CD Format

The computational application and source codes are provided with a Compact
Disc (CD). In this disc, we divided our study into three folders; Iterative Closest Point
Algorithm Application, 3-D Thin-Plate Splines Application and Example Files from
our Simulation Study.
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Preliminary functions
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Slice_contour function calculates the contour information of the selected slice
in 2-D.
The inputs are;

I = selected slice.
output = 2D coordinates of the selected slice contour.
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Add noise on landmarks function adds random noise with respect to Normal
distribution on point landmarks distributed onto the skull surface. This noise is added
on both template and target reference points.
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ICP Folder
In this folder, we have listed functions related with Iterative Closest Point Al-
gorithm;
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ICP function
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This function performs the registration of 3D points with respect to template
using ICP algorithm.
The inputs are;

model (mx3) = set of template points.
pts (nx3) = set of target points.
flag = control parameter; it has two states: 'o' : nothing displayed on screen.
'on' : information displayed on screen while iteration is taking place.

The outputs are;

ptsnew = registered points.
Rnew = rotation matrix calculated by ICP Algorithm.
vtnew = translation matrix calculated by ICP Algorithm.

The inner function update located in the same function performs the update
when the algorithm prepares the next iteration.
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Dist function
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This function calculates the Euclidean 3-D distance between two inputs x; y.
The output of this function is needed for other functions.
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Mean Rms function
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This function performs the evaluation of the registration results through the
formulation of distance dierences. The mean values and the corresponding Root-
Mean Square measurements can be obtained via this function.

The inputs are;

target = target point sets.
registered = registered point sets.

The outputs are;

moyenne = mean value of distance dierences between target and registered point
sets.
rms = root mean square value of distance dierences between target and regis-
tered point sets.
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Stdevicp function
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This function perform a Standard Deviation Analysis of Distance Dierences
between Target and Registered point sets.
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Drawing function
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This function draws the template, target and registered points sets using mesh
and 3-D plots. The inputs are 20 volumes of the simulation study.
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TPS Folder
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In this folder, we have listed functions related with 3-D Thin Plate Splines
Method;
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Base function
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A 3-D radial basis function of our Thin-Plate Splines is set here. We calculate
the output result through the value that we set with ro.
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Thinplate function
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This function calculates a pair of Thin-Plate Splines that represent this elastic
transformation.

The inputs are;

S = Input points.
Q = Control points.

The outputs are;

C2 = The target function of Thin-Plate Splines.
E = Bending energy of Thin-Plate Splines.
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Evaltps function
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This function nds the singular value decomposition to solve the equations and
calculate the transformed image (i.e. registered point sets).
The inputs are;
S = Template control points.
params = Target function of Thin-Plate Splines.
S = Target control points.
The outputs are;
C2 = Final form of transformed points.
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Dist function
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This function calculates the Euclidean 3-D distance between two inputs x; y.
The output of this function is needed for other functions. This function is similar to
the file in ICP folder.
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Mean Rms function
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This function performs the evaluation of the registration results through the
formulation of distance dierences. The mean values and the corresponding Root-
Mean Square measurements can be obtained via this function. This function is similar
to the file in ICP folder.
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Drawing function
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This function draws the template, target and registered points sets using mesh
and 3-D plots. The inputs are 20 volumes of the simulation study. This function is
similar to the file in ICP folder.
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Examples from Multimodal Registration
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In this folder, several MATLAB files have been introduced. In order to run
these files some data files with .mat extensions are also provided. At the same folder,
noisy and raw data files are provided.
As an example file like PDPET-tps16.m, we perform a TPS based registration
with 16 landmarks. Our template image is PD-weighted MR volume and the target
image is PET. We can analyze the output; registered volume via other functions and
also plot it.