Error in ProjectToSO3(mat) (Python) function *** CHAPTER 3: RIGID-BODY MOTIONS ***

[DjoleMNE]

In Chapter 3, exercise 3.10 and in Appendix E (Linear Algebra Review, section E.3.2), the problem of a 3x3 matrix "escaping" the SO(3) manifold due to numerical roundoff errors, is presented. For the case when a given matrix is close to the SO(3), the solution for projecting the matrix to the closest matrix in SO(3) using singular-value decomposition, is defined. However, for the case when the matrix is not sufficiently close to SO(3), i.e. the determinant of resulting (SVD processed) matrix is < 0, the solution is not described theoretically, but it has been coded in the ProjectToSO3(mat) (Python) function. More specifically:

   if np.linalg.det(R) < 0:
    # In this case the result may be far from mat.
        R[:, s[2, 2]] = -R[:, s[2, 2]]
    return R

Nevertheless, the given solution code is falling and the error is the following:

---> 26         R[:, s[2, 2]] = -R[:, s[2, 2]]
     27     return R

IndexError: too many indices for array

Is it possible to share the reference/s (article, book), where a theoretical solution is provided for this special case, so readers of "CHAPTER 3: RIGID-BODY MOTIONS" and users of this function have better theoretical background for the aforementioned coded solution, and maybe implement the fix for the above error in the code?

[HuanWeng]

Hi Djordje, Thank you for pointing this out! This is a bug and should be

R[:, 2] = -R[:, 2]

Section E.3.2 of this file was our reference. A paper called Least-Squares Estimation of Transformation Parameters Between Two Point Patterns is also quite useful. I will fix this and add the reference to this function soon. Let me know if you have other questions. Many thanks, Huan Weng

[DjoleMNE]

Hi Huan,

thank you for the solution and references!

Best regards, Djordje Vukcevic