how the area of particles is calculated

[Mohamed Tleis]

Dear Folks,

I am trying to understand the unit of area, imageJ is giving me.
I processed an image to get a binary mask with objects, I analyzed the
particles in the binary image and I get the area of a specific object =
543. I checked Analyze --> Set Scale , and i saw that unit of length is
pixel, and pixel aspect ratio is 1.0. other values are zero.
for the same particle I did measurement on the original grey image, and I
got area of 18.863. Looks like my image is calibrated, so i checked Set
Scale and the unit length is micro-meter with 5.365 pixels / micro-meter.

Doing a simple math, I found that 543 pixels are scattered over 101.21 (not
18.863) micro-meters(square).
So there is something i am missing. How to know more about this topic as it
is crucial in my application?

Best Regards,
Mohamed Tleis

[Gabriel Landini]

On Friday 02 Dec 2011 14:47:56 you wrote:
> Doing a simple math, I found that 543 pixels are scattered over 101.21 (not
> 18.863) micro-meters(square).
> So there is something i am missing. How to know more about this topic as it
> is crucial in my application?

Yes, the simple math is not that simple :-)
The 543 pixels are area units, so you need to square the pixel (linear)
calibration to get the area conversion factor. Then divide 543 by that result
(and that gives your more or less the area you measured in the greyscale)

Cheers
G.

[Mohamed Tleis]

Thank you,

what I thought initially is that number of pixels /micro-meter means in a
squared micro-meter we have that number of pixels. But I understood now
that it is not that but just the length of these numbers.
Anyhow, I did some measurements on binary objects to get the area, and I am
having different results in imageJ than from my old tool I was using. I am
wondering which one is accurate, do you think counting manually the pixels
gives me more clear idea about that?

Best Regards,
Mohamed tleis

On Fri, Dec 2, 2011 at 3:57 PM, Gabriel Landini <[hidden email]>wrote:

> On Friday 02 Dec 2011 14:47:56 you wrote:
> > Doing a simple math, I found that 543 pixels are scattered over 101.21
> (not
> > 18.863) micro-meters(square).
> > So there is something i am missing. How to know more about this topic as
> it
> > is crucial in my application?
>
> Yes, the simple math is not that simple :-)
> The 543 pixels are area units, so you need to square the pixel (linear)
> calibration to get the area conversion factor. Then divide 543 by that
> result
> (and that gives your more or less the area you measured in the greyscale)
>
> Cheers
> G.
>

[Gabriel Landini]

On Friday 02 Dec 2011 15:19:21 you wrote:
> Thank you,
>
> what I thought initially is that number of pixels /micro-meter means in a
> squared micro-meter we have that number of pixels. But I understood now
> that it is not that but just the length of these numbers.
> Anyhow, I did some measurements on binary objects to get the area, and I am
> having different results in imageJ than from my old tool I was using. I am
> wondering which one is accurate, do you think counting manually the pixels
> gives me more clear idea about that?

There are several ways of measuring. IJ's particle analyzer uses the number of
pixels as the area, but see for example the Particles8 and Particles4 plugins
here:
http://www.dentistry.bham.ac.uk/landinig/software/software.html

From that site:
These plugins do not return exactly the same values as the built-in ImageJ
Analyze Particles command because they use an alternative concept to extract
area and perimeter. Here, Perimeter and Area are measured from the centres of
the boundary pixels of a particle, i.e. the length of the 8-neighbours chain
code (Freeman algorithm).
Area disregards "holes" in the particles (i.e. it returns the area bounded by
the perimeter), but Pixels returns the number of pixels forming the particle
(a particle with holes will therefore have more Area than Pixels.
Also note that as Area is calculated from the polygon formed by the boundary
pixels (the chain code), if the particle has no holes, then Area is likely to
be smaller than Pixels (since the polygon is positioned in the centres of
boundary pixels). Using this logic, the Area of 1 pixel particles is 0, for a
2x2 square it is 1, etc. while the value of Pixels in each particle is what
you see.
Likewise, a single pixel particle has a Perimeter of 0, for a 2x2 square it is
4, and so on.

I hope it helps
G.

[Tim McMillen]

I am quantifying intimal lesions in cross-sectional images of carotid arteries by using the free hand tool to draw an ROI's around the layers of elastic lamina.  Unfortunately, I set the measurements to report only area.  

My issue is this.  Most of the sections approximate a circle as one would expect.  However, sometimes a section is somewhat flattened to an elliptical shape.  Since an ellipse and a circle with the same perimeter do not have the same area, my area measurements are "artificially" low.  That is to say, I would like to assume the section is circular as it naturally would have been.  In retrospect, I should have collected the perimeter data and used it to calculate the area of a circle.

My question is whether it is possible to back-calculate perimeter from my area measurements.  I assume the answer is "no" but I thought I'd ask.  I would save me a whole lot of work.

Thanks, Tim