CODEWITHSUNDEEP
pythonopencvmatrixhomography
userX
userX

Reputation: 315

Why does OpenCV decomposed homography translation matrix have three values?

In a nutshell...the translation matrix returned from decomposing a homography matrix is actually a 3X1 matrix (a vector really). Yet, every description of a translation matrix is a 3X2 matrix.

Here are the two images (IR camera), the position 1 image (approx camera cartesian coords x = 0mm, y=300mm): initial image, x=0mm, y=300mm

This is the position 2 image (approx camera cartesian coords x = 680mm, y=0mm): final image, x=680 mm, y=0mm

I used the following with +90 points to determine the homography matrix (M):

M, mask = cv2.findHomography(source_pts, destination_pts, cv2.RANSAC,5.0)

This process picked out a good number of keypoints: matching keypoints between the two images

If you apply this homography matrix to the original image -- it works perfectly:

im_out = cv2.warpPerspective(img1,M, (640,480) )

homography applied to original image

and the output of the difference between the point set:

np.mean(dst_pts-src_pts , axis = 0)

array([[-305.16345, -129.94157]], dtype=float32)

is fairly close to the dot product of the homography matrix for a single point....

np.dot(M,[1,1,1])

array([-293.00352303, -132.93478376, 1.00009461])

I decomposed the homography matrix with the following command:

num, Rs, Ts,Ns = cv2.decomposeHomographyMat(M, camera_matrix)

This returns 4 solutions (num), a rotation matrix, a translation matrix, and Ns (cant remember what it is).

I'm interested in the translation matrix.

Firstly... The translation matrix, lists the 4 solutions (Is this correct?):

 Ts =
[array([[-0.60978834],[-0.26268874],[ 0.01638967]]), 
array([[ 0.60978834], [ 0.26268874],[-0.01638967]]), 
array([[-0.19035409],[-0.06628793],[ 0.63284046]]), 
array([[ 0.19035409], [ 0.06628793],[-0.63284046]])]

Secondly, and most puzzling is that each of the solutions has 3 values...

e.g., the first solution: [-0.6097, -0.2626, 0.01638967].

My understanding is that a translation matrix would have the form of : translation matrix

Here is my reference

How do I get from the values returned from the decomposition matrix to the translation matrix in the form above? **ie... how do I convert this: [-0.6097, -0.2626, 0.01638967]

to this format:** translation matrix

Thanks for your help.

Upvotes: 1

Views: 1446

Answers (1)

user7804910
user7804910

Reputation:

Let's take your first translation vector:

np.array([-0.60978834, -0.26268874, 0.01638967])

To me it looks like those are your tx, ty and tz estimated translation component. Plus those quantities make sense when I look at the image with the green dots. So I guess that your translation matrix in homogeneous coordinates would be:

M = np.array([[1, 0, 0, -0.60978834], [0, 1, 0, -0.26268874], [0, 0, 1, 0.01638967]])

Or simply:

M = np.array([[1, 0, -0.60978834], [0, 1, -0.26268874]])

If you ignore the tz component. Isn't this what you're looking for ?

Upvotes: 1

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