Fundamental Matrix
Step 1: Have two images
Step 2: Select at least 8 corresponding points. Use This tool. Example:
Points
pts1 = np.array([
(782, 189),
(778, 250),
(774, 304),
(771, 364),
(769, 415),
(767, 475),
(43, 499),
(44, 423),
(41, 356),
(40, 278),
(39, 207),
(40, 129)])
pts2 = np.array([
(892, 157),
(886, 234),
(879, 303),
(874, 378),
(869, 443),
(864, 515),
(172, 451),
(174, 396),
(174, 343),
(175, 285),
(174, 231),
(175, 170)])
Step 3: Construct A Matrix.
A = np.empty((len(pts1), 9))
A[:, 0] = pts1[:, 0] * pts2[:, 0]
A[:, 1] = pts1[:, 0] * pts2[:, 1]
A[:, 2] = pts1[:, 0]
A[:, 3] = pts1[:, 1] * pts2[:, 0]
A[:, 4] = pts1[:, 1] * pts2[:, 1]
A[:, 5] = pts1[:, 1]
A[:, 6] = pts2[:, 0]
A[:, 7] = pts2[:, 1]
A[:, 8] = 1.0
Step 4: Solve equation
U, D, Vt = np.linalg.svd(A)
F = Vt[8, :].reshape(3, 3).T
Step 5: Cleanup Matrix
U, D, Vt = np.linalg.svd(F)
D[2] = 0.0
F = U.dot(np.diag(D)).dot(Vt)
Bonus: Draw point from A as line into B
L2 = F.dot(np.hstack((pts1[0], 1)))
def f(x, L):
a, b, c = L
return int((-a*x-c) / b)
p1 = (-10000, f(-10000, L2))
p2 = (10000, f(10000, L2))
cv2.line(img2, p1, p2, (114, 38, 249))
Output:
Bonus: Draw point from B as line into A
L1 = F.T.dot(np.hstack((pts2[0], 1)))
def f(x, L):
a, b, c = L
return int((-a*x-c) / b)
p1 = (-10000, f(-10000, L1))
p2 = (10000, f(10000, L1))
cv2.line(img1, p1, p2, (114, 38, 249))
Output:
