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

[Gabor Herman]

Dear Pawel:

If that is the only statement with which you disagree, 
then I see no point in wasting time arguing about it.,
since I agree with your earlier statement that
 there is no “general” or “absolute” definition of resolution.
However, having carefully studied the concept for over forty years
(see Frieder, G., Herman, G.T.: Resolution in reconstructing 
objects from electron micrographs, Journal of Theoretical 
Biology 33:189-211, 19710), I must say that I cannot think of 
any reasonable (whatever that means) definition of resolution
that would be properly measured by the FSC curve (except,
of course, if you use the FSC curve to "define" resolution).

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: "Gabor Herman" <gabortherman at yahoo.com>
 Cc: "3dem at ncmir.ucsd.edu" <3dem at ncmir.ucsd.edu>
 Date: Sunday, August 30, 2015, 4:02 PM
 
 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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