[Albert Rose][1] studied this question in the 1940's and developed the [Rose Criterion][2] which states that the signal-to-noise ratio ($SNR$):

$$SNR=\dfrac{\mu}{\sigma}$$

For $100$% identification of an object by the human eye is $SNR \approx 5$.  He based this off of quantum arguments where he looked at the [average number of photons per unit area in an photo image][3] and stated gave the equation $\Delta N = kN^{\frac{1}{2}}$ where $\Delta N$ is the smallest perceptible change and $N$ is the average number of quanta absorbed in a pixel and $k$ is the $SNR$ (see eq 1, 1a and figure 1).

If one uses this ratio, then in two independent pixels one can distinguish one from the other if there are an average of $100$ quanta absorbed in the pixels, then one would be able to distinguish between the two, if one had $50$ quanta more than the other.  This relationship has an obvious limit when the average number of quanta are $> 7$ and all the photon ($> 14$ total for two pixels) are found in one pixel and not the other, as shown in the table below.

![rose][4]



  [1]: http://en.wikipedia.org/wiki/Albert_Rose_%28physicist%29
  [2]: http://en.wikipedia.org/wiki/Signal-to-noise_ratio#Alternative_definition
  [3]: http://www.opticsinfobase.org/josa/abstract.cfm?uri=josa-38-2-196
  [4]: https://i.sstatic.net/dOUIb.jpg
  [5]: http://en.wikipedia.org/wiki/Absolute_threshold