I'm trying to find the fundamental matrix between two images. The points of correspondence in my images are given as follows -
pts1_list =
[
[224.95256042, 321.64755249],
[280.72879028, 296.15835571],
[302.34194946, 364.82437134],
[434.68283081, 402.86990356],
[244.64321899, 308.50286865],
[488.62979126, 216.26953125],
[214.77470398, 430.75869751],
[299.20846558, 312.07217407],
[266.94125366, 119.36679077],
[384.41549683, 442.05865479],
[475.28448486, 254.28138733]
]
pts2_list =
[
[253.88285828, 335.00772095],
[304.884552, 308.89205933],
[325.33914185, 375.91308594],
[455.15515137, 411.18075562],
[271.48794556, 322.07028198],
[515.11816406, 221.74610901],
[245.31390381, 441.54830933],
[321.74771118, 324.31417847],
[289.86627197, 137.46456909],
[403.3711853, 451.08905029],
[496.16610718, 261.36074829]
]
I have found a code that does what I'm looking for, but it looks like it works only for 3D points. I've linked the reference code links here and here, but fundamentally, the code snippets that I am looking at are -
def compute_fundamental(x1, x2):
'''Computes the fundamental matrix from corresponding points x1, x2 using
the 8 point algorithm.'''
n = x1.shape[1]
if x2.shape[1] != n:
raise ValueError('Number of points do not match.')
# Normalization is done in compute_fundamental_normalized().
A = numpy.zeros((n, 9))
for i in range(n):
A[i] = [x1[0, i] * x2[0, i], x1[0, i] * x2[1, i], x1[0, i] * x2[2, i],
x1[1, i] * x2[0, i], x1[1, i] * x2[1, i], x1[1, i] * x2[2, i],
x1[2, i] * x2[0, i], x1[2, i] * x2[1, i], x1[2, i] * x2[2, i],
]
# Solve A*f = 0 using least squares.
U, S, V = numpy.linalg.svd(A)
F = V[-1].reshape(3, 3)
# Constrain F to rank 2 by zeroing out last singular value.
U, S, V = numpy.linalg.svd(F)
S[2] = 0
F = numpy.dot(U, numpy.dot(numpy.diag(S), V))
return F / F[2, 2]
and
def setUp(self):
points = array([
[-1.1, -1.1, -1.1], [ 1.4, -1.4, -1.4], [-1.5, 1.5, -1], [ 1, 1.8, -1],
[-1.2, -1.2, 1.2], [ 1.3, -1.3, 1.3], [-1.6, 1.6, 1], [ 1, 1.7, 1],
])
points = homography.make_homog(points.T)
P = hstack((eye(3), array([[0], [0], [0]])))
cam = camera.Camera(P)
self.x = cam.project(points)
r = [0.05, 0.1, 0.15]
rot = camera.rotation_matrix(r)
cam.P = dot(cam.P, rot)
cam.P[:, 3] = array([1, 0, 0])
self.x2 = cam.project(points)
def testComputeFundamental(self):
E = sfm.compute_fundamental(self.x2[:, :8], self.x[:, :8])
In this code, the parameters that are being passed are 3 dimensional whereas my requirement is only a two-coordinate frame. I would like to know how to modify this code and how the A matrix should be calculated in my case. Thank you.
