calibration plate displacement means is shown in fig. 4, in which 1 is a calibration plate and 2 is a robot arm.
Thirdly, large-range accurate temperature measurement is realized through equipment deployment
By arranging the temperature measuring equipment and the temperature calibration black body, accurate temperature measurement with the coverage width of more than 5 meters is realized.
1. Calculation of Camera mounting height H, refer to FIG. 2
The height of the lens is as follows: h1.5 +0.18 × D (common individual pixel model)
D is the monitoring distance, and D is the monitoring distance,
the average height below the head of a person is 1.5 m,
alpha is the top view angle of the camera,
the recommended top view angle is 10 DEG, tan10 DEG approximatively 0.18
The H was about 2.58 meters.
2. The camera coverage width W is calculated, see FIG. 3
Taking a horizontal viewing angle of 45 degrees and a vertical viewing angle of 34 degrees of the infrared thermal imaging camera as an example, calculating:
the horizontal depression angle of the camera is 10-13 degrees, the calibration distance between the camera and the temperature calibration black body is 6m (the same as the monitoring distance),
W=tan22.5×L≈5.05m
L-H-1.5 m
From the above calculations, the device is field mounted, see fig. 1 (in the figure, 3 is the camera, 4 is the temperature calibration black).
Referring to fig. 5, as a technical key point and a technical difficulty, the step of matching the pixel points of the dual-lens images of the optical lens and the thermal imaging lens includes:
1) taking a camera and a chessboard calibration plate, and fixing the relative positions of the camera and the chessboard;
the camera respectively adopts an optical lens and a thermal imaging lens to shoot the chessboard calibration plate, and respectively records the position of the central point of each black grid in the chessboard calibration plate; obtaining an internal reference matrix K1 of the thermal imaging lens, and correcting the distortion of the thermal imaging lens by adopting the internal reference matrix K1;
the distortion of the image includes: radial distortion and tangential distortion.
Radial distortion is due to processing problems of the lens itself and tangential distortion is due to mounting problems.
The correction process is divided into two steps:
1. converting a source image pixel coordinate system into a camera coordinate system through an internal reference matrix, and correcting the camera coordinate of the image through a distortion coefficient;
2. and the corrected camera coordinate system is converted into an image pixel coordinate system through the internal reference matrix, and is assigned to a new image coordinate according to the pixels of the source image coordinate.
The specific method comprises the following steps:
the internal reference matrix is:
Figure BDA0002800292300000041
the known camera has a focal length f (unit: mm), a picture size m × n (unit: pixel), a sensor size i × j (unit: micrometer), and a pixel size p × p. The internal reference matrix can be obtained from the above known conditions as follows:
Figure BDA0002800292300000042
the tilt parameter β is usually 1
Namely, it is
Figure BDA0002800292300000043
The internal reference matrix is understood to mean that the values in the matrix are related to the camera internal parameters only and do not change with the position of the object.
fx, fy is a parameter representing the focal length (which is the distance of the vacuum from the projection screen, similar to the human eye and retina, and is measured in pixels), representing the physical dimensions of each pixel in the x and y directions of the image plane.
U0, v0 represents the coordinates of the origin of the image coordinate system in the pixel coordinate system, and is therefore m/2, n/2.
If the image pixel coordinate system has distortion-free coordinates (u, v), the distortion-free coordinates fall into uOv coordinate system (u, v) after warp distortion and tangential distortion d ,v d ) Upper part of
Comprises the following steps:
Figure BDA0002800292300000051
for the distortion:
radial distortion:
Figure BDA0002800292300000052
tangential distortion:
Figure BDA0002800292300000053
x ', y' are normalized coordinates of a pixel value in the image coordinate system, and u, v are distortion-free coordinates. The distortion location coordinate is a combination of the radial distortion coordinate and the tangential distortion coordinate.
