Table of contents
2. The concept of camera calibration
3. Application of camera calibration
Abstract: Camera calibration is an important technology in computer vision. It is used to determine the internal and external parameters of the camera in order to accurately convert the pixel coordinates in the image into physical coordinates in the real world. This article will introduce the concept, application and commonly used calibration methods of camera calibration.
1 Introduction
Computer vision is an important branch in the field of artificial intelligence. It realizes the understanding, analysis and processing of images and videos by simulating the human visual system. Camera calibration is one of the key technologies in computer vision. It is essential for achieving tasks such as accurate image measurement, three-dimensional reconstruction and attitude estimation.
2. The concept of camera calibration
Camera calibration refers to the process of determining the internal and external parameters of the camera through a series of images and known reference points. The intrinsic parameters include focal length, principal point position and distortion, etc., and the extrinsic parameters include the rotation matrix and translation vector of the camera. Through calibration, we can establish the conversion relationship from pixel coordinates to real-world coordinates, thereby achieving accurate mapping of images to the physical world.
3. Application of camera calibration
Camera calibration is widely used in the field of computer vision. Here are some common application scenarios:
- Three-dimensional reconstruction: By calibrating the camera, the size and position of the object can be accurately measured, thereby achieving three-dimensional reconstruction and modeling.
- Attitude estimation: By calibrating the camera, the attitude and rotation angle of the object can be accurately measured, thereby achieving target tracking and attitude estimation.
- Video surveillance: By calibrating the camera, objects in the video surveillance screen can be accurately positioned and tracked.
The following is a simple camera calibration example code, implemented using the OpenCV library:
pythonCopy codeimport cv2
import numpy as np
# 读取标定板上的角点坐标
def read_corners(file_path):
with open(file_path, 'r') as file:
lines = file.readlines()
corners = []
for line in lines:
x, y = line.strip().split(',')
corners.append((int(x), int(y)))
return corners
# 相机标定
def camera_calibration(image_paths, corner_file_path, board_size):
obj_points = [] # 世界坐标系中的角点坐标
img_points = [] # 图像平面中的角点坐标
objp = np.zeros((board_size[0] * board_size[1], 3), np.float32)
objp[:, :2] = np.mgrid[0:board_size[0], 0:board_size[1]].T.reshape(-1, 2) # 生成标定板上的角点坐标
for image_path in image_paths:
img = cv2.imread(image_path)
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, corners = cv2.findChessboardCorners(gray, board_size, None)
if ret == True:
obj_points.append(objp)
img_points.append(corners)
# 相机标定
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(obj_points, img_points, gray.shape[::-1], None, None)
# 保存相机参数
np.savez("camera_params.npz", mtx=mtx, dist=dist)
# 计算误差
mean_error = 0
for i in range(len(obj_points)):
img_points2, _ = cv2.projectPoints(obj_points[i], rvecs[i], tvecs[i], mtx, dist)
error = cv2.norm(img_points[i], img_points2, cv2.NORM_L2) / len(img_points2)
mean_error += error
print("相机标定完成。平均重投影误差：", mean_error / len(obj_points))
# 可视化标定结果
img = cv2.imread(image_paths[0])
h, w = img.shape[:2]
new_camera_matrix, roi = cv2.getOptimalNewCameraMatrix(mtx, dist, (w, h), 1, (w, h))
undistort_img = cv2.undistort(img, mtx, dist, None, new_camera_matrix)
cv2.imshow('Original Image', img)
cv2.imshow('Undistorted Image', undistort_img)
cv2.waitKey(0)
cv2.destroyAllWindows()
# 主函数
if __name__ == '__main__':
image_paths = ["image1.jpg", "image2.jpg", "image3.jpg"] # 输入标定图像路径
corner_file_path = "corners.txt" # 输入标定板上的角点坐标文件路径
board_size = (9, 6) # 输入标定板上的角点数量
corners = read_corners(corner_file_path)
if len(corners) != board_size[0] * board_size[1]:
print("角点数量不正确，请检查角点文件！")
else:
camera_calibration(image_paths, corner_file_path, board_size)Please note that the above code is only a sample code, and the specific implementation may require some adjustments based on the actual situation. At the same time, you need to specify the path of the image and the path of the corner coordinate file in the code. Before running the code, make sure you have the OpenCV library installed.
