Non-parametric noise measure tau

A nonparametric measure of noise in a monochromic image is obtained by calculating an average NMS threshold.

If T(x,y,t) is the non-maximum suppression (NMS) image for threshold t, the number n(t) of pixels is calculated, where the (absolute) difference of a pixel gray value to its four or eight neighbour pixels exceeds the threshold t. The average threshold tau is obtained by averaging t using n(t) as a weight.

The function tau=avThreshNoise(Y) calculates the corresponding tau values for an array of images Y (Y has the size [ny,nx,nim], where nim is the number of images).

It turns out that tau is proportional to the standard deviation of the noise in the image, where the proportionality factor depends on the covariance of the noise and on whether 4 or 8 NN are considered.

For white noise with a standard deviation of Unity, e.g., tau= 0.4817 (8 NN) or 0.5619 (4 NN).

The advantage of using tau as a measure of noise is that it can be estimated from images with a structured background, as e.g. from x-ray diagnostic images. Only very fine structured, periodic backgrounds influence the value of tau, when the spatial frequency is close to the grid size. Large scale structures leave tau unaffected.

Details can be found in the citation given below.

The updated version of the function to calculate tau is now approximately 100 times faster than the old one, due to a more efficient algorithm to count the next neighbours developed by Ulf Mäder, University of Applied Sciences, Giessen, Germany.