How to calculate the area of one Pixel?

Hi,

I would like to calculate the circularity of a particle using the following formula: circ = 4*pi*area / perimeter^2 and for this I need the area of one pixel to be able to determine the area of the whole particle. According to my research the area of the particle is the number of pixels that make it up multiplied by the area of one pixel.

Or is there another way to determine the circularity of a non-circular particle?

[KSSV]

Do you have any input image?

[Christelle Demgne]

hi,

Yes, I have one. I'll tie it up.

Answer 1

[Diego Hens]

I'm no expert and maybe I'll say the obvious, but I'd say you need the resolution of your image, meaning the amount of pixels in a known space. Then the calculation of the dimensions of one pixel should be obvious.

Or is your problem that you don't have any known distances?

[Christelle Demgne]

That's exactly the problem. I don't have a known space and on my picture I don't have a single particle.

Answer 2

[Bruno Luong]

The formula you get doesn't depend on the UNIT assuming you use the same unit everywhere.

If length is pixel, then use area with pixel^2.

So for AREA you just count the number pixels in the object. No need to wonder of the size of the pixel.

Compute the perimeter as pixel length. The apply directly for formula.

[Christelle Demgne]

thank you I'll try so.

Answer 3

[Image Analyst]

Circularity is a unitless metric. The units in terms of mm per pixel, or whatever units, don't matter. Even if you did convert perimeter by multiplying it by mmPerPixel, and area by multiplying it by mmPerPixel^2, those spatial calibration factors would exactly cancel out and you'd end up with the same value as it you had just simply used the pixel-based values. Look

circPixels = 4*pi*areaInPixels / perimeterInPixels^2
circReal = 4*pi*areaInPixels*mmPerPixel^2 / (perimeterInPixels*mmPerPixel)^2

See, in circReal you have mmPerPixel^2 in both the numerator and denominator and so they cancel out and so you end up with the same equation as circPixels.

[Christelle Demgne]

Thank you very much for the explanation.