[ACCEPTED]-Essential Matrix from Fundamental Matrix in OpenCV-3d-reconstruction

Accepted answer
Score: 13

I don't know where you got that formulae, but 15 the correct one is E = K'^T . F . K (see Hartley & Zisserman, §9.6, page 14 257 of second edition)

K is the intrinsic 13 camera parameters, holding scale factors 12 and positions of the center of the image, expressed 11 in pixel units.

    | \alpha_u     0     u_0 |
K = |    0      \alpha_u v_0 |
    |    0         0      1  |

(sorry, Latex not supported 10 on SO)

Edit : To get those values, you can either:

  • calibrate the camera
  • compute an approximate value if you have the manufacturer data. If the lens is correctly centered on the sensor, then u_0 and v_0 are the half of, respectively, width and height of image resolution. And alpha = k.f with f: focal length (m.), and k the pixel scale factor: if you have a pixel of, say, 6 um, then k=1/6um. Example, if the lens is 8mm and pixel size 8um, then alpha=1000

Computing E

Sure, there 9 are several of ways to compute E, for example, if 8 you have strong-calibrated the rig of cameras, then 7 you can extract R and t (rotation matrix 6 and translation vector) between the two 5 cameras, and E is defined as the product 4 of the skew-symmetric matrix t and the matrix 3 R.

But if you have the book, all of this 2 is inside.

Edit Just noticed, there is even a 1 Wikipedia page on this topic!

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