Difference-Based Image Noise Modeling Using Skellam Distribution

By the laws of quantum physics, pixel intensity does not have a true value, but should be a random variable. Contrary to the conventional assumptions, the distribution of intensity may not be an additive Gaussian. We propose to directly model the intensity difference and show its validity by an experimental comparison to the conventional additive model. As a model of the intensity difference, we present a Skellam distribution derived from the Poisson photon noise model. This modeling induces a linear relationship between intensity and Skellam parameters, while conventional variance computation methods do not yield any significant relationship between these parameters under natural illumination. The intensity-Skellam line is invariant to scene, illumination, and even most of camera parameters. We also propose practical methods to obtain the line using a color pattern and an arbitrary image under natural illumination. Because the Skellam parameters that can be obtained from this linearity determine a noise distribution for each intensity value, we can statistically determine whether any intensity difference is caused by an underlying signal difference or by noise. We demonstrate the effectiveness of this new noise model by applying it to practical applications of background subtraction and edge detection.