I'm an engineering student and encountered a problem to which I did not find a solution yet, and wondered if someone could give me the benefit of their expert opinion.

I'm going to perform an experiment in which I'll cook an egg using standing electromagnetic waves, only for a short period of time. This way there are only some regions that are cooked (regions A,B,C and D). The goal is to measure the distance between these regions as accurately as possible and tell something about the accuracy of the measurement. Assume we know the distance between regions A&B, B&C, C&D and D&A are the same.

I came up with some methods to handle the data:

1) Visually make a guess of the centers of the cooked regions (red dots) and measure the distance between them. This creates an extra 'human' error, since it's just a visual guess. With those 4 values I could calculate a 95% confidence interval and thus am able to tell something about the accuracy.

But then I posed myself the question: Maybe we could use the fact that we can measure the green and orange distances to our advantage.

2) Measuring the longest and shortest distance between A&B, B&C, C&D and D&A. Then calculating the mean between the two and using these four values for calculating the confidence interval. The problem is, I won't be able to work in an ideal environment and the eggs aren't ideal either, so the shapes of the cooked regions will be irregular (like on the drawing).

So I had another thought: Maybe combining both methods?

3) Using the red dots to calculate the mean and using the other measures (green & orange lines) to say something about the confidence? Maybe use the confidence interval made with the red dot data and combine it in some way with the confidence interval data of the longest distances and the shortest distances respectively?

Can you come up with a suiting statistical method for interpreting the data of this experiment?

Happy to hear how you would tackle this problem!

Thanks in advance, John