[Insight-users] Question about ICP convergence

[Luis Ibanez]

Hi Jose,

In ICP there is no guarantee that the metric is going to
decrease monotonically. In fact, there is no guarantee
that the optimization is going to converge at all.

The directions in which the optimization jumps are computed
based on local derivatives, but the Metric itself is based
not in a C1 continuous function but in a reconfigurable function,
because the association of closest points is renewed at every
iteration.

In other words, you are optimizing a piece-wise function with
many small little pieces that are only C0 continuous, not C1
continous.

You could only improve the probability of a monotonic behavior
if you limit the optimizer to perform steps that are very small
compared to the topography of the cost function.


This, of course, if you are using the LevenbergMarquard optimizer.





BTW:   An experiment *always* is a better proof of truth
        than a demonstration in a Paper.    :-)



   Lord Kelvin mathematically demonstrated in the 1900s that
   it was impossible to build flying machines that were heavier
   than air.., still there are thousands of airplanes in the air
   at this very moment.


   That's why science is made out of *reproducible* claims.
   That's why reading Journals that only have text, pictures
   and equations is not good enough for a serious technical
   community.



     Regards,


       Luis



----------------------------
José Santamaría López wrote:
> Hi all,
> 
>   I have tested the ICP algorithm for several point
> sets and noticed how, in some executions of the method,
> the value of the error metric increases in (aprox.) first
> five iterations and, after that, it turns and decreases
> for remaining iterations, achieving a good registration ...
> Is it a correct behaviour ? The author of the original
> ICP proposal demonstrated the monotonic behaviour of the
> method.
> 
> Thanks all.
> 
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