This is also reminiscent of the Gumbel trick[1] If your noise is Gumbel noise, you can actually get the probability to exceed the threshold to be proportional t

This is also reminiscent of the Gumbel trick[1] If your noise is Gumbel noise, you can actually get the probability to exceed the threshold to be proportional to the intensity of the pixel. [1] https://hips.seas.harvard.edu/blog/2013/04/06/the-gumbel-max-trick-for-discrete-distributions/ https://hips.seas.harvard.edu/blog/2013/04/06/the-gumbel-max...