On the basis of studying the calibration method of the camera and the rotating platform, we designed an automatic camera calibration scheme based on four azimuth circles, which can realize the automatic sorting of the mark points. In order to improve the efficiency of identifying the center of the calibration plate, this paper uses RANSAC to improve the RED ellipse center detection algorithm. Experimental verification shows that the improved RED algorithm has increased 29.34% in anti-noise interference ability and 30.10% in center detection accuracy, which effectively guarantees the measurement stability and accuracy of the measurement system. Then, with the aid of the designed calibration board, we fit the rotation center of the turntable using the principle of three points in a circle, which provides a basis for the subsequent point cloud splicing. Experiments show that the back-projection error of the calibration method in this paper is less than 1 pixel, and the calibration accuracy is better than Zhang’s algorithm.
Stomatology is one of the first disciplines to introduce digital technology, and it is the dominant discipline in digitalization. In 1987, CAD/CAM technology has been applied in clinical denture restoration. The three-dimensional measurement of the dental jaw model is the basis of the oral CAM/CAD system. Only on the basis of obtaining the digital model of the dental jaw by measuring the three-dimensional point cloud, the doctor can use computer-aided technology to design and process the digital plan model of the dental jaw. In addition, most of the dental models commonly used in hospitals today are plaster models [
The dental model measurement system needs to include the following functions:
Aiming at the dental model, which is a small object with smooth surface and complex texture adjustment, this topic specially designed and processed a rotating table dedicated to the dental jaw model; built a dental jaw model measurement platform, and determined the hardware selection of the measurement system Models and software modules.
The software and hardware design diagram of the system is shown in
The measurement system
Selection requirements: This project is expected to control the average error of the dental model measurement to 0.05mm, the camera measurement range is 110mm×90mm, the camera to the object distance is 200~350mm, and the measurement depth of field is required to be 50mm.
CCD camera pixel resolution: The resolution of the captured image is determined by the camera resolution and the size of the target scene. In this measurement system, the resolution of the CCD camera in the horizontal and vertical directions should be 110mm/0.05 respectively. Only when mm=2200 and 90mm/0.05mm=1800 can meet the measurement standards.
The three-dimensional point cloud measurement system can ignore the color and texture characteristics of the tooth surface, and the dental model measurement system has certain requirements for noise and transmission speed. Therefore, in order to introduce as little noise as possible to increase the transmission speed, two models are selected in this article It is a CCD series USB3.0 camera of Hikvision MV-CE100-30M. The resolution of the camera is 3840×2748, the maximum frame rate is 7.1 fps, and the target surface size is 1/2.3 inches (6.41mm×4.59mm).
System magnification:
Lens focal length:
Normally, it is required that the size of the target surface of the lens should not be smaller than the size of the camera’s target surface. This topic chooses ZX-SF1620C, the target surface size is 1/3 inches, the focal length is 16mm, the TV distortion of the lens is less than 0.1%, and the aperture is F1.4. ~F16C.
The clarity of the projection of the projector directly affects the accuracy of the measurement, and the image of a general projector is not clear within 110mm×90mm. This measurement system selects the micro projector optical machine with LCoS projection technology. The optical machine projection control chip model is Texas Instruments DLP3010EVM-LC. The projector luminous flux is 50 lumens, the projection size is 5-200 inches, and the projection distance is 100mm~2500mm. The pixel resolution is 1280×720, and the micro-mirror pitch is 5.4um. Experiments show that it can clearly project in the range of 110mm×90mm at a distance of 200~400mm. DLP3010EVM-LC supports the burning of programming graphics. Burn the raster pictures of the specific frequency needed during the measurement, the image capture card will save the images taken by the camera and transmit them to the computer. The turntable control module is connected to the computer and cooperates with the rotating platform to perform high-precision object postures for the rotation angle.
The angle between the two CCD cameras is about 30°, the angle between the single camera and the projector is 15°, and the actual working distance is about 317mm. The measurement software part mainly completes the system calibration and the resolution of the grating structured light. Combining the results of the camera calibration and the rotation center calibration module, the software system can solve the three-dimensional information of the object surface under a certain angle of view, and finally according to the rotation direction and rotation of the turntable The angle unifies the measurement results under the same coordinate system, and obtains the surface profile information of the object.
