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<div class="moz-cite-prefix">Hi, <br>
<br>
In geometry point of view, a criterion is the minimal angle
between any two points (i.e. the minimal angle provided by <span
style="font-family:monospace,monospace">OrientationStatistics</span>).
<br>
I cannot say anything for a single scheme. <br>
You have to compare two schemes in terms of their minimal angles.
<br>
For example, you can compare the first shell (60 samples) you got
with the scheme from CAMINO which is in
~/.dmritool/Data/ElectricRepulsion/Elec060.txt .<br>
<br>
best,<br>
Jian Cheng<br>
<br>
<br>
On 05/17/2016 05:27 PM, Michael Dayan wrote:<br>
</div>
<blockquote
cite="mid:CAK8FaMM8pxLApVkcvX_Tfp4onjcjEor4ZMOF9WhgVhdAc0Ug4Q@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>
<div>
<div>Hi Jian Cheng,<br>
<br>
</div>
Many thanks for your feedback. I will follow your suggestion
for point #1. For point #2, would you have a rule of thumb
to estimate the quality of the scheme? Once one has the
(min, max, mean, std) statistics, how to assess the scheme
quality? For example what would you say of the quality of
the 60-shell, 90-shell and 60x90 scheme I provided and why
would you reach your conclusion?<br>
<br>
</div>
Best,<br>
<br>
</div>
Michael<br>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Tue, May 17, 2016 at 3:25 PM, Jian
Cheng <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:jian.cheng.1983@gmail.com" target="_blank">jian.cheng.1983@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
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<div text="#000000" bgcolor="#FFFFFF">
<div>Hi Michael, <br>
<br>
Thanks for your feedback. <br>
<br>
1) SamplingSchemeQSpaceIMOCEstimation implemented IMOC
method proposed in the paper <br>
<a moz-do-not-send="true"
href="https://hal.archives-ouvertes.fr/hal-01154774/file/sampling_MICCAI2015.pdf"
target="_blank">https://hal.archives-ouvertes.fr/hal-01154774/file/sampling_MICCAI2015.pdf</a><br>
It is a greedy method which can provide an
initialization for optimization method (CNLO) to get a
further improved scheme. <br>
I will release CNLO later when I have time. At this
moment, you can just use IMOC for your task. <br>
<br>
You cannot use tessellation order more than 7 directly
for SamplingSchemeQSpaceIMOCEstimation, because it uses
the stored gradient tables in
~/.dmritool/Data/Tessellation. You did not see the
warning message because you build the code with
VERBOSITY_LEVEL=0. I just modified the code and pushed
it to github so that you can see the warning message. <br>
If you want to try tessellation order more than 7, you
can use: <br>
SphereTessellator --tessorder 8 --hemisphere grad_t8.txt<br>
SamplingSchemeQSpaceIMOCEstimation grad.txt
--numberOfSamples 60,90 --fineOrientations grad_t8.txt<br>
In my laptop, it takes 18 seconds. <br>
Tessellation order of 7 is much faster, and practically
enough for your usage. <br>
<br>
2) For the shell with 60 samples, there is a minimal
angle for each sample. Then we have 60 minimal angles. <span
style="font-family:monospace,monospace">OrientationStatistics
shows (min, max, mean, std)</span> for these 60
minimal angles, also for shell with 90 samples and the
combined shell with 150 samples. <br>
<br>
best,<br>
Jian Cheng
<div>
<div class="h5"><br>
<br>
On 05/17/2016 01:24 PM, Michael Dayan wrote:<br>
</div>
</div>
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<blockquote type="cite">
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<div class="h5">
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<div>
<div>dmritool has been very useful to generate
multi-shell scheme but I would like to know
more about the optimal protocol to generate
such shemes:<br>
<br>
</div>
1) Is SamplingSchemeQSpaceIMOCEstimation the
most adequate function for this purpose? What
parameters to change to improve the results? I
tried to use higher "tesselate orders" than 7
(e.g. 8, 11, ...) but kept getting a
"Segmentation fault (core dumped)" error.<br>
<br>
</div>
2) To assess the quality of the results how to
interpret the statistics of the generated scheme,
in particular the minimum and maximum angle
values? Below is an example of statistics for a
2-shell scheme with 60 and 90 directions in the
first and second shell.<br>
<br>
<span style="font-family:monospace,monospace"> OrientationStatistics
imoc_60x90_shell1.txt imoc_60x90_shell2.txt
--combine<br>
file: imoc_60x90_shell1.txt<br>
size = 60<br>
60 unique samples, 0 antipodal samples, 0
repeated samples.<br>
minimal angle = 14.1538, radian=0.24703
(covering radius)<br>
maximal angle = 14.7301, radian=0.257089<br>
mean angle = 14.3346<br>
std angle = 0.144217<br>
upper bound (120 points) = 19.9391,
radian=0.348003<br>
upper bound (60 points) = 28.2194,
radian=0.492521<br>
electrostaticEnergy (order=2) = 3.05481<br>
electrostaticEnergy (order=1) = 1.98694<br>
<br>
file: imoc_60x90_shell2.txt<br>
size = 90<br>
90 unique samples, 0 antipodal samples, 0
repeated samples.<br>
minimal angle = 11.5536, radian=0.201648
(covering radius)<br>
maximal angle = 19.6656, radian=0.34323<br>
mean angle = 12.3677<br>
std angle = 1.45567<br>
upper bound (180 points) = 16.2761,
radian=0.284071<br>
upper bound (90 points) = 23.0295,
radian=0.401941<br>
electrostaticEnergy (order=2) = 2.8735<br>
electrostaticEnergy (order=1) = 1.92306<br>
<br>
Combine 2 orientations<br>
size = 150<br>
150 unique samples, 0 antipodal samples, 0
repeated samples.<br>
minimal angle = 8.95306, radian=0.15626
(covering radius)<br>
maximal angle = 14.4468, radian=0.252144<br>
mean angle = 10.2967<br>
std angle = 1.42696<br>
upper bound (300 points) = 12.6048,
radian=0.219995<br>
upper bound (150 points) = 17.8313,
radian=0.311216<br>
electrostaticEnergy (order=2) = 2.79829<br>
electrostaticEnergy (order=1) = 1.89174<br>
Spherical code cost function = 0.1903</span><br>
<br>
<br>
</div>
<br>
<fieldset></fieldset>
<br>
</div>
</div>
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