[dmritool-discussion] Generating optimal multi-shell scheme

Tue May 17 15:03:11 PDT 2016

Hi,

In geometry point of view, a criterion is the minimal angle between any 
two points (i.e. the minimal angle provided by OrientationStatistics).
I cannot say anything for a single scheme.
You have to compare two schemes in terms of their minimal angles.
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 .

best,
Jian Cheng

On 05/17/2016 05:27 PM, Michael Dayan wrote:
> Hi Jian Cheng,
>
> 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?
>
> Best,
>
> Michael
>
> On Tue, May 17, 2016 at 3:25 PM, Jian Cheng <jian.cheng.1983 at gmail.com 
> <mailto:jian.cheng.1983 at gmail.com>> wrote:
>
>     Hi Michael,
>
>     Thanks for your feedback.
>
>     1) SamplingSchemeQSpaceIMOCEstimation implemented IMOC method
>     proposed in the paper
>     https://hal.archives-ouvertes.fr/hal-01154774/file/sampling_MICCAI2015.pdf
>     It is a greedy method which can provide an initialization for
>     optimization method (CNLO) to get a further improved scheme.
>     I will release CNLO later when I have time. At this moment, you
>     can just use IMOC for your task.
>
>     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.
>     If you want to try tessellation order more than 7, you can use:
>     SphereTessellator --tessorder 8 --hemisphere grad_t8.txt
>     SamplingSchemeQSpaceIMOCEstimation grad.txt --numberOfSamples
>     60,90 --fineOrientations grad_t8.txt
>     In my laptop, it takes 18 seconds.
>     Tessellation order of 7 is much faster, and practically enough for
>     your usage.
>
>     2) For the shell with 60 samples, there is a minimal angle for
>     each sample. Then we have 60 minimal angles. OrientationStatistics
>     shows (min, max, mean, std) for these 60 minimal angles, also for
>     shell with 90 samples and the combined shell with 150 samples.
>
>     best,
>     Jian Cheng
>
>
>     On 05/17/2016 01:24 PM, Michael Dayan wrote:
>>     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:
>>
>>     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.
>>
>>     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.
>>
>>      OrientationStatistics imoc_60x90_shell1.txt
>>     imoc_60x90_shell2.txt --combine
>>     file: imoc_60x90_shell1.txt
>>     size = 60
>>     60 unique samples, 0 antipodal samples, 0 repeated samples.
>>     minimal angle = 14.1538, radian=0.24703 (covering radius)
>>     maximal angle = 14.7301, radian=0.257089
>>     mean angle = 14.3346
>>     std angle = 0.144217
>>     upper bound (120 points) = 19.9391, radian=0.348003
>>     upper bound (60 points) = 28.2194, radian=0.492521
>>     electrostaticEnergy (order=2) = 3.05481
>>     electrostaticEnergy (order=1) = 1.98694
>>
>>     file: imoc_60x90_shell2.txt
>>     size = 90
>>     90 unique samples, 0 antipodal samples, 0 repeated samples.
>>     minimal angle = 11.5536, radian=0.201648 (covering radius)
>>     maximal angle = 19.6656, radian=0.34323
>>     mean angle = 12.3677
>>     std angle = 1.45567
>>     upper bound (180 points) = 16.2761, radian=0.284071
>>     upper bound (90 points) = 23.0295, radian=0.401941
>>     electrostaticEnergy (order=2) = 2.8735
>>     electrostaticEnergy (order=1) = 1.92306
>>
>>     Combine 2 orientations
>>     size = 150
>>     150 unique samples, 0 antipodal samples, 0 repeated samples.
>>     minimal angle = 8.95306, radian=0.15626 (covering radius)
>>     maximal angle = 14.4468, radian=0.252144
>>     mean angle = 10.2967
>>     std angle = 1.42696
>>     upper bound (300 points) = 12.6048, radian=0.219995
>>     upper bound (150 points) = 17.8313, radian=0.311216
>>     electrostaticEnergy (order=2) = 2.79829
>>     electrostaticEnergy (order=1) = 1.89174
>>     Spherical code cost function = 0.1903
>>
>>
>>
>>
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