[Insight-developers] RE: Demons voodoo

Thu, 8 Apr 2004 15:31:59 -0400

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The mapping in Thirion's paper looks like it is from a position in g (moving
image) to a position in f (fixed image). When the deformation field is used
by the WarpImageFilter, it (always) looks like a reverse mapping. I consider
what I am proposing for the Demons as the reverse mapping and what current
implementation does as a forward mapping :) 

By swapping what image is the fixed and what is the moving image, you can
always produce a registration that performs the mapping that you want.
Course the two deformation fields are not inverse equivalent.

The warp that is calculated by the Demons paper, "warps" the coordinate
frame of g onto the corrdinate frame of f. The WarpImageFilter assigns
pixels values at the prescribed positions in the output image by sampling
the input image at positions dictated by transforming a position from the
output coordinate frame to the input coordinate frame as defined by the
prescribed deformation field.

I did do the experiment swapping the circle and the square, the results are
attached.

For the scheme I am using now, you interpolate f (and grad f) instead of
interpolating g.

Again, my concern with the current implementation is that it does not match
the original paper. It may be ugly (though not so such so that we do it) to
support both approaches. The tricky part is that some of the types are
defined via the fixed image in one implementation and via the moving image
in the other. Most of the changes are within the DemonsRegistrationFunction.
However, there are some changes to PDEDeformableRegistrationFilter to
propagate the appropriate information to the pipeline that is based on the
fixed image in one case and on the moving image in another. 

-----Original Message-----
From: Lydia Ng [mailto:lng at insightful.com]
Sent: Thursday, April 08, 2004 2:00 PM
To: Miller, James V (Research); Insight-developers (E-mail)
Subject: RE: Demons voodoo

Hi Jim,

>From my understanding of your email, what you are proposing is to estimate
the "forward mapping" instead of the "reverse mapping". 
Both of which do allow you to warp the moving image to the fixed image - the
difference as you pointed out is that one keeps tracks of where a pixel goes
to and the other keeps track of where a pixel comes from.

Out of curiosity, could you also repeat the experiment with the circle and
square swapped? I would be interested at the reverse behavior as well.

For your forward mapping scheme, how do you compute (f-g)? Do you
interpolate f?

As previously discussed in the list, "reverse mapping" is essential for
image resampling to avoid problems of holes (where no points map to an
output pixel - simple example is uniform scaling) and overlap (where several
points of different intensity maps to the same output pixel). While is it
not strictly essential for registration (because you can always interpolate
f instead of g), I have been also doing "reverse mapping" for registration
so that the mapping can be used for resampling.

Although I don't have Thiron's technical with me right now - I believe it
did mention somewhere that the "reverse mapping" might be more convenient to
estimate (I will need to find the reference.)

It could well be that "reverse mapping" is my personal soapbox but since the
implementation have shown to be useful for me for inter-subject brain
mapping - I really loathe to have it yanked out. Would it be possible to
somehow have both forward and reverse mapping?

- Lydia 

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<DIV><SPAN class=3D050222018-08042004><FONT color=3D#0000ff =
size=3D2>The mapping in=20
Thirion's paper looks like it is from a position in g (moving image) to =
a=20
position in f (fixed image). When&nbsp;the deformation field is used by =
the=20
WarpImageFilter,&nbsp;it&nbsp;(always) looks like a reverse=20
mapping.&nbsp;I&nbsp;consider what I am proposing for the Demons as the =
reverse=20
mapping and what current implementation does&nbsp;as a forward mapping=20
:)&nbsp;</FONT></SPAN></DIV>
<DIV><SPAN class=3D050222018-08042004><FONT color=3D#0000ff=20
size=3D2></FONT></SPAN>&nbsp;</DIV>
<DIV><SPAN class=3D050222018-08042004><FONT color=3D#0000ff size=3D2>By =
swapping what=20
image is the fixed and what is the moving image, you can always produce =
a=20
registration that performs the mapping that you want. Course the two =
deformation=20
fields are not inverse equivalent.</FONT></SPAN></DIV>
<DIV><SPAN class=3D050222018-08042004><FONT color=3D#0000ff=20
size=3D2></FONT></SPAN>&nbsp;</DIV>
<DIV><SPAN class=3D050222018-08042004><FONT color=3D#0000ff =
size=3D2>The warp that is=20
calculated by the Demons paper, "warps" the coordinate frame of g onto =
the=20
corrdinate frame of f. The WarpImageFilter assigns pixels values at the =