I.e. u d =u‘ Diameter of pipe +u‘ Cutting machine ,v d =v‘ Diameter of a pipe +v‘ Cutting machine
Wherein
u‘ Diameter of a pipe =u‘=u(1+k 1 r 2 +k 2 r 4 +k 3 r 6 ),
u‘ Cutting machine =v‘=v(1+k 1 r 2 +k 2 r 4 +k 3 r 6 )
K 1 ,k 2 ,k 3 ,p 1 ,p 2 Is the distortion parameter, K 1 ,k 2 ,k 3 Is the radial distortion parameter, p 1 And p is a tangential distortion parameter. r is 2 =x 2 +y 2
2) The camera shoots the chessboard calibration plate by adopting an optical lens and records the angular point position of the chessboard calibration plate; obtaining an internal reference matrix of the optical lens, and correcting the distortion of the optical lens by adopting the internal reference matrix;
3) based on steps 1) and 2), adopting a calibration plate shifting device; fixing an optical lens and a thermal imaging lens; sequentially electrifying each resistance wire of the chessboard calibration plate at the position d to obtain the optical coordinates and the infrared coordinates of the central point of each black lattice at the position and obtain an affine transformation matrix G;
the process of obtaining the affine transformation matrix G from the optical coordinates and the infrared coordinates comprises the following steps:
recording optical coordinates (x, y) and infrared coordinates (m, n); the translation and flip experienced by the imaging of the optical lens to the infrared lens image:
Figure BDA0002800292300000054
wherein A represents a rotation matrix, B represents a translation matrix,
for example, if the picture is rotated by θ, A is
Figure BDA0002800292300000055
When the picture is shifted by (x, y), then B is
Figure BDA0002800292300000056
The affine transformation method comprises the following steps:
Figure BDA0002800292300000061
convert it to a homogeneous coordinate matrix, with a unique solution
Figure BDA0002800292300000062
This system of equations has 6 unknowns, so at least 6 equations (3 systems of equations) are required, i.e. at least 3 points in the coordinates of the optical and infrared lenses are required.
4) The positions of the chessboard are changed to d 1 、d 2 ,...d n Obtaining an affine transformation matrix G between two lens images in respective positions 1 、G 2 ,...G n
5) Performing least square fitting (without constraint conditions) on each element in the affine transformation matrix obtained in the step 4) to obtain an affine transformation matrix G' corresponding to the picture pixels at each position;
the process of step 5):
Figure BDA0002800292300000063
recording the relative displacement (x, y, z) of the transformed board position from the initial board, then there is a unique k 1 ,k 2 ,k 3 And b, after any position is transformed, the variance of the affine transformation matrix and the affine transformation matrix of the initial position is minimum.
Namely:
Figure BDA0002800292300000064
therefore, when obtaining
Figure BDA0002800292300000065
b, G' satisfies the condition.
Figure BDA0002800292300000066
Namely, it is
Figure BDA0002800292300000067
The chessboard calibration plate is an 8X 8 chessboard calibration plate made of optical glass, and black lattices and white lattices are sequentially arranged on the surface of the chessboard at intervals; a round hole is arranged at the center of the black lattice, and a resistance wire is placed in the round hole;
when recording the black grid central points under the optical lens and the thermal imaging lens, sequentially electrifying each resistance wire, and then photographing by using different lenses by using a camera to obtain the positions of the black grid central pixel coordinate points of the resistance wires under the optical lens and the thermal imaging lens.
The technical scheme overcomes the defects of the prior art, can obtain the affine transformation matrix more accurately, effectively solves the problem of position mismatching during pedestrian identification and body temperature detection, and can ensure the accuracy of pedestrian identification and the accuracy and efficiency of measurement of the body surface temperature of pedestrians.

Claims (3)

1. A large-range accurate temperature measurement system based on affine transformation and optical/infrared double lenses comprises a background system, terminal equipment and a binocular camera with an optical lens and a thermal imaging lens; image information acquired by the camera is sent to the terminal equipment for processing, and a processing result is sent to the background system; the background system sends control information to the terminal equipment, and the terminal equipment sends a control instruction to the camera;
the human target and the position needing temperature measurement in the coverage range are detected through the optical lens, the body temperature information in the coverage range is obtained through the thermal imaging lens, and the body temperature of each human target is obtained through matching of double-lens image pixel points of an optical lens image and a thermal imaging lens image, and the human target temperature detection system is characterized in that: the camera is arranged in the pedestrian passage, and a temperature calibration black body is deployed at the farthest end of the detection range;
a lens mounting height H ═ H + tan α × D of the camera, in which: d is the monitoring distance, h is the height below the human head, and alpha is the overlooking angle of the lens axis;
the matching step of the double-lens image pixel points of the optical lens of the camera and the thermal imaging lens comprises the following steps:
1) taking a camera and a chessboard calibration plate, and fixing the relative positions of the camera and the chessboard; black lattices and white lattices which are sequentially alternated are arranged on the surface of the chessboard calibration plate, and a round hole is arranged at the center of each black lattice for placing a resistance wire;
