Analysis and Extension of the Percentile Method, Estimating a Noise Curve from a Single Image

Given a white Gaussian noise signal Nσ on a sampling grid, its variance σ 2 can be estimated from a small w × w pixels sample. However, in natural images we observe Ũ = U + Nσ, the combination of the geometry of the scene that is photographed and the added noise. In this case, estimating directly the standard deviation of the noise from w × w samples of Ũ is not reliable since the measured standard deviation is not explained just by the noise but also by the geometry of U. The Percentile method tries to estimate the standard deviation σ from w × w blocks of a high-passed version of Ũ by a small p-percentile of these standard deviations. The idea behind is that edges and textures in a block of the image increase the observed standard deviation but they never make it decrease. Therefore, a small percentile (0.5%, for example) in the list of standard deviations of the blocks is less likely to be affected by the edges and textures than a higher percentile (50%, for example). The 0.5%-percentile is empirically proven to be adequate for most natural, medical and microscopy images. The Percentile method is adapted to deal with signal-dependent noise, which is realistic with the Poisson noise model obtained by a CCD device in a digital camera. Source Code The C++ implementation of the Percentile noise estimator has been peer reviewed and accepted by IPOL. The source code, the code documentation, and the online demo are available in the IPOL web page of this article1.