Determination of Probabilistic Distribution Function of Background and Defect Optical Densities for X-Ray Radiography Images of a Steel Plate

Abstract

Usually Gaussian function is used in mathematical modeling of radiographic images output and designing the related image processing filters. The aim of this work is to examine 40 distribution functions which can be used to define the probability distribution function of radiographic films. For this purpose, steel plates with dimensions of 30 \(\times \) 30 cm\(^{2 }\) and thickness of 2 and 8 mm were initially exposed to 80–200 keV X-ray with different radiation intensities as referred in the text. These plates were initially fault-free but some defects were embedded intentionally in selected parts. After radiography, the obtained films were converted to digital images using a laser scanner. Using the digital images, 39 different probability distribution functions were fitted to the obtained histograms. In addition, a new fitting function to predict the histograms treatments is developed by the authors and named Sasanpour–Taheri-proposed Function (STF). The best fitted probability distribution function for the background optical density was STF. Fitting operation was also done for prediction of defects related to density function, where the STF show best results.