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Ever decreasing circles

Posted by John Brear on Dec 11, 2016; 1:38pm
URL: http://imagej.273.s1.nabble.com/Ever-decreasing-circles-tp5017755.html

Hi,

 

We are metallurgists, studying the microstructural changes that occur in
stainless steels.  Our application is the structural integrity of critical
components in power generation and petrochemical plant.

With time at high temperature, various species of precipitate particles
form, grow and dissolve.  The different, co-existing species have different
size ranges, morphologies and spatial distributions - but considerable
overlap occurs.

Quantifying the kinetics of precipitation, growth and dissolution requires
measurement of the numbers and sizes of each species after ageing at various
combinations of time and temperature.

The precipitates are revealed by polishing and etching the steel samples.
Some separation of species can be obtained by using different etches (though
one cannot view the same area after re-polishing and re-etching).

However, full separation requires discrimination by size range and
morphology - and it is with the latter that we have a problem.

 

ImageJ allows selection by size range and circularity.

Circularity is defined in the User Guide as:  "Circularity = 4 x Pi x Area /
Perimeter squared, with a value of 1.0 indicating a perfect circle. As the
value approaches 0.0, it indicates an increasingly elongated shape. Values
may not be valid for very small particles."

The definition is conventional, but the caveat on validity misunderstands
measure on pixelated images.  In the real plane, where area and perimeter
measures occupy the continuum, the circularity of a circle is indeed 1.  But
in the integer plane both areal and linear measures are quantised.  Area is
limited to integer values (pixel count) and perimeter is a Banach-like
measure which may have only orthogonal components or which may allow
diagonal elements.  Using artificial images (Bresenham approximations to the
circle and totally random shapes) it appears that perimeters in ImageJ are
of the form a + b x sqrt(2), where a, b are integers.  This gives a limiting
circularity (for a single pixel) of Pi / 2.

Calculating the circularities of our observed precipitates shows that we
would obtain much better discrimination by selecting on circularity values
greater than 1.  At present ImageJ does not allow this.

 

Is there a simple way of overriding this limit?

 

As background, we typically average over 20 random images of a sample -
after each of two etches (one of which reveals some species and one of which
reveals all of them).  Images size is 1280 x 960 pixels, representing a
field of view of 320 x 240 microns.  Our steels have a grain size of around
132 pixels (33 micron mean linear intercept) and some precipitates
concentrate on the grain boundaries.

A typical set of results is:


AC792

Species 1

 

Species 2

 

Species 3

 


 

Count

Average size

Count

Average size

Count

Average size


Mean

941.3

11.67

262.4

84.33

6573.4

4.62


St Dev

193.2

3.07

40.0

23.49

2521.9

0.56

                                                               

Species 1 is revealed by the first etch, all three species by the second.
Average sizes are Total area / Count, so the tabulated means and standard
deviations are of averages, not of values.  Thus actual size ranges are
wider and species 1 overlaps considerably with species 2 and 3.  Species 1
and 3 are potentially differentiable by circularity.  (Sometimes we have
more than 3 coexistent species.)

 

Any help with this specific issue would be appreciated.

In addition, we would be very pleased to exchange ideas and experience with
other materials scientists in the ImageJ community.

 

Best wishes

John

 

John M Brear

Director

John Brear - Plant Integrity Cyfyngedig

Abergefryn, Capel Seion, Drefach, Llanelli, SA14 7BP, UK

 

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