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Not sure but in epipolar constraint x2^T * E * x1 = 0 where x2 is a 2d point in second image, and x1 is in first image.

when x1 = x2, we expect that the R is identity right? Than we can rewrite above as x1^T * [t]x * x1 = 0 whew [t]x is a skew-symmetric form of t.

In linear algebra, product the same vector with a skew-symmetric matrix always give 0 so there is no solution for t I guess.