[eigen] Re: scaling in Umeyama

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Maybe to make a correction: the math does look good (i.e., properly implemented as in the original paper), however the values that we obtain for the translation are all off. Looking at our own implementation (and a few other implementations around the web), we calculate the translation simply by: t = u_y - R * u_x, so without multiplying with the c Scalar.

Did anyone perform any regression tests on ground truth data to see how it performs (with and without (42) as in the Umeyama paper)?



On 09/24/2012 12:23 PM, Radu B. Rusu wrote:
I noticed a small discrepancy between the documentation for Umeyama and the actual implementation, and I was wondering
if this is a bug.

http://eigen.tuxfamily.org/dox/group__Geometry__Module.html#gab3f5a82a24490b936f8694cf8fef8e60 states "with_scaling
Sets c=1  when false is passed." However, looking at http://eigen.tuxfamily.org/dox/Umeyama_8h_source.html, I see:

00157 const Scalar c = 1/src_var * svd.singularValues().dot(S);

which is then applied to the translation component. In our tests, this led to a bad translation while the rotation was
correct when with_scaling was set to false.


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