How to quantify the asymmetry of an image?

Now I have two images: Figure 1, Figure 2

(These plots are grids plotted with plt.contourf)

We can see that Figure 1 shows obviously asymmetry while Figure 2 is totally symmetric. Now I would like to quantify the asymmetry of Figure 1. Is there any reliable and elegant way to do so?

I would use the measurement of the asymmetry to find its relation with some physics property.


related: How to quantify the asymmetry of an image using openCV or something else? - Stack Overflow

i wonder, what the input data for this is.
(its probably better, to work on that, not what matplotlib generated, false colors, numbers, etc)


Please check the link here:

This is the data file of asymmetry.

IF you want to work on images to find mirror symmetry about the x-axis, ideally you’d flip the bottom half and compare it to the top one like sum(absdiff(top,bottom))
but you need “machine friendly” images, not “made for humans” (no false colors, no tick marks, no grid, no printed numbers)