A nonparametric measure of contrast in x-ray images

Objective. We propose a nonparametric figure of merit, the contrast equivalent distance CED, to measure contrast directly from clinical images. Approach. A relative brightness distance delta is calculated by making use of the order statistic of the pixel values. By multiplying delta with the grey value range R, the mean brightness distance MBD is obtained. From the MBD, the CED and the distance-to-noise ratio DNR can be derived. The latter is the ratio of the MBD and a previously suggested nonparametric measure tau for the noise. Since the order statistic is independent of the spatial arrangement of the pixel values, the measures can be obtained directly from clinical images. We apply the new measures to mammography images of an anthropomorphic phantom and of a phantom with a step wedge as well as to CT images of a head phantom. Main results. For low-noise images of a step wedge, the MBD is equivalent to the conventional grey value distance. While this measure permits the evaluation of clinical images, it is sensitive to noise. Therefore, noise has to be quantified at the same time. When the ratio sigma/tau of the noise standard deviation sigma to tau is available, validity limits for the CED as a measure of contrast can be established. The new figures of merit can be calculated for entire images as well as on regions of interest (ROI) with an edge length not smaller than 32 px. Significance. The new figures of merit are suited to quantify the quality of clinical images without relying on the assumption of a linear, shift-invariant system. They can be used for any kind of greyscale image, provided the ratio sigma/tau can be estimated. This will hopefully help to achieve the optimisation of image quality vs dose required by radioprotection laws.