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

[Penczek, Pawel A]

In case of 'true' independence one can convert FSC values to SSNR values and argue that resolution is a point at which SSNR drops below certain threshold.  One can further argue that SSNR =1 would be sensible.

In this sense you are right, FSC is a measure of resolution as defined in a certain way.  The point I was making was that all resolution measures are introduced in the same manner.

Regards,
Pawel

> On Aug 30, 2015, at 3:17 PM, Gabor Herman <gabortherman at yahoo.com> wrote:
> 
> 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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