prescribed positions in the output image by sampling the input image at =

positions dictated by transforming a position from the output =
coordinate frame=20
to the input coordinate frame as defined by the prescribed deformation=20
field.</DIV>
<DIV>&nbsp;</DIV>
<DIV>I =
did do the=20
experiment swapping the circle and the square, the results are=20
attached.</DIV>
<DIV>&nbsp;</DIV>
<DIV>For the scheme I=20
am using now, you interpolate f (and grad f) instead of interpolating=20
g.</DIV>
<DIV>&nbsp;</DIV>
<DIV>Again, my concern=20
with the current implementation is that it does not match the original =
paper. It=20
may be ugly (though not so such so that we do it) to support both =
approaches.=20
The tricky part is that some of the types are defined via the fixed =
image in one=20
implementation and via the moving image in the other. Most of the =
changes are=20
within the DemonsRegistrationFunction.&nbsp; However, there are some =
changes to=20
PDEDeformableRegistrationFilter to propagate the appropriate =
information to the=20
pipeline that is based on the fixed image in one case and on the moving =
image in=20
another. </DIV>
<DIV>&nbsp;</DIV>
<DIV>&nbsp;</DIV>
<BLOCKQUOTE dir=3Dltr style=3D"MARGIN-RIGHT: 0px">
 <DIV class=3DOutlookMessageHeader dir=3Dltr align=3Dleft>-----Original Message----- From: Lydia Ng=20
 [mailto:lng at insightful.com] Sent: Thursday, April 08, 2004 =
2:00=20
 PM To: Miller, James V (Research); Insight-developers=20
 (E-mail) Subject: RE: Demons voodoo </DIV>
 <DIV class=3DSection1>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">Hi=20
 Jim,<o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial"><o:p>&nbsp;</o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">From my =
understanding=20
 of your email, what you are proposing is to estimate the =
&#8220;forward mapping&#8221;=20
 instead of the &#8220;reverse mapping&#8221;. =
<o:p></o:p>
 Both of =
which do=20
 allow you to warp the moving image to the fixed image &#8211; the =
difference as you=20
 pointed out is that one keeps tracks of where a pixel goes to and the =
other=20
 keeps track of where a pixel comes from.<o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial"><o:p>&nbsp;</o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">Out of =
curiosity,=20
 could you also repeat the experiment with the circle and square =
swapped? I=20
 would be interested at the reverse behavior as=20
 well.<o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial"><o:p>&nbsp;</o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">For your =
forward=20
 mapping scheme, how do you compute (f-g)? Do you interpolate=20
 f?<o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial"><o:p>&nbsp;</o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">As =
previously=20
 discussed in the list, &#8220;reverse mapping&#8221; is essential for =
image <SPAN=20
 class=3DSpellE>resampling to avoid problems of holes (where no =
points map=20
 to an output pixel &#8211; simple example is uniform scaling) and =
overlap (where=20
 several points of different intensity maps to the same output pixel). =
While is=20
 it not strictly essential for registration (because you can always =
interpolate=20
 f instead of g), I have been also doing &#8220;reverse mapping&#8221; =
for registration so=20
 that the mapping can be used for <SPAN=20
 class=3DSpellE>resampling.<o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial"><o:p>&nbsp;</o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">Although I =
don&#8217;t have=20
 Thiron&#8217;s technical with me right =
now - I believe it=20
 did mention somewhere that the &#8220;reverse mapping&#8221; might be =
more convenient to=20
 estimate (I will need to find the =
reference.)<o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial"><o:p>&nbsp;</o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">It could =
well be that=20
 &#8220;reverse mapping&#8221; is my personal soapbox but since the =
implementation have=20
 shown to be useful for me for inter-subject brain mapping &#8211; I =
really loathe to=20
 have it yanked out. Would it be possible to somehow have both forward =
and=20
 reverse mapping?<o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial"><o:p>&nbsp;</o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">-=20
 <st1:country-region><st1:place><SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: =
Arial">Lydia</st1:place></st1:country-region><FONT=20
 face=3DArial color=3Dnavy size=3D2><SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">=20
 <o:p></o:p>
 <SPAN=20
 style=3D"FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p>&nbsp;=
</o:p></DIV></BLOCKQUOTE></BODY></HTML>

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