Error calculation of physical quantities calculated from a image

Question

I have an assignment related with the physical characterization of some images taken in a SEM (microscope). I have images of some salt grains and the goal is to find the area and perimeter of those grains.

So far I have achieved this by using some image processing techniques (a python script to read the image, clean the noise and count the pixels in the regions of interest) and using a scale that is provided in the image, I convert the pixel units measured to physical units (millimeters or micrometers; depends on the image). As usual in experimental physics, the errors related to the quantities measured are needed.

In this case how is the best approach to report the measures? I can't simply say that my value is $x$ and not saying with what precision.

Thanks for your answer. If someone has worked with SEM images and reported their results in a professional way, I will really appreciate some insight.

Answer 1

Sometimes it's difficult to determine what precision or random error to assign to a data point, and your case is an example of that. You might try assigning random error values based on what error you would get if you overestimated or underestimated the boundaries of the grains by, say, one pixel. But even that might not accurately reflect the true uncertainties if, for example, some of the boundaries are blurred or diffuse so that there may be more than just one pixel of error.

My typical approach in such cases is to come up with some reasonable, rough precisions or random errors to assign to the data points but not go too deeply into the rabbit hole of trying to precisely figure out the individual random errors since any such detailed estimates will most likely be highly subjective. Rather, plot up all the data points and the average random error of your data set will probably be revealed when you try doing least-squares fits of your data to whatever model that you are using to interpret the data. So in your case, I would just assign individual random errors based on a simple method such as the +/- 1 pixel approach described above and then proceed from there to fitting the data to your model.

BTW, I think the "Fiji" freeware package to be a pretty good one for analyzing images (Fiji).

Answer 2

Using Fiji mentioned in Samuel Weir's answer or just the basic ImageJ core on which Fiji is build, you can do your measurements. By translating and rotating your image you can make many independent measurements of the same grains, the statistical distribution of measurements of the same grain will give you a good estimate of the measurement error.