使用基本矩阵校准相机的对极线是错误的

Question

我想获得校准相机的基本或基本矩阵（已给出 R、T、Ks）。

有两个摄像头。此步骤是否正确以获得基本矩阵和对极线？。我得到的结果是完全错误的。

# P1 - first transformation matrix world to cam1
# P2 - second transformation matrix world to cam2



def skew(x):
    x = x.flatten()
    return np.array([[0, -x[2], x[1]],
                    [x[2], 0, -x[0]],
                    [-x[1], x[0], 0]])

P21 = np.linalg.inv(P2) @ P1



R = P21[:3, :3]
T = P21[:3, 3]

# projection matrices
P1 = np.c_[np.eye(3), np.zeros(3)]
P2 = np.c_[R, T]

#essential matrix
E1 = skew(T) @ P2 @ np.linalg.pinv(P1)

pt1=(x1,y1)

pt1=undistort((x1,y1))

Pt1=[(x1-cx)/fx, (y1-cy)/fy]

Pt1h=[pt1[0], pt[1], 1.0]

Epliline1= E1@pt1h

如果我想使用失真参数，上述步骤是否正确？

在这里我将详细介绍相机：

相机1.

K1 = array([[1.13423076e+03, 0.00000000e+00, 1.02850079e+03],
       [0.00000000e+00, 8.25907478e+02, 5.63612899e+02],
       [0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])
dist1 = array([[-0.3921685 ,  0.18873927, -0.00285428, -0.00478303, -0.0478105 ]])
R1: array([[ 0.87748302,  0.47592599, -0.05931269],
       [-0.306075  ,  0.65090299,  0.69472541],
       [ 0.36924469, -0.59145562,  0.71682537]])
T1: array([[-1.86579737],
           [ 0.43997991],
           [ 2.80324197]])

相机2.

K2: array([[1.13968506e+03, 0.00000000e+00, 9.85549834e+02],
       [0.00000000e+00, 8.26601887e+02, 5.86985726e+02],
       [0.00000000e+00, 0.00000000e+00, 1.00000000e+00]]), 
dist2: array([[-3.80880220e-01,  1.83123508e-01, -5.59300663e-04,
         1.97688021e-04, -5.11559635e-02]])
R2 : array([[-0.99235374,  0.12149541, -0.0217467 ],
       [-0.10731501, -0.76228259,  0.63828578],
       [ 0.06097166,  0.63573903,  0.76949226]]), 
T2 : array([[0.5810168 ],
       [1.86135225],
       [1.6348977 ]])

Answer 1

您的 skew 函数只是叉积矩阵。像 OpenCV 一样，我首先移动第一台摄像机的世界原点（所以我只有 R 和 T 相对于第二台摄像机），然后我使用以下代码计算基本矩阵 F :

# Alternative formula by
# Multiple View Geometry in Computer Vision, by Richard Hartley and Andrew Zisserman
vv = skew( K1.dot(R.T).dot(T) )
F = (np.linalg.inv(K2).T).dot(self.R).dot(K1.T).dot(vv)

然后可以得到基本矩阵：

E = K2.T.dot(F).dot(K1)

结果是：

F [[ 1.13278823e-01 -1.35253176e+00 -4.88980254e+02]
 [-1.06844252e+00  4.04566728e-01  1.88300039e+02]
 [-5.54697063e+02  1.71231655e+03  6.35764837e+05]]

E [[  146431.66676676 -1273103.54255988 -1293288.66957507]
 [-1001726.06809778   276196.36212759  -564217.70767202]
 [-1213871.5038731    509423.0312259   -488699.08411468]]

我厌倦了编写这样的样板文件，所以我想出了一个 simple library 来管理立体声装置。我使用的完整代码如下：

import numpy as np
import simplestereo as ss

if __name__ == "__main__":
    
    res1 = (1280,720) # Camera resolution is required by initialisation 
    res2 = (1280,720) # but should not change F end E results.
    
    # Raw camera 1 parameters (an NumPy arrays)
    K1 = np.array([[1.13423076e+03, 0.00000000e+00, 1.02850079e+03],
           [0.00000000e+00, 8.25907478e+02, 5.63612899e+02],
           [0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])
           
    dist1 = np.array([[-0.3921685 ,  0.18873927, -0.00285428, -0.00478303, -0.0478105 ]])
    
    R1 = np.array([[ 0.87748302,  0.47592599, -0.05931269],
           [-0.306075  ,  0.65090299,  0.69472541],
           [ 0.36924469, -0.59145562,  0.71682537]])
    
    T1 = np.array([[-1.86579737],
               [ 0.43997991],
               [ 2.80324197]])
    
    # Camera 2           
    K2 = np.array([[1.13968506e+03, 0.00000000e+00, 9.85549834e+02],
           [0.00000000e+00, 8.26601887e+02, 5.86985726e+02],
           [0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])
            
    dist2 = np.array([[-3.80880220e-01,  1.83123508e-01, -5.59300663e-04,
             1.97688021e-04, -5.11559635e-02]])
    
    R2 = np.array([[-0.99235374,  0.12149541, -0.0217467 ],
           [-0.10731501, -0.76228259,  0.63828578],
           [ 0.06097166,  0.63573903,  0.76949226]])
            
    T2 = np.array([[0.5810168 ],
           [1.86135225],
           [1.6348977 ]])

    
    # As a convention, the world origin must be in the left camera.
    # Move the world origin into the first camera (IMPORTANT)
    R, T = ss.utils.moveExtrinsicOriginToFirstCamera(R1, R2, T1, T2)
    
    # Create the StereoRig
    rig = ss.StereoRig(res1, res2, K1, K2, dist1, dist2, R, T) 

    print("F", rig.getFundamentalMatrix())
    print("E", rig.getEssentialMatrix())

使用基本矩阵校准相机的对极线是错误的

Epipolar line using essential matrix for calibrated camera is wrong

python

opencv

computer-vision

stereo-3d

camera-calibration