[Insight-users] RE: VersorRigid3DTransform & Optimization

Fri, 9 Jan 2004 11:49:36 -0800

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Hi Luis,

Sorry about that. Here it is. I also forgot to add in my previous message
that I manually set the Translation parameters all to 0, so they are not
what would come back from the CenteredTransformIntiializer.

Thanks
Radhika

-----Original Message-----
From: Luis Ibanez [mailto:luis.ibanez at kitware.com] 
Sent: Friday, January 09, 2004 11:49 AM
To: Radhika Sivaramakrishna
Cc: 'insight-users at itk.org'
Subject: Re: [Insight-users] RE: VersorRigid3DTransform & Optimization

Hi Radhika,

It seems that you forgot to attach the optimization
results to your previous message.

Could you please resend ?

---

In any case,
about your questions:

1) Using multi resolution is always good.
    It increases robustness and speeds up
    the registration process.

    You will find multi-resolution examples
    in the SoftwareGuide

    http://www.itk.org/ItkSoftwareGuide.pdf

    Section 8.6, pdf-page 281.

2) There is not a direct way to set a tolerance
    for the Metric value in the optimizer. However
    you can easily implement this in the Observer
    of the Optimizer. Simply check for the metric
    value on the Execute() method of the Command/
    Observer and if it matches your stopping
    criteria you invoke

       optimizer->StopOptimization()

     Otherwise you could use the GradientMagnitudeTolerance
     which is a stopping criterion based on the magnitude
     of the gradient. Therefore indicating how flat is
     the metric value in the current position. In theory,
     the gradient will tend to be zero when you are in
     critical point (minimum/maximum/saddle) of the metric.

     Please look at the documentation of the RegularStep
     GradientDescentOptimizer.
http://www.itk.org/Insight/Doxygen/html/classitk_1_1RegularStepGradientDesce
ntBaseOptimizer.html

3)  The step length stopping criteria is based on the
     fact that each time the value of the metric increases
     the step length is divided by two and its direction
     is reversed.  If the optimizer enters a valley this
     process may lead convergence at the bottom of the valley.
     What you specify with MinimumStepLength is how much you
     care about precision.

     In other words, if you set the minimum step length to
     0.001 you are saying that you are satisfied with a
     rotation precision of +- 0.01 radians which is about
     0.57 degrees.  If you are too exigent on the precision,
     e.g. 10-7 radians, the optimizer will take a long time
     to converge until its oscillations are smaller than this
     value.  So you basically have a trade-off between
     precision and optimization time.

Thanks

    Luis

-------------------------------
Radhika Sivaramakrishna wrote:

> Hi Luis,
> 
> I decided to start with an initial rotation of 9 degrees (my real 
> rotation is 10 degrees) and I was trying to study what parameters to use 
> to recover this. I am attaching part of the results at each iteration.
> 
> I used the following:
> 
> Maximum step length = 0.1
> Minimum step length = 0.01
> 
> I find the metric comes down to a low value of about 37 and then starts 
> climbing again. Looking at these results, would you recommend
> 
> 1) going to a smaller max step length
>           OR
> 2) Using a hierarchical multiresolution approach.
> 
> I also have another question:
> 
> Is there a way to set a minimum value of metric to go down to? How is 
> this related to the parameter MinimumStepLength?
> 
> Thanks
> Radhika
> 
>  
> 

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<P><FONT SIZE=3D2>Hi Luis,</FONT>
</P>

Sorry about that. Here it is. I also forgot to add in =
my previous message that I manually set the Translation parameters all =
to 0, so they are not what would come back from the =
CenteredTransformIntiializer.

<P><FONT SIZE=3D2>Thanks</FONT>
<BR><FONT SIZE=3D2>Radhika</FONT>
</P>
<BR>

<P><FONT SIZE=3D2>-----Original Message-----</FONT>
<BR><FONT SIZE=3D2>From: Luis Ibanez [<A =
HREF=3D"mailto:luis.ibanez at kitware.com">mailto:luis.ibanez at kitware.com</=
A>] </FONT>
<BR><FONT SIZE=3D2>Sent: Friday, January 09, 2004 11:49 AM</FONT>
<BR><FONT SIZE=3D2>To: Radhika Sivaramakrishna</FONT>
<BR><FONT SIZE=3D2>Cc: 'insight-users at itk.org'</FONT>
<BR><FONT SIZE=3D2>Subject: Re: [Insight-users] RE: =
VersorRigid3DTransform &amp; Optimization</FONT>
</P>
<BR>

<P><FONT SIZE=3D2>Hi Radhika,</FONT>
</P>

<P><FONT SIZE=3D2>It seems that you forgot to attach the =
optimization</FONT>
<BR><FONT SIZE=3D2>results to your previous message.</FONT>
</P>
<BR>

<P><FONT SIZE=3D2>Could you please resend ?</FONT>
</P>
<BR>
<BR>

<P><FONT SIZE=3D2>---</FONT>
</P>
<BR>

<P><FONT SIZE=3D2>In any case,</FONT>
<BR><FONT SIZE=3D2>about your questions:</FONT>
</P>
<BR>

<P><FONT SIZE=3D2>1) Using multi resolution is always good.</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp; It increases robustness and =
speeds up</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp; the registration process.</FONT>
</P>

