I don't know where to link you to, but here is a more detailed statement, which I think could be straightforwardly expanded into something precise.
Consider a signal S[i], i=1...N. The human eye isn't actually perceiving S[i], it's perceiving some convolution of it S[i] \conv w[i] (for a window function w). I.e., an area with 50% white pixels and 50% black pixels appears grey.
Suppose for simplicity w[i] = 1/k on i=0...k.
Now add noise g[i] to the signal in a region where S[i] = alpha. Then S[i] + g[i] = alpha + g[i]. The number of pixels above a threshold T within the window are then 1-cdf(T-alpha), where cdf is the cdf of the distribution of g.
Assuming your cdf is approximately linear near T, then 1-cdf(T-alpha) \approx C + alpha.
Consider a signal S[i], i=1...N. The human eye isn't actually perceiving S[i], it's perceiving some convolution of it S[i] \conv w[i] (for a window function w). I.e., an area with 50% white pixels and 50% black pixels appears grey.
Suppose for simplicity w[i] = 1/k on i=0...k.
Now add noise g[i] to the signal in a region where S[i] = alpha. Then S[i] + g[i] = alpha + g[i]. The number of pixels above a threshold T within the window are then 1-cdf(T-alpha), where cdf is the cdf of the distribution of g.
Assuming your cdf is approximately linear near T, then 1-cdf(T-alpha) \approx C + alpha.