Verification of projective reconstruction

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Hello

I'm trying to verify if the projective reconstruction that I've estimated is correct. I have an image dataset with given values of camera matrices Pm(i) (for metric reconstruction). Then, I found camera matrices P(i) using an algorithm of projective factorization.

From Hartley and Zisserman (p.460) we know that : Pm(i) = P(i)*H

So, I can find H corresponding using the pseudoinverse of P(1) : H = pinv(P(1))*Pm(1)

Than, by multilpying all others P(i) by H, I should obtain all others Pm(i). Is this approach correct? Thanks in advance!