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Editorial Team
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Asked: 2026-05-16T20:01:14+00:00

I created a simple test application to perform translation ( T ) and rotation

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I created a simple test application to perform translation (T) and rotation (R) estimation from the essential matrix.

  1. Generate 50 random Points.
  2. Calculate projection pointSet1.
  3. Transform Points via matrix (R|T).
  4. Calculate new projection pointSet2.
  5. Then calculate fundamental matrix F.
  6. Extract essential matrix like E = K2^T F K1 (K1, K2 – internal camera matrices).
  7. Use SVD to get UDV^T.

And calculate restoredR1 = UWV^T, restoredR2 = UW^T. And see that one of them equal to initial R.

But when I calculate translation vector, restoredT = UZU^T, I get normalized T.

restoredT*max(T.x, T.y, T.z) = T

How to restore correct translation vector?

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1 Answer

  1. Editorial Team

    I understand! I don’t need real length estimation on this step.
    When i get first image, i must set metric transformation (scale factor) or estimate it from calibration from known object. After, when i recieve second frame, i calculate normilized T, and using known 3d coordinates from first frame to solve equation (sx2, sy2, 1) = K(R|lambdaT)(X,Y,Z); and find lambda – than lambdaT will be correct metric translation…

    I check it, and this is true/ So… maybe who know more simple solution?

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