对极几何体姿势估计：对极线看起来不错但姿势错误

Question

我正在尝试使用OpenCV通过SIFT特征跟踪，FLANN匹配以及基本矩阵和基本矩阵的后续计算来估计摄像机相对于另一摄像机的一个姿势。分解基本矩阵后，我检查退化的配置并获得“正确的” R和t。

问题是，它们似乎永远都不对。我包括几个图像对：

1. 图像2沿Y轴旋转45度并与图像1处于相同位置。

图像对

结果

2. 图片2取自大约。沿负X方向几米远，沿负Y方向略有位移。大约 照相机沿Y轴姿势旋转45-60度。

图像对

结果

在第二种情况下，平移矢量似乎高估了Y方向的运动，而低估了X方向的运动。将旋转矩阵转换为Euler角时，在两种情况下均得出错误的结果。许多其他数据集也会发生这种情况。我尝试过在RANSAC，LMEDS等之间切换基本矩阵计算技术，现在使用RANSAC进行此操作，并且仅使用8点法的内点进行第二次计算。更改特征检测方法也无济于事。对极线似乎是正确的，并且基本矩阵满足x'.Fx = 0

我在这里错过根本上是错的东西吗？假设程序正确理解了对极几何，那么可能发生什么导致完全错误的姿势？我正在检查以确保点都位于两个摄像头的前面。任何想法/建议都将非常有帮助。谢谢！

编辑：尝试使用相同技术，将两个不同的校准摄像机间隔开；并将基本矩阵计算为K2'.F.K1，但平移和旋转仍然相去甚远。

参考代码

import cv2
import numpy as np

from matplotlib import pyplot as plt

# K2 = np.float32([[1357.3, 0, 441.413], [0, 1355.9, 259.393], [0, 0, 1]]).reshape(3,3)
# K1 = np.float32([[1345.8, 0, 394.9141], [0, 1342.9, 291.6181], [0, 0, 1]]).reshape(3,3)

# K1_inv = np.linalg.inv(K1)
# K2_inv = np.linalg.inv(K2)

K = np.float32([3541.5, 0, 2088.8, 0, 3546.9, 1161.4, 0, 0, 1]).reshape(3,3)
K_inv = np.linalg.inv(K)

def in_front_of_both_cameras(first_points, second_points, rot, trans):
    # check if the point correspondences are in front of both images
    rot_inv = rot
    for first, second in zip(first_points, second_points):
        first_z = np.dot(rot[0, :] - second[0]*rot[2, :], trans) / np.dot(rot[0, :] - second[0]*rot[2, :], second)
        first_3d_point = np.array([first[0] * first_z, second[0] * first_z, first_z])
        second_3d_point = np.dot(rot.T, first_3d_point) - np.dot(rot.T, trans)

        if first_3d_point[2] < 0 or second_3d_point[2] < 0:
            return False

    return True

def drawlines(img1,img2,lines,pts1,pts2):
    ''' img1 - image on which we draw the epilines for the points in img1
        lines - corresponding epilines '''
    pts1 = np.int32(pts1)
    pts2 = np.int32(pts2)
    r,c = img1.shape
    img1 = cv2.cvtColor(img1,cv2.COLOR_GRAY2BGR)
    img2 = cv2.cvtColor(img2,cv2.COLOR_GRAY2BGR)
    for r,pt1,pt2 in zip(lines,pts1,pts2):
        color = tuple(np.random.randint(0,255,3).tolist())
        x0,y0 = map(int, [0, -r[2]/r[1] ])
        x1,y1 = map(int, [c, -(r[2]+r[0]*c)/r[1] ])
        cv2.line(img1, (x0,y0), (x1,y1), color,1)
        cv2.circle(img1,tuple(pt1), 10, color, -1)
        cv2.circle(img2,tuple(pt2), 10,color,-1)
    return img1,img2


img1 = cv2.imread('C:\\Users\\Sai\\Desktop\\room1.jpg', 0)  
img2 = cv2.imread('C:\\Users\\Sai\\Desktop\\room0.jpg', 0) 
img1 = cv2.resize(img1, (0,0), fx=0.5, fy=0.5)
img2 = cv2.resize(img2, (0,0), fx=0.5, fy=0.5)

sift = cv2.SIFT()

# find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(img1,None)
kp2, des2 = sift.detectAndCompute(img2,None)

# FLANN parameters
FLANN_INDEX_KDTREE = 0
index_params = dict(algorithm = FLANN_INDEX_KDTREE, trees = 5)
search_params = dict(checks=50)   # or pass empty dictionary

flann = cv2.FlannBasedMatcher(index_params,search_params)

matches = flann.knnMatch(des1,des2,k=2)

good = []
pts1 = []
pts2 = []

