Decomposition of Euclidean homography matrix

Question

I am investigating Homography decomposition for some applications in control.

From the reference text of Ma which is a good and comprehensive one, I have implemented the code.

However, when I want to verify the resulting solutions i.e. 4 of them, I see not correct results. Specifically, we have (Re1, tde1) and (Re2, tde2) (stands for R_estimated_1...) By definition, X1 and X2 should be related by X2=R*X1+t (R, t are the real rotations and translation). Therefore, the estimated solutions should show the same characteristics i.e. X2=Re1*X1+tde1 in some sense (even tde1 = t/d with d unknown)

Since the book does not give explicit derivations of the 4 solutions, I'm actually doubting their correctness

If you have any comments, please lend me some help

Thank you

Answer 1

I've the missing step and concept and solved this problem. The chapter is correct. But some concepts are not very comprehensively explained.

The input to Ma's book's flow is Euclidean homography whereas I fed in a Projective homography which results in a wrong answer.