The method employed by us:
- Convert the picture issued by the OP to Windows Bitmap format
- Load the BMP file into a computer program, developed for the purpose
- Map the color content onto real (double precision) numbers
- Define a zero level of this mapping; in our case white = -0.2
- Define empirically limitations for the area that looks interesting
- Use a contouring module for making isolines at level zero
- Use all sort of limitations for distinguishing relevant data from the rest
- Calculate second order moments (variances) for the relevant isolines
- Take a look at the theory in the webpage Two-dimensional Moments
- Especially take notice of the formula $\;\tan(2 \theta) = 2 \sigma_{xy}/(\sigma_{xx} - \sigma_{yy})$
- Calculate mean value $\pm$ spread of relevant angles $\alpha=-\theta$ and Output
The numerical end result obtained is:
Alpha = 38 +/- 2 degrees
Picture produced:
Note.
A more robust method may be to consider instead the angles of the minor axes of the ellipses of inertia
$\;\sigma_{yy}(x-\mu_x)^2-2\sigma_{xy}(x-\mu_x)(y-\mu_y)+\sigma_{xx}(y-\mu_y)^2=\sigma_{xx}\sigma_{yy}-\sigma_{xy}^2\;$ with the x-axis.
Free accompanying source-only software (Delphi Pascal) has been made available at:
MSE publications / references 2021
Disclaimer. Anything free comes without guarantee :-(and without referee)