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<div>Dear Benjamin,</div>
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<div>Different spatial sampling, including under sampling, is definitely an issue. I am not sure what you mean with concern, but it is something to keep in mind. You have to understand the limiting factor in the data and the measurements in order to not over
interpret any data. Doing concial FSC on tomographic data is definitely not a perfect “resolution” measurement criterion (is there is any). I would not put any emphasis on the actual values that originate from the individual cones. However, I hope we showed
that can be useful when one want to compare similar data or reconstruction techniques in a relative and qualitative manner.</div>
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<div>We did try other than 200 cones and this number is optimised for spatial distribution against signal to noise. </div>
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<div>Interesting though to scale the resolution relatively. I am not sure I understand what would be 1 then. It probably does not matter since the power is in the relative values anyway. Only maybe when one has a subtomogram average with more data than from
one tomogram the values might be somewhat more meaningful. </div>
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<div>I am not sure if I understand you last remark. The cones are chosen such that they cover the whole Fourier Space but in opposite directions they are not necessarily exactly the same (there is no symmetry in the cone distribution). So the choice of cone
angles is not symmetrical.</div>
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<div><font class="Apple-style-span" color="#000000"><font class="Apple-style-span" face="Calibri">Best regards,</font></font></div>
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<div><font class="Apple-style-span" color="#000000"><font class="Apple-style-span" face="Calibri">Roman</font></font></div>
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<span style="font-weight:bold">From: </span>Benjamin Himes <<a href="mailto:himes.benjamin@gmail.com">himes.benjamin@gmail.com</a>><br>
<span style="font-weight:bold">Date: </span>Sunday 6 September 2015 15:30<br>
<span style="font-weight:bold">To: </span>Roman Koning <<a href="mailto:r.i.koning@lumc.nl">r.i.koning@lumc.nl</a>><br>
<span style="font-weight:bold">Cc: </span>"<a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>" <<a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>><br>
<span style="font-weight:bold">Subject: </span>RE: [3dem] Anisotropic resolution<br>
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<p dir="ltr">Dear Roman & Misha,</p>
<p dir="ltr">Thank you both for pointing out your respective papers regarding the subdivision of Fourier space by shells & cones in order to estimate resolution anisotropy.</p>
<p dir="ltr">Follow up questions:</p>
<p dir="ltr">1) are you concerned with the effect of undersampling an already sparse transform (particularly in the case of the tomogram work?)</p>
<p dir="ltr">Roman - you report use of 200 cones. Did you try other numbers, and what did you observe; I would guess the overall pattern to be very similar with different "resolution" values?</p>
<p dir="ltr">2) both papers reference resolution comparing in either pixel^-1 or nm^-1. Depending on your answer to question 1, do you think this is appropriate, or would a relative measure (scale the highest to 1) perhaps be a better representation.</p>
<p dir="ltr">3) Neither presentation seemed to reflect friedel symmetry. While your choice of cone axis could result in asymmetric sampling, I find this curious. Comments?
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<p dir="ltr">Thanks again! </p>
<p dir="ltr">Benjamin Himes<br>
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<p dir="ltr">Dear Benjamin,</p>
<p dir="ltr"> </p>
<p dir="ltr">We recently published a paper on how to measure the anisotropy in electron tomograms (<a href="http://www.ncbi.nlm.nih.gov/pubmed/25843950">http://www.ncbi.nlm.nih.gov/pubmed/25843950</a>). Though we did not test this on subtomogram averages it
might be useful to have a look at the paper (in case you did not do that yet).</p>
<p dir="ltr"> </p>
<p dir="ltr">Best regards,</p>
<p dir="ltr"> </p>
<p dir="ltr">Roman</p>
<p dir="ltr"> </p>
<p dir="ltr"><b>Dr. R.I.Koning (Roman)</b></p>
<p dir="ltr"> </p>
<p dir="ltr">Department of Cell Biology, Leiden University Medical Center</p>
<p dir="ltr">Postal Zone S1-P, P.O.Box 9600, 2300 RC Leiden, The Netherlands</p>
<p dir="ltr"><b>visiting address</b>: Einthovenweg 20, Building 2, zone S1-P, room R-90-20</p>
<p dir="ltr"><b>tel.</b> (31) 71 526 9296<b> fax.</b><a href="tel:%28%2B31%29%2071%20526%208270"> (+31) 71 526 8270</a><b> mail.</b><a href="mailto:r.i.koning@lumc.nl"> r.i.koning@lumc.nl</a><b> web.</b><a href="http://electronmicroscopy.lumc.nl"> electronmicroscopy.lumc.nl</a></p>
<p dir="ltr"> </p>
<p dir="ltr">Netherlands Centre for Electron Nanoscopy, Institute Biology Leiden, Leiden University</p>
<p dir="ltr"><b>visiting address:</b> Einsteinweg 55, 2333 RC Leiden, The Netherlands, room 05.11</p>
<p dir="ltr"><b>tel.</b> (31) 71 527 1423<b> mail.</b><a href="mailto:r.i.koning@biology.leidenuniv.nl"> r.i.koning@biology.leidenuniv.nl</a><b> web.</b><a href="http://www.necen.nl"> www.necen.nl</a></p>
<p dir="ltr"> </p>
<p dir="ltr"> </p>
<p dir="ltr"><b>From:</b> 3dem [mailto:<a href="mailto:3dem-bounces@ncmir.ucsd.edu">3dem-bounces@ncmir.ucsd.edu</a>]<b> On Behalf Of</b> Benjamin Himes<br>
<b>Sent:</b> maandag 24 augustus 2015 15:44<br>
<b>To:</b><a href="mailto:3dem@ncmir.ucsd.edu"> 3dem@ncmir.ucsd.edu</a><br>
<b>Subject:</b> [3dem] Anisotropic resolution</p>
<p dir="ltr"> </p>
<p dir="ltr">Dear colleagues,</p>
<p dir="ltr">I hate to stir the pot on the resolution discussion, however, I have a question regarding any progress on analyzing the anisotropy potentially present in a 3d em map.</p>
<p dir="ltr">Aside from some discussion on 3d ssnr, particularly by P.P. and a recent paper on 3d covariance estimation from J.F. Has anybody tried to implement a concrete way of assessing this issue?</p>
<p dir="ltr">I am particularly concerned with maps generated from subTomogram averaging and classification: even with an angular distribution that is well sampled, I am concerned about the fact that cumulative dose, and increased sample thickness on tilting
create a situation where the individual projections do not have equivalent SNR and therefore a simple plot of angular distributions would not accurately reflect the quality of the sampling in Fourier space.</p>
<p dir="ltr">It seems a 3d SSNR might work, but the interpretation of such a plot, beyond its "potato" like quality, even in terms of the eigenvalues of the principle axes is not immediately clear to me.</p>
<p dir="ltr">Many thanks,</p>
<p dir="ltr">Benjamin Himes</p>
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