Ideally, the camera’s imaging process is small hole imaging (as shown in
Schematic diagram of camera imaging
• Coordinate system
The optical imaging system of the camera uses a convex lens to map the image of a three-dimensional object in reality onto a two-dimensional plane, as shown in
Principle of camera imaging
• Coordinate system
The optical imaging system of the camera uses a convex lens to map the image of a three-dimensional object in reality onto a two-dimensional plane, as shown in
As shown in
The relationship between image coordinates and camera coordinates is:
The relationship between camera coordinates and world coordinates is shown in formula (
The pixel coordinates to world coordinates are sorted out as shown in formula (
The above formula can be converted as:
Among them, the parameters of the x matrix and the actual focal length matrix and the actual focal length, the distortion coefficient is related to the coordinates of the image center (principal point) and the angle between the camera and the lens. These are the internal parameters of the camera and have nothing to do with the movement of the camera and the pose of the camera. Therefore, the
• Coordinate system
Ideally, the camera is a pinhole model, but due to component manufacturing and processing technology, the optical imaging components of the camera often have nonlinear geometric distortions. In the 3D reconstruction process, if you do not consider correcting the camera distortion, then you cannot Restore the true coordinate value of the measured object, resulting in measurement failure. Camera distortion models can generally be divided into two types: radial distortion and tangential distortion. Radial distortion shows that all light rays are closer to the center of the image, so it is also called pincushion distortion, while tangential distortion is the opposite. The light will deviate to the surroundings. Also called barrel distortion, the two distortions are shown in
Camera distortion
The radial distortion model of the camera can be expressed as:
The tangential distortion model of the camera can be expressed as:
Unlike tangential distortion, radial distortion may need to be considered for higher orders but considering higher-order radial distortion coefficients may cause the calculation results to not converge and obtain high-precision calibration results. The calculation also increases the difficulty of solving. In actual measurement, only second-order or third-order distortion can be considered in camera calibration.
Zhang proposed a non-linear optimization method for camera calibration. The camera calibration can be completed by shooting the checkerboard pattern at multiple angles. The algorithm only needs to print a specific checkerboard pattern to achieve high-precision calibration of the camera., Low cost and simple to implement. However, in the process of using this method, the characteristic points on the calibration board, that is, the corner points between the checkerboards, must be accurately extracted, and the extracted points must be arranged in a certain order.
In order to ensure the accuracy of corner extraction, high-quality images are usually required. However, in practical applications, considering the cost factor, the quality of the camera and the calibration board are often uneven, making it possible to rasterize during the calibration process, leading to deviations in corner recognition, as shown in
Rasterization of the checkerboard calibration board
In order to solve the rasterization problem of the checkerboard calibration board, Xia Renbo et al. proposed a fully automatic camera calibration method based on circular marking points. The essence of this algorithm is to improve the corner detection to the center detection of the circular mark. The circular mark points have lower requirements for image quality and stronger anti-interference ability, but the mark point sorting process of the calibration algorithm proposed by Xia Renbo is more cumbersome. Liang Li et al. proposed a design plan for a plane calibration board with a progressive circle as the primitive. The checkerboard calibration template was retained, and the detection and sorting algorithm for the characteristic points of the circle was given. However, when the plane of the calibration target is relative to the optical axis of the camera, there is a risk of failure of the automatic sorting algorithm when it exceeds 90°. Hou Junjie and others proposed a calibration scheme based on concentric circles. The advantage of concentric circles is that the concentric circles in the world coordinate system are still concentric circles when they are mapped to the image coordinates, which can better ensure the accuracy of the center of the circle, and finally use the double Obtain the camera parameters based on the constraint relationship of the eye vision [
In view of this, this paper proposes an automatic detection and matching algorithm for the feature points of the calibration plate based on 4 concentric circular mark points. With Zhang’s camera parameter calculation method, it can realize the automatic calibration of the camera. The calibration board used in this paper is shown in
Design drawing of calibration board
The calibration process based on circular marking points is shown in the
The calibration process based on circular marking points
In order to facilitate the extraction of the dots directly through threshold segmentation after the image is collected, the calibration plate uses a black background and white pattern, and the surface is treated with aluminum oxide to prevent reflection. The physical picture of the calibration plate is shown in
Main view of calibration board
Since the dot will become an ellipse after the perspective transformation, the ellipse detection method can be used to obtain the set P of ellipses in the calibration plate.
