python - 对极几何姿态估计 : Epipolar lines look good but wrong pose

Question

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

问题是，他们似乎从来都不是对的。我包括几个图像对:

1. 图像 2 沿 Y 轴旋转 45 度且位置与 w.r.t. 相同。图 1。

图像对

结果

1. 图片 2 取自大约。沿负 X 方向几米远，负 Y 方向轻微位移。约相机姿势沿 Y 轴旋转 45-60 度。

图像对

结果

第二种情况下的平移向量似乎高估了 Y 方向的运动而低估了 X 方向的运动。在这两种情况下，转换为欧拉角的旋转矩阵都会给出错误的结果。许多其他数据集也会发生这种情况。我已经尝试在 RANSAC、LMEDS 等之间切换基本矩阵计算技术，现在我正在使用 RANSAC 进行计算，第二次计算仅使用 8 点法的内点。更改特征检测方法也无济于事。对极线似乎是适当的，基本矩阵满足x'.F.x = 0

我是否遗漏了一些根本性的错误？如果程序正确理解对极几何，可能会发生什么导致完全错误的姿势？我正在检查以确保点位于两个摄像头前面。任何想法/建议都会非常有帮助。谢谢!

编辑:尝试使用相同的技术，将两个不同的校准相机隔开；并计算基本矩阵为 K2'.F.K1，但平移和旋转仍然有很大差距。

Code供引用

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

有很多因素会导致根据点对应关系对相机位姿的估计不准确。您必须考虑的一些因素:-

(*) 8 点法最小化代数误差 ( x'.F.x = 0)。通常最好找到一个能最小化有意义的几何误差的解决方案。例如，您可以在 RANSAC 实现中使用重新投影误差。

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

(*) 特征点定位和匹配导致噪声点匹配，因此通过求解代数方程 x'Fx 得到的解应该真正用作初始估计，并且需要应用参数优化等进一步步骤优化解决方案。

(*) 一些双 View 相机配置可能会导致模糊的解决方案，因此需要进一步的方法(例如第三 View 消歧)以获得可靠的结果。