shooting a chessboard calibration plate by a camera thermal imaging lens, and recording the position of the central point of each black grid in the chessboard calibration plate; obtaining an internal reference matrix of the thermal imaging lens, and correcting the distortion of the thermal imaging lens by adopting the internal reference matrix of the thermal imaging lens; the method of correction comprises the steps of:
1.1) converting a source image pixel coordinate system into a camera coordinate system through an internal reference matrix, and correcting the camera coordinate of an image through a distortion coefficient;
1.2) converting the corrected camera coordinate system into an image pixel coordinate system through an internal reference matrix, and assigning a new image coordinate according to the pixel of the source image coordinate;
2) the camera shoots the chessboard calibration plate by adopting an optical lens and records the angular point position of the chessboard calibration plate; obtaining an internal reference matrix of the optical lens, and correcting the distortion of the optical lens by adopting the internal reference matrix of the optical lens;
the correction method is the same as the steps 1.1) to 1.2);
3) fixing an optical lens and a thermal imaging lens; sequentially electrifying each resistance wire for the chessboard calibration plate at the position d to obtain the optical coordinates and the infrared coordinates of each black grid central point of the chessboard calibration plate at the position d to obtain an affine transformation matrix G;
4) the positions of the chessboard are changed to d 1 、d 2 ,...d n Obtaining the corresponding bit by adopting the method of the step 3)Affine transformation matrix G between images obtained by an underlying optical lens and thermal imaging lens 1 、G 2 ,...G n
5) Performing least square fitting on each element in the affine transformation matrix obtained in the step 4) to obtain an affine transformation matrix G' corresponding to the picture pixel at each position;
the specific method of the step 1.2) comprises the following steps:
setting an internal reference matrix as:
Figure FDA0003640805790000011
given that the focal length of the camera is f, the size of the image is m × n, the size of the sensor is i × j, and the pixel size is p × p, the internal reference matrix is obtained as follows:
Figure FDA0003640805790000021
Figure FDA0003640805790000022
the tilt parameter beta is equal to 1 and,
namely that
Figure FDA0003640805790000023
Each value in the internal reference matrix is only related to the internal parameters of the camera and does not change along with the position change of the object; f. of x ,f y Is a parameter of focal length, which is the distance of the vacuum from the projection screen, the measure of focal length being pixel-specific;
u 0 ,v 0 representing the coordinates of the origin of the image coordinate system in the pixel coordinate system, so the coordinates are m/2, n/2;
if the image pixel coordinate system has distortion-free coordinates (u, v), the coordinates fall into uOv coordinate system (u, v) after radial distortion and tangential distortion d ,v d ) In the above, there are:
Figure FDA0003640805790000024
for the distortion:
radial distortion:
Figure FDA0003640805790000025
tangential distortion:
Figure FDA0003640805790000026
x ', y' are normalized coordinates of a pixel value in a camera coordinate system, and u, v are undistorted coordinates; the distortion location coordinate is a combination of the radial distortion coordinate and the tangential distortion coordinate,
i.e. u d =u′ Diameter of pipe +u′ Cutting machine ,v d =v′ Diameter of a pipe +v′ Cutting machine Wherein:
u′ diameter of pipe =u′=u(1+k 1 r 2 +k 2 r 4 +k 3 r 6 ),
v′ Cutting machine =v′=v+[p 1 (r 2 +2v 2 )+2p 2 uv)],
k 1 ,k 2 ,k 3 Is the radial distortion parameter, p 1 ,p 2 Is a tangential distortion parameter; r is 2 =x 2 +y 2
2. The large-range accurate temperature measurement system based on the affine transformation and the optical/infrared dual lens as claimed in claim 1, wherein in the step 1), the chessboard calibration plate is an 8 x 8 chessboard calibration plate made of optical glass;
recording the center points of the black grids under the optical lens and the thermal imaging lens, sequentially electrifying each resistance wire, and then photographing by using different lenses by using a camera to obtain the positions of the pixel coordinate points of the center points of the black grids where the resistance wires are positioned under the optical lens and the thermal imaging lens.
3. The system according to claim 1, wherein in step 3), the process of obtaining the affine transformation matrix G from the optical coordinates and the infrared coordinates comprises:
setting optical coordinates (x, y) and infrared coordinates (m ', n'); the translation and flipping experienced by the imaging of the optical lens to the thermal imaging lens image:
Figure FDA0003640805790000031
wherein A is an internal reference matrix of the optical lens, and B is an internal reference matrix of the thermal imaging lens;
the affine transformation method comprises the following steps:
Figure FDA0003640805790000032
it is converted into a homogeneous coordinate matrix, with a unique solution:
Figure FDA0003640805790000033
the equation set has 6 unknowns, so at least 6 equations are needed, namely at least 3 points are needed to correspond to the coordinates of the images of the optical lens and the thermal imaging lens;
wherein A 'represents a rotation matrix, B' represents a translation matrix,
if the image is rotated by θ, then A' is
Figure FDA0003640805790000034
When the image is translated by (x, y), then B' is
Figure FDA0003640805790000035
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