I'm reading an article about Direct Linear Transformation which processes data using SVD, and the data set is standardized so that it has zero mean and unit standard deviation (n.b., some people call this transformation 'normalized').
In that article, it is said that for numerical reasons, the data set has to be normalized to make sure the DLT algorithm stable.
I wonder what are those numerical reasons? Does it mean if I have 2 data sets of the same objects, if no standardization is done, the DLT algorithm will give out 2 numerically different results?
In computer vision, Direct Linear Transform (DLT for short) is a method of homography estimation, it solves the overdetermined linear system via SVD $$Ah=b$$to find a solution $h$ under constraint $\|h\|=1$. Actually it finds the least square solution which minimize $\|Ah - b\|$.
I understand the basic idea of this algorithm, but it is recommended to standardize the data set before applying DLT on it, and here is a intro about how to do the standardization. It is lectured that data standardization is important to DLT, without standardization the results from DLT are not stable, and the reason is that DLT is quite dependent on the coordinates of the points in the data set.
I wonder why? Just because DLT involves solving the linear system using SVD and $A$ might be singular?