Ken,
I suspect you want to know inclusion particle density in order to establish some relationship with wear rate or failure rate. For this an operational definition of density (or area) at some specified magnification (say 500x, with specified lighting and camera) might suffice. An operational definition might suffice even if the smallest inclusions are well below what can be imaged with your system, as appears to be the case. Consider that the number of inclusions larger than some measureable size, or the total area of the 100 largest, may be a repeatable measure of potential utility, and within the size/visibility range were all your 'experts' still agree about what is or is not an inclusion.
If your background subtraction is inadequate around the edges, you must exclude that border from analysis. Similarly, you must have an estimate of the radius of the largest inclusion. Search for inclusions, marking the centers, and then exclude an additional border of width equal to the radius. Otherwise estimates of counts or area will be biased because large particles near edges are not correctly counted or measured. Perhaps you can establish this bias is negligible.
Examining several smaller fields would allow estimation of a mean and a variance.
The biggest difficulty may be in that "Threshold may vary based on judgment--requires sufficient experience and verification is not entirely self-evident." As a wild idea, consider doing the automated count at various thresholds, then fitting a model with a linear piece and then an exponential piece, using the count at the break point as the measure of interest (or a similar p-spline).
I doubt you really trying to estimate the upper asymptotic particle density as magnification increases. I suspect it is an artifact of limits of microscopy rather than a physical minimum inclusion size. You would need more than four points (and repeated comparisons on more than one metal piece) to establish the relationship is asymptotic. Then you would have to show that counts at 500x, say, always give about 70% of the asymptote. Or that counts at four standard magnifications are enough to fit the asymptotic model for each piece.
Charles
-----Original Message-----
From: ImageJ Interest Group [mailto:
[hidden email]] On Behalf Of Ken George
Sent: Tuesday, October 22, 2013 11:03 AM
To:
[hidden email]
Subject: Particle Count Verification using a Patch Test
Dear Group,
I think that a "patch test" sample may a reasonable approach to verifying particle counts for images containing thousands of particles and perhaps estimating error on the population based on the statistics of the sample.
I have prepared a PPT and have shared it via the Google Drive link below. It includes the development of a standard and example particle counts. I would GREATLY appreciate any comments/suggestions.
Especially interested in applying statistics in Image J such as, but not limited to, the Histogram function to estimate error.
https://docs.google.com/file/d/0B52y_sgs5kU9N3lkOXhyMWtCS3M/edit?usp=sharingThank you in advance.
-Ken
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