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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">&lt;<a moz-do-not-send="true"
              href="mailto:jian.cheng.1983@gmail.com" target="_blank">jian.cheng.1983@gmail.com</a>&gt;</span>
          wrote:<br>
          <blockquote class="gmail_quote" style="margin:0 0 0
            .8ex;border-left:1px #ccc solid;padding-left:1ex">
            <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>
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                <div>
                  <div class="h5">
                    <div dir="ltr">
                      <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>
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