[dmritool-discussion] Generating optimal multi-shell scheme

[Michael Dayan]

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>
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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