之前在https://blog.csdn.net/fengbingchun/article/details/130039337 中介绍了相机的内参和外参，这里通过OpenCV中的接口实现对内参和外参的求解。
      估计相机参数的过程称为相机标定(camera calibration)。相机标定是使用已知的真实世界模式(例如棋盘)来估计相机镜头和传感器的外在参数(旋转和平移, Rotation(R) and Translation(t), 相机相对于某些世界坐标系的方向)和内在参数(例如镜头的焦距fx,fy、光学中心cx,cy、畸变系数k1,k2,k3,p1,p2)的过程，以减少相机缺陷引起的畸变误差。
      棋盘标定是执行相机标定和估计未知参数值的常用技术。棋盘非常适合用于相机标定：
      (1).它是平坦的(flat),棋盘上的所有点都在同一平面上；
      (2).有清晰的corners和points,它们都出现在直线上，易于在图像中检测到，棋盘上的正方形角非常适合定位它们，便于将3D真实世界坐标系中的点映射到相机2D像素坐标系上的点。
      OpenCV中相机标定步骤：
      (1).使用已知大小的棋盘格定义3D点的真实世界坐标；
      (2).从多幅图像捕获棋盘格的不同视点(different viewpoints)；
      (3).查找不同图像的棋盘格的2D坐标：
            查找棋盘角：findChessboardCorners
            完善棋盘角：cornerSubPix
      (4).标定相机：calibrateCamera

     以下是C++的实现：

int test_opencv_camera_calibration()
{
#ifdef _MSC_VER
	std::string path = "../../../test_images/camera_calibration/*.jpg";
#else
	std::string path = "test_images/camera_calibration/*.jpg";
#endif
	std::vector<std::string> images;
	cv::glob(path, images, false);
	if (images.size() == 0) {
		std::cout << "Error: the requested images were not found: " << path << "\n";
		return -1;
	}

	auto pos = path.find_last_of("/");
	std::string path_result = path.substr(0, pos + 1);

	auto get_image_name = [](const std::string& image) {
#ifdef _MSC_VER
		auto pos = image.find_last_of("\\");
#else
		auto pos = image.find_last_of("/");
#endif
		auto name = image.substr(pos + 1, image.size());
		return name.substr(0, name.size() - 4);
	};

	// the dimensions of checkerboard
	const int CHECKERBOARD[2] = { 11, 13 }; // rows,cols

	// the world coordinates for 3D points
	std::vector<cv::Point3f> pts_3d_world_coord;
	for (auto i = 0; i < CHECKERBOARD[1]; ++i) {
		for (auto j = 0; j < CHECKERBOARD[0]; ++j)
			pts_3d_world_coord.push_back(cv::Point3f(j, i, 0));
	}

	// vector to store the pixel coordinates of detected checker board corners 
	std::vector<cv::Point2f> pts_corners;
	cv::Mat frame, gray;
	bool success = false;

	// store vectors of 3D points for each checkerboard image
	std::vector<std::vector<cv::Point3f> > pts_3d;
	// store vectors of 2D points for each checkerboard image
	std::vector<std::vector<cv::Point2f> > pts_2d;

	for (auto i = 0; i < images.size(); ++i) {
		frame = cv::imread(images[i]);
		if (frame.empty()) {
			std::cout << "Error: fail to read image: " << images[i] << "\n";
			return -1;
		}
		cv::cvtColor(frame, gray, cv::COLOR_BGR2GRAY);

		// finding checker board corners
		success = cv::findChessboardCorners(gray, cv::Size(CHECKERBOARD[0], CHECKERBOARD[1]), pts_corners, cv::CALIB_CB_ADAPTIVE_THRESH | cv::CALIB_CB_FAST_CHECK | cv::CALIB_CB_NORMALIZE_IMAGE);
		if (!success) {
			std::cout << "Error: fail to find chess board corners: " << images[i] << "\n";
			return -1;
		}

		cv::TermCriteria criteria(cv::TermCriteria::EPS | cv::TermCriteria::MAX_ITER, 30, 0.001);

		// refining pixel coordinates for given 2d points
		cv::cornerSubPix(gray, pts_corners, cv::Size(11, 11), cv::Size(-1, -1), criteria);

