[Insight-users] question about MultiResMIRegistration
XU, Dongrong
xdr@rad.upenn.edu
Wed, 19 Feb 2003 23:06:37 -0500
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HI, there,
I am a beginner using ITK, especially the part of mutual information. I
need to register PET images to MRI images. I use MultiResMIRegistration,
which results in the following:
Overall transform matrix: (R)
0.995239 -0.0614973 -0.0756162
0.0611396 0.998104 -0.00703878
0.0759057 0.00238212 0.997112
Overall transform offset:
-39.3246 -4.51031 35.7883 (Tx, Ty, Tz)
I suppose the first is a rotation matrix R, and the latter is a
translation vector. Suppose I am using the PET image as the moving
image, and the MRI image as the fixed image, if I need to apply the
above mentioned matrices to another PET image to warp it to the MRI
space, how should I use them?
What is the center of that rotation matrix? And are they in the unit of
mili-meter?
If the MRI space is 256x256x124, and resolution is Rx Ry Rz
The PET space is 128x128x15 and resolution is rx, ry, rz
I am doing the following
For each grid point (x,y,z) in MRI space (256x256x124)
Let V=(x*Rx, y*Ry, z*Rz)
Let V = V- (Tx, Ty, Tz)
Map V to the coordinates in PET space by : V1 = R * V = (x1, y1, z1)
Calculate the coordinates (a,b,c) in PET by
a = x1/rx
b = y1/ry
c = z1/rz
get value H at (a,b,c) in the PET volume using trilinear
interpolation
so that grid point (x,y,z) in MRI space should have the value H
Is there anything wrong in this procedure? Would anybody please kindly
point out any potential error? My result seems not correct.
Thank you very much for your time and help!
-Dongrong
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<div class=3DSection1>
<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'>HI, there,<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'>I am a beginner using ITK, especially the part of mutual =
information. I
need to register PET images to MRI images. I use <span =
class=3DSpellE>MultiResMIRegistration</span>,
which results in the following:<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>Overall transform matrix: =
(R)<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>0.995239 -0.0614973
-0.0756162 <o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>0.0611396 0.998104
-0.00703878 <o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>0.0759057 =
0.00238212
0.997112 <o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>Overall transform offset: =
<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>-<span =
class=3DGramE>39.3246<span
style=3D'mso-spacerun:yes'> </span>-</span>4.51031<span
style=3D'mso-spacerun:yes'> </span>35.7883<span
style=3D'mso-spacerun:yes'> </span>(<span =
class=3DSpellE>Tx</span>, <span
class=3DSpellE>Ty</span>, <span =
class=3DSpellE>Tz</span>)<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>I
suppose the first is a rotation matrix R, and the latter is a =
translation vector.
Suppose I am using the PET image as the moving image, and the MRI image =
as the
fixed image, if I need to apply the above mentioned matrices to another =
PET
image to warp it to the MRI space, how should I use =
them?<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>What
is the center of that rotation matrix? And are they in the unit of <span
class=3DSpellE>mili</span>-meter?<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>If
the MRI space is 256x256x124, and resolution is Rx <span =
class=3DSpellE>Ry</span>
<span class=3DSpellE>Rz</span><o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>The
PET space is 128x128x15 and resolution is <span class=3DSpellE><span =
class=3DGramE>rx</span></span>,
<span class=3DSpellE>ry</span>, <span =
class=3DSpellE>rz</span><o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>I
am doing the following<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span><o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>For
each grid point (<span class=3DSpellE>x<span =
class=3DGramE>,y,z</span></span>) in
MRI space (256x256x124)<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>Let V=3D(x*Rx, y*<span =
class=3DSpellE>Ry</span>,
z*<span class=3DSpellE>Rz</span>)<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>Let V =3D V- (<span =
class=3DSpellE><span
class=3DGramE>Tx</span></span>, <span class=3DSpellE>Ty</span>, <span =
class=3DSpellE>Tz</span>)<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>Map V to the coordinates =
in PET
space <span class=3DGramE>by :</span> V1 =3D R * V =3D (x1, y1, =
z1)<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>Calculate the coordinates =
(<span
class=3DSpellE>a<span class=3DGramE>,b,c</span></span>) in PET by =
<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>a =3D =
x1/rx<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>b =3D =
y1/ry<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span>c =3D =
z1/rz<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span><span =
class=3DGramE>get</span> value
H at (<span class=3DSpellE>a,b,c</span>) in the PET volume using <span
class=3DSpellE>trilinear</span> =
interpolation<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> </span><span =
class=3DGramE>so</span> that
grid point (<span class=3DSpellE>x,y,z</span>) in MRI space should have =
the value
H<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>Is
there anything wrong in this procedure? Would anybody please kindly =
point out
any potential error? My result seems not =
correct.<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>Thank
you very much for your time and help!<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'>-Dongrong
<o:p></o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier =
New"'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal =
style=3D'mso-layout-grid-align:none;text-autospace:none'><font
size=3D2 face=3D"Courier New"><span =
style=3D'font-size:10.0pt;font-family:"Courier New"'><span
style=3D'mso-spacerun:yes'> =
</span><o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'><o:p> </o:p></span></font></p>
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