[dmritool-discussion] Generating optimal multi-shell scheme

[Jian Cheng]

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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