<P><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp; You will find multi-resolution =
examples</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp; in the SoftwareGuide</FONT>
</P>

<P><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp; <A =
HREF=3D"http://www.itk.org/ItkSoftwareGuide.pdf" =
TARGET=3D"_blank">http://www.itk.org/ItkSoftwareGuide.pdf</A></FONT>
</P>

<P><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp; Section 8.6, pdf-page 281.</FONT>
</P>
<BR>

2) There is not a direct way to set a =
tolerance
 &nbsp;&nbsp;&nbsp; for the Metric value in the =
optimizer. However
 &nbsp;&nbsp;&nbsp; you can easily implement this in =
the Observer
 &nbsp;&nbsp;&nbsp; of the Optimizer. Simply check =
for the metric
 &nbsp;&nbsp;&nbsp; value on the Execute() method of =
the Command/
 &nbsp;&nbsp;&nbsp; Observer and if it matches your =
stopping
 &nbsp;&nbsp;&nbsp; criteria you invoke

<P><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =
optimizer-&gt;StopOptimization()</FONT>
</P>

&nbsp;&nbsp;&nbsp;&nbsp; Otherwise you could use the =
GradientMagnitudeTolerance
 &nbsp;&nbsp;&nbsp;&nbsp; which is a stopping =
criterion based on the magnitude
 &nbsp;&nbsp;&nbsp;&nbsp; of the gradient. Therefore =
indicating how flat is
 &nbsp;&nbsp;&nbsp;&nbsp; the metric value in the =
current position. In theory,
 &nbsp;&nbsp;&nbsp;&nbsp; the gradient will tend to =
be zero when you are in
 &nbsp;&nbsp;&nbsp;&nbsp; critical point =
(minimum/maximum/saddle) of the metric.

<P><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; Please look at the =
documentation of the RegularStep</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; =
GradientDescentOptimizer.</FONT>
<BR><FONT SIZE=3D2><A =
HREF=3D"http://www.itk.org/Insight/Doxygen/html/classitk_1_1RegularStepG=
radientDescentBaseOptimizer.html" =
TARGET=3D"_blank">http://www.itk.org/Insight/Doxygen/html/classitk_1_1Re=
gularStepGradientDescentBaseOptimizer.html</A></FONT>
</P>
<BR>

<P><FONT SIZE=3D2>3)&nbsp; The step length stopping criteria is based =
on the</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; fact that each time the =
value of the metric increases</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; the step length is divided =
by two and its direction</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; is reversed.&nbsp; If the =
optimizer enters a valley this</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; process may lead =
convergence at the bottom of the valley.</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; What you specify with =
MinimumStepLength is how much you</FONT>
<BR><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp;&nbsp; care about =
precision.</FONT>
</P>

&nbsp;&nbsp;&nbsp;&nbsp; In other words, if you set =
the minimum step length to
 &nbsp;&nbsp;&nbsp;&nbsp; 0.001 you are saying that =
you are satisfied with a
 &nbsp;&nbsp;&nbsp;&nbsp; rotation precision of +- =
0.01 radians which is about
 &nbsp;&nbsp;&nbsp;&nbsp; 0.57 degrees.&nbsp; If you =
are too exigent on the precision,
 &nbsp;&nbsp;&nbsp;&nbsp; e.g. 10-7 radians, the =
optimizer will take a long time
 &nbsp;&nbsp;&nbsp;&nbsp; to converge until its =
oscillations are smaller than this
 &nbsp;&nbsp;&nbsp;&nbsp; value.&nbsp; So you =
basically have a trade-off between
 &nbsp;&nbsp;&nbsp;&nbsp; precision and optimization =
time.

<P><FONT SIZE=3D2>Thanks</FONT>
</P>
<BR>

<P><FONT SIZE=3D2>&nbsp;&nbsp;&nbsp; Luis</FONT>
</P>
<BR>

<P><FONT SIZE=3D2>-------------------------------</FONT>
<BR><FONT SIZE=3D2>Radhika Sivaramakrishna wrote:</FONT>
</P>

&gt; Hi Luis,
 &gt; 
 &gt; I decided to start with an initial rotation of =
9 degrees (my real 
 &gt; rotation is 10 degrees) and I was trying to =
study what parameters to use 
 &gt; to recover this. I am attaching part of the =
results at each iteration.
 &gt; 
 &gt; I used the following:
 &gt; 
 &gt; Maximum step length =3D 0.1
 &gt; Minimum step length =3D 0.01
 &gt; 
 &gt; I find the metric comes down to a low value of =
about 37 and then starts 
 &gt; climbing again. Looking at these results, would =
you recommend
 &gt; 
 &gt; 1) going to a smaller max step length
 &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
; OR
 &gt; 2) Using a hierarchical multiresolution =
approach.
 &gt; 
 &gt; I also have another question:
 &gt; 
 &gt; Is there a way to set a minimum value of metric =
to go down to? How is 
 &gt; this related to the parameter =
MinimumStepLength?
 &gt; 
 &gt; Thanks
 &gt; Radhika
 &gt; 
 &gt;&nbsp; 
 &gt;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
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sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
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is prohibited. If you are not the intended recipient, please contact =
the sender by reply email and destroy all copies of the original =
message. If you are the intended recipient, please be advised that the =
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<P><FONT SIZE=3D2>&nbsp;</FONT>=20
</P>

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