# ratio test as per Lowe's paper
for i,(m,n) in enumerate(matches):
    if m.distance < 0.7*n.distance:
        good.append(m)
        pts2.append(kp2[m.trainIdx].pt)
        pts1.append(kp1[m.queryIdx].pt)

pts2 = np.float32(pts2)
pts1 = np.float32(pts1)
F, mask = cv2.findFundamentalMat(pts1,pts2,cv2.FM_RANSAC)

# Selecting only the inliers
pts1 = pts1[mask.ravel()==1]
pts2 = pts2[mask.ravel()==1]

F, mask = cv2.findFundamentalMat(pts1,pts2,cv2.FM_8POINT)

print "Fundamental matrix is"
print 
print F

pt1 = np.array([[pts1[0][0]], [pts1[0][1]], [1]])
pt2 = np.array([[pts2[0][0], pts2[0][1], 1]])

print "Fundamental matrix error check: %f"%np.dot(np.dot(pt2,F),pt1)
print " "


# drawing lines on left image
lines1 = cv2.computeCorrespondEpilines(pts2.reshape(-1,1,2), 2,F)
lines1 = lines1.reshape(-1,3)
img5,img6 = drawlines(img1,img2,lines1,pts1,pts2)

# drawing lines on right image
lines2 = cv2.computeCorrespondEpilines(pts1.reshape(-1,1,2), 1,F)
lines2 = lines2.reshape(-1,3)
img3,img4 = drawlines(img2,img1,lines2,pts2,pts1)

E = K.T.dot(F).dot(K)

print "The essential matrix is"
print E
print 

U, S, Vt = np.linalg.svd(E)
W = np.array([0.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0]).reshape(3, 3)

first_inliers = []
second_inliers = []
for i in range(len(pts1)):
    # normalize and homogenize the image coordinates
    first_inliers.append(K_inv.dot([pts1[i][0], pts1[i][1], 1.0]))
    second_inliers.append(K_inv.dot([pts2[i][0], pts2[i][1], 1.0]))

# Determine the correct choice of second camera matrix
# only in one of the four configurations will all the points be in front of both cameras
# First choice: R = U * Wt * Vt, T = +u_3 (See Hartley Zisserman 9.19)

R = U.dot(W).dot(Vt)
T = U[:, 2]
if not in_front_of_both_cameras(first_inliers, second_inliers, R, T):

    # Second choice: R = U * W * Vt, T = -u_3
    T = - U[:, 2]
    if not in_front_of_both_cameras(first_inliers, second_inliers, R, T):

        # Third choice: R = U * Wt * Vt, T = u_3
        R = U.dot(W.T).dot(Vt)
        T = U[:, 2]

        if not in_front_of_both_cameras(first_inliers, second_inliers, R, T):

            # Fourth choice: R = U * Wt * Vt, T = -u_3
            T = - U[:, 2]

# Computing Euler angles

thetaX = np.arctan2(R[1][2], R[2][2])
c2 = np.sqrt((R[0][0]*R[0][0] + R[0][1]*R[0][1]))

thetaY = np.arctan2(-R[0][2], c2)

s1 = np.sin(thetaX)
c1 = np.cos(thetaX)

thetaZ = np.arctan2((s1*R[2][0] - c1*R[1][0]), (c1*R[1][1] - s1*R[2][1]))

print "Pitch: %f, Yaw: %f, Roll: %f"%(thetaX*180/3.1415, thetaY*180/3.1415, thetaZ*180/3.1415)

print "Rotation matrix:"
print R
print
print "Translation vector:"
print T

plt.subplot(121),plt.imshow(img5)
plt.subplot(122),plt.imshow(img3)
plt.show()

Answer 1

有很多因素可能导致从点对应关系中无法准确估计相机位姿。您必须考虑的一些因素：-

(*) 8 点法可最大限度地减少代数误差 ( x'.Fx = 0)。通常最好找到一个最小化有意义的几何误差的解决方案。例如，您可以在 RANSAC 实现中使用重投影误差。

(*) 从 8 个点求解基本矩阵的线性算法对噪声敏感。亚像素精确点匹配、适当的数据归一化和准确的相机校准对于获得更好的结果都很重要。

(*) 特征点定位和匹配会导致噪声点匹配，因此通过求解代数方程 x'Fx 获得的解实际上应该用作初始估计，并且需要应用参数优化等进一步步骤来细化解。

(*) 某些双视图相机配置可能会导致解决方案不明确，因此需要进一步的方法（例如第三视图消歧）才能获得可靠的结果。