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

[Penczek, Pawel A]

The earlier statement:

""FSC measures self-consistency, and not resolution" I cannot resist saying 
that OF COURSE this is so."

Regards,
Pawel

> On Aug 30, 2015, at 2:44 PM, Gabor Herman <gabortherman at yahoo.com> wrote:
> 
> 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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