		// displaying the detected corner points on the checker board
		cv::drawChessboardCorners(frame, cv::Size(CHECKERBOARD[0], CHECKERBOARD[1]), pts_corners, success);

		pts_3d.push_back(pts_3d_world_coord);
		pts_2d.push_back(pts_corners);

		//cv::imshow("Image", frame);
		//cv::waitKey(0);
		cv::imwrite(path_result + "result_" + get_image_name(images[i]) + ".png", frame);
	}

	cv::Mat camera_matrix, dist_coeffs, R, t;
	cv::calibrateCamera(pts_3d, pts_2d, cv::Size(gray.rows, gray.cols), camera_matrix, dist_coeffs, R, t);
	std::cout << "camera_matrix:\n" << camera_matrix << "\n"; // 3*3 matrix
	std::cout << "dist_coeffs:\n" << dist_coeffs << "\n"; // 5*1 vector
	std::cout << "R:\n" << R << "\n"; // each image, 3*1 vector
	std::cout << "t:\n" << t << "\n"; // each image, 3*1 vector

	return 0;
}

      终端输出结果如下：5幅测试图像来自于手机拍摄

      其中测试图像1.jpg角点检测结果如下所示：

      以下是参考C++实现的Python代码：

import cv2
import numpy as np
import glob
from sys import platform

def get_image_name(path):
	if platform == "win32":
		pos = path.rfind("\\")
	elif platform == "linux":
		pos = path.rfind("/")
	else:
		raise Exception(f"Error: Unsupported platform: {platform}")
	
	return path[pos+1:len(path)-4]

def camera_calibration(checkerboard_size, path):
	images = glob.glob(path)
	if len(images) == 0:
		raise Exception(f"Error: the requested images were not found: {path}")

	if platform == "win32":
		pos = images[0].rfind("\\")
	elif platform == "linux":
		pos = images[0].rfind("/")
	else:
		raise Exception(f"Error: Unsupported platform: {platform}")

	path_result = images[0][0:pos+1]

	# the world coordinates for 3D points
	pts_3d_world_coord = np.zeros((1, checkerboard_size[0] * checkerboard_size[1], 3), np.float32)
	pts_3d_world_coord[0,:,:2] = np.mgrid[0:checkerboard_size[0], 0:checkerboard_size[1]].T.reshape(-1, 2)
	#print(f"pts_3d_world_coord: {pts_3d_world_coord}")

	# store vectors of 3D points for each checkerboard image
	pts_3d = []
	# store vectors of 2D points for each checkerboard image
	pts_2d = []

	for name in images:
		frame = cv2.imread(name)
		if frame is None:
			raise Exception(f"Error: fail to read image: {frame}")

		gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
		ret, pts_corners = cv2.findChessboardCorners(gray, checkerboard_size, cv2.CALIB_CB_ADAPTIVE_THRESH + cv2.CALIB_CB_FAST_CHECK + cv2.CALIB_CB_NORMALIZE_IMAGE)
		if ret != True:
			raise Exception(f"Error: fail to find chess board corners: {name}")
		
		criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
		# refining pixel coordinates for given 2d points
		pts_corners = cv2.cornerSubPix(gray, pts_corners, (11,11), (-1,-1), criteria)

		# displaying the detected corner points on the checker board
		frame = cv2.drawChessboardCorners(frame, checkerboard_size, pts_corners, ret)

		pts_3d.append(pts_3d_world_coord)
		pts_2d.append(pts_corners)

		#cv2.imshow("Image", frame)
		#cv2.waitKey(0)
		cv2.imwrite(path_result + "result_" + get_image_name(name) + ".png", frame)

	ret, camera_matrix, dist_coeffs, R, t = cv2.calibrateCamera(pts_3d, pts_2d, gray.shape[::-1], None, None)
	print(f"Camera matrix:\n{camera_matrix}")
	print(f"dist_coeffs:\n{dist_coeffs}")
	print(f"R:\n{R}")
	print(f"t:\n{t}")

if __name__ == "__main__":
	# the dimensions of checkerboard
	CHECKERBOARD = (11, 13)
	# images path
	path = "../../test_images/camera_calibration/*.jpg"
	camera_calibration(CHECKERBOARD, path)

	print("test finish")

      终端输出结果如下：与C++一致

      GitHub：https://github.com/fengbingchun/OpenCV_Test