EssentialMatrix

import cv2
import numpy as np

from matplotlib import pyplot as plt

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

# Camera matrix from chessboard calibration
K = np.float32([[3541.5, 0, 2088.8], [0, 3546.9, 1161.4], [0, 0, 1]])
K_inv = np.linalg.inv(K)

def degeneracyCheckPass(first_points, second_points, rot, trans):
    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

# Read the images

img1 = cv2.imread('sam1.jpg',0)   # Query image
img2 = cv2.imread('sam1.jpg',0)  # Train image
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:
        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, 0.1, 0.99)

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

# 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)

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

print pt1
print pt2

print
print "The fundamental matrix is"
print F
print

# Should be close to 0
print "Fundamental matrix error check: %f"%np.dot(np.dot(pt2,F),pt1)
print

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)):
    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]))

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

# Start degeneracy checks
if not degeneracyCheckPass(first_inliers, second_inliers, R, T):
    # Second choice: R = U * W * Vt, T = -u_3
    T = - U[:, 2]
    if not degeneracyCheckPass(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 degeneracyCheckPass(first_inliers, second_inliers, R, T):
            # Fourth choice: R = U * Wt * Vt, T = -u_3
            T = - U[:, 2]

print "Translation matrix is"
print T
print "Modulus is %f" % np.sqrt((T[0]*T[0] + T[1]*T[1] + T[2]*T[2]))
print "Rotation matrix is"
print R

# Decomposing rotation matrix
pitch = np.arctan2(R[1][2], R[2][2]) * 180/3.1415
yaw = np.arctan2(-R[2][0], np.sqrt(R[2][1]*R[2][1] + R[2][2]*R[2][2])) * 180/3.1415
roll = np.arctan2(R[1][0],  R[0][0]) * 180/3.1415

print "Roll: %f, Pitch: %f, Yaw: %f" %(roll , pitch , yaw)

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