The four large circles on the calibration board are arranged as shown in
As shown in
According to the positioned ellipses I and II, the point on the left side of the line and the farthest distance from the line in the calculation P is point A. Similarly, the position of the BCD point can be determined. The direction and position relationship between the calculated point and the straight line is as follows: If
In formula (
The sorting method of circular marker points in this article is as follows:
• Camera calibration experiment
In order to verify the feasibility of the system calibration algorithm in this chapter, this article has photographed the calibration board from multiple angles. Using the method in this chapter, the matching effect of different angles is shown in
Position relationship diagram between points and straight lines
Automatic matching of marking points at different angles
Reprojection Error, the correctness and accuracy of the algorithm can be matched with the verification mark point, which refers to the error between the point on the projection and the point on the image. Assuming that the mark point A on the calibration board is in the calibration process, the theoretical pixel point a will be obtained after the projection transformation, and the pixel point of the measured point after the distortion correction is set to a’, then at this time, between the two points Euclidean distance ǁ
In order to verify the accuracy of the calibration algorithm, this paper collected three sets of calibration data under different lighting environments and different angles, and compared the collected data with Zhang’s calibration method under the same conditions. In order to verify the reliability of the calibration algorithm, random noise was added to the collected calibration images. Let be the average back-projection error and be the maximum back-projection error. The calculation results of the back-projection error of the two calibration algorithms are shown in
THE BACK PROJECTION ERROR RESULTS OF THE ALGORITHM
1 | 0.191 | 0.650 |
2 | 0.177 | 0.801 |
3 | 0.266 | 0.502 |
BACK-PROJECTION ERROR RESULTS OF ZHANG'S CALIBRATION METHOD
1 | 0.613 | 1.124 |
2 | 0.691 | 2.316 |
3 | 0.827 | 1.528 |
On the basis of camera calibration, we used structured light three-dimensional measurement equipment to measure the dental jaw model and obtained the point cloud model.
Due to the noise of the system, after the complete 3D point cloud data of the dental jaw is obtained, since the point cloud data is discrete, it is also necessary to use OpenGL to render the point cloud data to obtain a complete 3D model of the dental jaw, and then the dental jaw model can be performed. In the measurement comparison, the standard dental jaw model was provided by the School of Stomatology of the Fourth Military Medical University (Air Force Military Medical University), and the standard dental jaw was used as the object to be measured. Then use the LJV7000 (with a measurement accuracy of 0.005mm), and use the measurement result as the true three-dimensional value of the standard jaw. Geomagic measures the distance between the feature points of the digital model of the tooth in this article, and compares it with the measurement result of the LJ-V7000 Compare [
MEASUREMENT INFORMATION OF DENTAL MODEL (UNIT: MM)
Name | Average measurement result of this system | Measurement standard deviation | LJ-V7000measurement results |
---|---|---|---|
Arch length | 63.87 | 0.10 | 63.91 |
Arch width | 58.02 | 0.12 | 58.03 |
41 teeth | 5.58 | 0.12 | 5.63 |
42 teeth | 6.52 | 0.09 | 6.45 |
43 teeth | 7.28 | 0.11 | 7.32 |
44 teeth | 7.89 | 0.17 | 7.89 |
45 teeth | 7.48 | 0.06 | 7.46 |
46 teeth | 11.00 | 0.07 | 10.97 |
31 teeth | 5.41 | 0.08 | 5.41 |
32 teeth | 6.39 | 0.10 | 6.31 |
33 teeth | 6.98 | 0.07 | 7.06 |
34 teeth | 7.79 | 0.12 | 7.76 |
35 teeth | 7.45 | 0.07 | 7.43 |
36 teeth | 11.05 | 0.13 | 10.95 |
Based on the calibration methods of Zhang Zhengyou and Xia Rinpo, a calibration plate based on four azimuth circles is designed. Based on this calibration plate, a corresponding camera calibration is proposed. The calibration method of the rotating platform and the ellipse detection part of the traditional RED ellipse detection algorithm uses RANSAC instead of the least square method to improve calibration accuracy. Finally, the calculation experiment proved the accuracy of the calibration method, guaranteed the accuracy and stability of the measurement system, which provides a theoretical basis for the subsequent point cloud splicing.
This work is partially supported by Science & Technology Program of Shaanxi Province with project “2021GY-005”.