CODEWITHSUNDEEP
computer-visioncamera-calibrationpose-estimation
crazyduck
crazyduck

Reputation: 147

Essential Matrix: Pure Rotation

I am trying to estimate an Essential Matrix from point correspondences. I set my init values to [rx,ry,rz,tx,ty,tz] to 0. But the first problem I encounter is, the Essential Matrix will be zero if all translation vector entries are zero. Am I right that Essential Matrix can not be used if I got pure rotation?

Math:

E = R [R^T t]x

Hartley,Zisserman: Multiple View Geometry p.257

Should I use a linear Algorithm like 'normalized 8-point' for calculating init values?

Upvotes: 2

Views: 1701

Answers (2)

Richard Hartley
Richard Hartley

Reputation: 127

If you try to estimate the essential matrix from a pure rotation (no motion) then here is what should happen. Suppose that x'_i = R x_i. We are looking for an essential matrix E = [t]x R' (possibly not the same as R, so I write it as R'). However, if t is anything at all and R' = R, then you find that x_i'^t [t]x R x_i = x_i'^t [t]x x_i', which will always be 0, because [t]x is skew-symmetric. Since this holds for any t, it follows that you cannot compute translation t from purely rotational motion. You should get the right value of R, however.

Upvotes: 3

Francesco Callari
Francesco Callari

Reputation: 11785

Under a pure rotation images are related by a homography.

Upvotes: 1

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