4. Camera calibration method
There are many methods for camera calibration. The following are some commonly used calibration methods:
- 2D image calibration: Use two-dimensional point pairs with known coordinates for calibration, and solve the camera parameters by minimizing the reprojection error.
- 3D object calibration: Use a three-dimensional object with known coordinates for calibration, and solve the camera parameters by minimizing the reprojection error.
- Linear calibration: Use image line segments with parallel straight lines for calibration, and use linear algebra methods to solve camera parameters.
- Nonlinear calibration: Use nonlinear optimization algorithms, such as Levenberg-Marquardt algorithm, to solve camera parameters.
The following is a simple camera calibration algorithm example code:
pythonCopy codeimport numpy as np
def camera_calibration(image_points, object_points, image_size):
num_images = len(image_points)
num_corners = len(object_points[0])
# 构建方程组
A = np.zeros((2 * num_corners * num_images, 12 + num_images))
b = np.zeros((2 * num_corners * num_images, 1))
for i in range(num_images):
for j in range(num_corners):
X, Y, Z = object_points[i][j]
x, y = image_points[i][j]
A[2 * (i * num_corners + j)] = [-X, -Y, -Z, -1, 0, 0, 0, 0, x * X, x * Y, x * Z, x]
A[2 * (i * num_corners + j) + 1] = [0, 0, 0, 0, -X, -Y, -Z, -1, y * X, y * Y, y * Z, y]
b[2 * (i * num_corners + j)] = -x
b[2 * (i * num_corners + j) + 1] = -y
# 解方程组
params = np.linalg.lstsq(A, b, rcond=None)[0]
params = np.append(params, 1) # 添加缩放因子
# 提取相机参数
fx = params[0]
fy = params[5]
cx = params[2]
cy = params[6]
k1 = params[-5]
k2 = params[-4]
p1 = params[-3]
p2 = params[-2]
# 构建相机矩阵
camera_matrix = np.array([[fx, 0, cx],
[0, fy, cy],
[0, 0, 1]])
# 构建畸变系数矩阵
distortion_coeffs = np.array([k1, k2, p1, p2])
return camera_matrix, distortion_coeffs
# 主函数
if __name__ == '__main__':
# 输入图像上的角点坐标
image_points = [
[(10, 20), (30, 40), (50, 60)],
[(15, 25), (35, 45), (55, 65)],
[(12, 22), (32, 42), (52, 62)]
]
# 输入世界坐标系中的角点坐标
object_points = [
[(0, 0, 0), (1, 0, 0), (2, 0, 0)],
[(0, 1, 0), (1, 1, 0), (2, 1, 0)],
[(0, 2, 0), (1, 2, 0), (2, 2, 0)]
]
# 输入图像尺寸
image_size = (100, 100)
# 进行相机标定
camera_matrix, distortion_coeffs = camera_calibration(image_points, object_points, image_size)
# 打印相机参数和畸变系数
print("Camera Matrix:")
print(camera_matrix)
print("Distortion Coefficients:")
print(distortion_coeffs)Please note that the above code is only a sample code, and the specific implementation may require some adjustments based on the actual situation. At the same time, the corner point coordinates on the image and the corner point coordinates in the world coordinate system need to be specified in the code.
5. Practical Guidelines
When calibrating the camera, you need to pay attention to the following points:
- Capture images from multiple angles and distances to cover different scenes and perspectives.
- Use high-quality reference points and make sure they are clearly visible in the image.
- Select an appropriate calibration plate or calibration object to meet the requirements of the calibration algorithm.
- Perform precise image preprocessing, including removal of distortion and noise.
- Use appropriate calibration methods and optimization algorithms to improve the accuracy and stability of calibration results.
6 Conclusion
Camera calibration is an important technology in computer vision, which plays a key role in achieving tasks such as accurate image measurement, three-dimensional reconstruction, and attitude estimation. This article introduces the concepts, applications and commonly used calibration methods of camera calibration, and provides some practical guidelines. Camera calibration is a complex process that requires comprehensive consideration of multiple factors, but through reasonable design and optimization, accurate and stable calibration results can be obtained. references:
- Zhang, Z. (2000). A flexible new technique for camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(11), 1330-1334.
- Hartley, R., & Zisserman, A. (2004). Multiple view geometry in computer vision. Cambridge University Press. Thank you for reading this article. I hope it will be helpful to your understanding of camera calibration. If you have any questions or ideas about camera calibration or other computer vision techniques, please feel free to leave a comment below.