详细相机标定方法与代码

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前言

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PnP(Perspective-n-Point)是求解3D到2D点的对应方法。不论是相机和雷达的标定还是相机和相机的标定都可以使用PNP来解决，即通过不同坐标系下相同的点对求解变换矩阵。
这里相机多用棋盘格中的角点来实现点的提取。流行方法为张正友标定法，至于详细原理可点击我的博客https://www.cnblogs.com/tangjunjun/p/16240878.html查看，本博客主要使用代码
实现外参求解与相机标定的内参和畸变系数求解。

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代码及标定图链接：https://pan.baidu.com/s/1ujX19IUV0EPSIMyIcBnClA?pwd=r63z （相机标定与外参求解.zip文件）
提取码：r63z

一、相机标定-内参/畸变系数求解

相机标定，求解内参与畸变系数，该部分需使用棋盘格采集数据获得参数，其代码如下：

# 相机标定，主要求内参和畸变系数
def calibration_camera(img_root, rand_count=20):
    board_h = 8
    board_w = 11
    objp = np.zeros((board_h * board_w, 3), np.float32)
    objp[:, :2] = np.mgrid[0:board_w, 0:board_h].T.reshape(-1, 2)  # 将世界坐标系建在标定板上，所有点的Z坐标全部为0，所以只需要赋值x和y
    objp = 60 * objp  # 打印棋盘格一格的边长为2.6cm
    obj_points = []  # 存储3D点
    img_points = []  # 存储2D点
    images = glob.glob(os.path.join(img_root, '*.jpg'))  # 黑白棋盘的图片路径
    random.shuffle(images)
    if rand_count > len(images):
        rand_count = len(images)

    for fname in images[:rand_count]:
        img = cv2.imread(fname)
        gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        size = gray.shape[::-1]
        ret, corners = cv2.findChessboardCorners(gray, (board_w, board_h), None)
        if ret:
            obj_points.append(objp)
            corners2 = cv2.cornerSubPix(gray, corners, (5, 5), (-1, -1),
                                        (cv2.TERM_CRITERIA_MAX_ITER | cv2.TERM_CRITERIA_EPS, 30, 0.001))
            if [corners2]:
                img_points.append(corners2)
            else:
                img_points.append(corners)
            cv2.drawChessboardCorners(img, (board_w, board_h), corners, ret)  # 记住，OpenCV的绘制函数一般无返回值
            cv2.imshow("img", img)
            cv2.waitKey(10)
    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(obj_points, img_points, size, None, None)
    # v_rot_mat, _ = cv2.Rodrigues(np.array(v_rot).reshape(-1))
    # print("旋转矩阵=", v_rot_mat)
    # print("内参=", mtx)
    # print("畸变系数=", dist)
    # print("旋转向量=", rvecs)
    # print("平移向量=", tvecs)

    # 反投影误差
    total_error = 0
    for i in range(len(obj_points)):
        imgpoints2, _ = cv2.projectPoints(obj_points[i], rvecs[i], tvecs[i], mtx, dist)
        error = cv2.norm(img_points[i], imgpoints2, cv2.NORM_L2) / len(imgpoints2)
        total_error += error
    # print("total error: ", total_error / len(obj_points))
    return mtx, dist, total_error

二、图像矫正

通过畸变系数矫正，获得矫正的图像，代码如下：

# 消除畸变
def revise_img(img_root, mtx, dist):
    mtx = np.array(mtx)
    dist = np.array(dist).reshape(1, 5)
    img = cv2.imread(img_root)
    h, w = img.shape[:2]
    newcameramtx, roi = cv2.getOptimalNewCameraMatrix(mtx, dist, (w, h), 1, (w, h))
    # undistort
    dst = cv2.undistort(img, mtx, dist, None, newcameramtx)
    # crop the image
    x, y, w, h = roi
    dst = dst[y:y + h, x:x + w]
    cv2.imwrite('./revise_img.jpg', dst)
    return dst

三、外参求解

使用PnP方法求解外参，代码如下：

# 旋转向量和平移向量求解
def calibration_RT(points_3D, points_2D, cameraMatrix, distCoeffs):
    points_3D = np.array(points_3D)
    points_2D = np.array(points_2D)
    cameraMatrix = np.array(cameraMatrix).astype(np.float32)
    distCoeffs = np.array(distCoeffs).astype(np.float32)
    _, rvecs, tvecs, inliers = cv2.solvePnPRansac(points_3D.reshape(-1, 1, 3),
                                                  points_2D.reshape(-1, 1, 2),
                                                  cameraMatrix,
                                                  distCoeffs
                                                  )
    R, _ = cv2.Rodrigues(rvecs)
    print('R:\n', R)
    print('rvecs:\n', rvecs)
    print('tvecs:\n', tvecs)

    return R, tvecs

四、结果展示

实验使用下图方格为一个单位，获得部分点进行参数标定实验。通过代码遍历每个方格点获得世界坐标系转像素坐标系的图，如下：

更具体内容可点击我的博客园

总结