Image Noise: Variance versus Mean Response

A plot of the computed variance versus the mean level of response is shown here. The data for this graph was taken from the BearFruitGrayB pre image. If the noise were additive, the plot would be a horizontal line, which it clearly is not. If the noise were Poisson, the data would lie along a line through the origin with unit slope. This is also not an accurate model. We fit the data with an equation of the form V = k1 + k2*M^p, where V is the variance, M the mean, and k1, k2, and p are free parameters. This parametric form can describe additive (k2 = 0), Poisson (k1 = 0, k2 = 1, p = 1), and multiplicative (k1 = 0, p = 2) noise. The plot shows the fit for the data shown. The fit is quite good.

Authors: David Brainard and Elizabeth Harding