[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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