[3dem] [ccpem] on FSC curve (A can of worms...)

Gabor Herman gabortherman at yahoo.com
Sun Aug 30 12:44:04 PDT 2015


Dear Pawel:

I wrote:
" "We wish to make a comment on the use of FRC as applied here 
for evaluating algorithms. If the FRC comparing reconstructions from two halves 
of the data is very low at a certain frequency, then it is reasonable to conclude 
that the reconstruction process is not reliable for recovering that frequency from 
the data. However, the converse is not necessarily true, it is possible to acquire 
by the described method FRC values that are near 1.0 at some frequency without 
the algorithm being reliable for that frequency. An extreme of this is an “algorithm” 
that totally ignores the data and always produces the same “reconstruction” 
irrespective of the data. Such an algorithm is clearly useless in practice, but when 
evaluated by the methodology we use here would result in an FRC of 1.0 at all 
frequencies. Thus one has to be careful not to overstate the significance of the 
FRC level near 1.0." 

What is in this statement with which you disagree?

Cheers,

Gabor

Gabor T. Herman, Ph.D.
Distinguished Professor of Computer Science
The Graduate Center of the City University of New York
www.dig.cs.gc.cuny.edu/~gabor/index.html 
.



--------------------------------------------
On Sun, 8/30/15, Penczek, Pawel A <Pawel.A.Penczek at uth.tmc.edu> wrote:

 Subject: Re: [3dem] [ccpem] on FSC curve (A can of worms...)
 To: "Edward Egelman" <egelman at virginia.edu>
 Cc: "3dem at ncmir.ucsd.edu" <3dem at ncmir.ucsd.edu>
 Date: Sunday, August 30, 2015, 2:47 PM
 
 Ed and Gabor, I have to
 respectfully disagree with your statements.
 
 Ed - there is no “general”
 or “absolute” definition of resolution.  What is called
 resolution differs from field to field
 so
 when you say FSC is not a measure of resolution, what
 resolution do you have in mind?  The one used in optics,
 or the one used in X-ray crystallography? 
 They are quite different from each other.
 
 For better or worth,
 definition of FSC allows one to estimate level of SNR in the
 data and it does just that,
 assuming that
 assumptions are fulfilled.
 
 These assumptions call, among other things, for
 full independence of two realizations of the signal.
 It is easy to see that it follows that thus
 defined FSC is not applicable to EM protocols as it would be
 always zero.
 Simply, a chance that two truly
 independent refinement processes would magically end up with
 two structures
 (or 2D averages) in the exact
 same orientation is infinitely small.
 
 Therefore, in practice we compromise
 independence to certain degree to make the machinery of FSC
 applicable to EM.
 I would submit that most
 of the confusion arises due to disagreements how much of
 independence one is allowed to compromise.
 
 One kind of “abuse” is
 some kind of deterministic protocol that increases
 correlation, as Gabor points out.
 In helical
 reconstruction, imposition of helical symmetry is such a
 step.  However, fundamentally this cannot be avoided
 if one is to apply FSC at all as pointed out
 above.  So, we use various tricks to keep two structures in
 sync.
 For example, a popular software
 package simply equates low frequency components between the
 two, which
 of course introduces correlations
 beyond the cut-off point.  How much nobody knows.
 
 
 In closing,
 as often in life there is a mathematical definition and
 there is little argument about its meaning and
 applicability,
 and then there is life. 
 Normally there is full understanding that the two differ to
 a degree and one has to simply live with it.
 We should keep in mind though that if FSC is
 applied to an outcome of an image processing protocol, its
 outcome becomes
 as function of this
 protocol, as the ‘purity” of the original definition is
 compromised.
 
 Regards,
 -
 Pawel Penczek
 pawel.a.penczek at uth.tmc.edu
 
 
 
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