python - 如何从 cv2.decomposeProjectionMatrix 理解欧拉角？

Question

我已经在互联网上搜索了几个小时关于如何理解cv2.decomposeProjectionMatrix.

我的问题似乎很简单，我有这架飞机的 2D 图像。 我希望能够从该图像中得出飞机相对于相机的方向。最终，我正在寻找外观和凹陷（即方位角和仰角）。我的图像中选择的 2D 特征有相应的 3D 坐标 - 在我的代码中列出。

# --- Imports ---
import os
import cv2
import numpy as np

# --- Main ---
if __name__ == "__main__":

    # Load image and resize
    THIS_DIR = os.path.abspath(os.path.dirname(__file__))
    im = cv2.imread(os.path.abspath(os.path.join(THIS_DIR, "raptor.jpg")))
    im = cv2.resize(im, (im.shape[1]//2, im.shape[0]//2))
    size = im.shape

    # 2D image points
    image_points = np.array([
                    (230, 410),     # Nose
                    (55, 215),      # right forward wingtip
                    (227, 170),     # right aft outboard horizontal
                    (257, 71),      # right forward vertical tail
                    (532, 96),      # left forward vertical tail
                    (605, 210),     # left aft outboard horizontal
                    (700, 283)      # left forward wingtip
                ], dtype="double")

    # 3D model points (estimated)
    model_points = np.array([
            (    0., -484.1, -18.4), # Nose
            (-758.1,  872.4, -15.9), # right forward wingtip
            (-470.3, 1409.4,  -7.9), # right aft outboard horizontal
            (-287.3, 1040.2, 323.3), # right forward vertical tail
            ( 287.3, 1040.2, 323.3), # left forward vertical tail
            ( 470.3, 1409.4,  -7.9), # left aft outboard horizontal
            ( 758.1,  872.4, -15.9)  # left forward wingtip
            ], dtype="double")

    # Estimated camera internals
    focal_length = size[1]
    center = (size[1]/2, size[0]/2)
    camera_matrix = np.array(
                             [[focal_length, 0, center[0]],
                             [0, focal_length, center[1]],
                             [0, 0, 1]], dtype = "double"
                             )
    # Lens distortion assumed to be zero 
    dist_coeffs = np.zeros((4,1)) 

    # Solving for persepective and point    
    _, rvec, tvec = cv2.solvePnP(model_points, image_points, camera_matrix, dist_coeffs, flags=cv2.SOLVEPNP_ITERATIVE)

    # Rotational matrix
    rmat = cv2.Rodrigues(rvec)[0]

    # Projection Matrix
    pmat = np.hstack((rmat, tvec))
    roll, pitch, yaw = cv2.decomposeProjectionMatrix(pmat)[-1]
    print('Roll: {:.2f}\nPitch: {:.2f}\nYaw: {:.2f}'.format(float(roll), float(pitch), float(yaw)))


    # Visualization
    # Points of interest from the nose
    poi = np.array([(model_points[0][0], model_points[0][1]+1e6, model_points[0][2])])     
    poi_end, jacobian = cv2.projectPoints(poi, rvec, tvec, camera_matrix, dist_coeffs)

    p1 = ( int(image_points[0][0]), int(image_points[0][1]) ) # nose
    p2 = ( int(poi_end[0][0][0]), int(poi_end[0][0][1]) ) # poi

    # Show the 2D features
    for p in image_points:
        cv2.circle(im, (int(p[0]), int(p[1])), 3, (0,0,255), -1)

    # Line from nose to projected point
    cv2.line(im, p1, p2, (255,0,0), 2)

    cv2.imshow("Output", im)
    cv2.waitKey(0)

下面是我的输出图像，如您所见，向后投影的点似乎没有遵循中心线。我不完全确定我的代码是否按预期工作，因此请随时提供有用的输入。

提前致谢！！