Re: Image registration/averaging and image quality
- From: "Michael" <mnewberry@xxxxxxxxxxxxxxx>
- Date: 7 Jul 2006 08:05:51 -0700
Peter,
You have described about what I suspected was the case. It appears that
the Affine transformation is a reasonable physical model for the
distortion, but the problem lies with the uncertainty of the
coefficients of the transformation equations (that is, the affine
transformation). You get those coefficients from mapping the reference
point positions and using them to solve the model equations. The more
noisy is your image, the less precise is each estimation of position,
and the higher the RMS of the solution to the Affine mapping based on
those references points. Said another way, the higher the RMS
unertainty of each reference point, then the higher will be the RMS
uncertainty of the transformation equations.
When you apply the "wavelet de-noising" prior to measuring the point
positions, you are combining the photon statistics of a neighborhood,
which beats down the per-pixel noise, giving you a more statistically
significant estimate of the position of each reference point. In this
case, you are trading (lower) spatial resolution for (higher)
signal-to-noise ratio around each of the reference points. The increase
in significance of the reference position goes something like
proportional to sqrt(c) where "c" net counts above background are
combinined into the "blob" at each reference point.
I think using a wavelet approach is probably overkill. The technique of
smoothing the reference points is not too unusual but typically people
use a simple smoothing filter to accomplish the noise reduction. Be
sure to use a filter that is symmetric (that is, its center of mass is
at the center of the filter mask) and no larger than the extent of the
blob at each reference point. There is actually an optimal size for the
smoothing filter which gives the greatest statistical significance for
the estimated position of a reference point. That optimal size depends
upon the ratio of the brightness of the blob and its local background.
But I don't think you should waste your time trying to model that
analytically! Just run some a number of simulations and pick the best:
Repeat the process using different size smoothing filters: 3x3, 5x5,
7x7, etc., and see how this affects the RMS of the solution to the
Affine transformation mapping. Use the solution having the smallest
RMS.
Finally, would you mind sending me 2 images to look at?
Michael
Michael Newberry
Mira Support
Mirametrics, Inc.
http://www.mirametrics.com
Peter wrote:
Hi Michael-
Thank you so much for your reply - your 'big picture' reply was EXACTLY
the kind of feedback I was hoping for!!!
One more question:
I have a set of images with a defined SNR (the main contribution of
noise being a photon limited, with a 'Poisson' distribution). I have
chosen a distortion model empirically: If I use pixel brightness as a
global search criteria, then there's too much noise for an 'Affine'
transformation. But, if I apply a wavelet de-noising algorithm prior to
mapping images to the target a 'Rigid' registration gives satisfactory
result. How can I describe this reasoning for choosing a particular
deformation model in a more formal language, or in scientific terms, if
you which...
-Peter
.
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