# Probability of stripes being distinguishable given probability density functions for each luminance

I have an image with seven stripes on it (or three stripes on a dark background), and the goal is to estimate the probability of whether they are distinguishable from one another.

If the values of luminance $$C_1, C_2, \ldots, C_7$$ of those stripes are given, then the event $$E$$ formulates that the difference in luminance between neighboring areas is at least 1: $$E:\ (C_2 - C_1\geq 1) \ \& \ (C_2 - C_3\geq 1) \ \& \ \ldots \ \& \ (C_6 - C_7\geq 1)$$ Suppose now that the luminance of $$i$$-th stripe is a random value with probability density function $$p_i(x)$$ and expected value $$C_i$$. How in this case should I compute $$P(E)$$—the probability of the event $$E$$?

• "whether they are distinguishable from one another" Actually it's whether they are distinguishable from the neighbours, no? It does not matter if the first and last stripes have the same luminances, right? ALso, are we assuming that the $C_i$ variables are independent? – leonbloy Feb 27 at 16:57
• @leonbloy, yes, neighbors should be distinguishable, so we can count the same number of stripes. They could be just alternating black and white. $C_i$ are independent, yes. – Glinka Feb 27 at 17:28