Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Monte Carlo Reconstruction: a concept for propagating uncertainty in computed tomography



Massimiliano Ferrucci, Evelina Ametova, Wim Dewulf


We present a concept for propagating uncertainty in X-ray computed tomography (CT) by a Monte Carlo Reconstruction (MCR) technique, comprising repeated reconstructions with varying input parameters. The proposed technique follows the framework for model-based X-ray CT uncertainty assessment per the Monte Carlo Method (JCGM 101), although provides several advantages over the conventional implementation, which relies on simulating all individual steps in the X-ray CT measurement procedure and therefore considered to be impractical due to its high computational demand. The proposed method requires only a single set of simulated projections. For each Monte Carlo trial, the instrument geometrical parameters in a filtered back projection reconstruction algorithm are randomly sampled from specified uncertainty distributions. The output is a four-dimensional volumetric model where each voxel, defined by its three-dimensional indices, is represented by a distribution of reconstructed gray values. We reduce the four-dimensional volumetric model to three single-gray-value voxel models by calculating descriptive statistics: a voxel-wise lower gray confidence limit, a central gray value, and an upper gray value confidence limit. Dimensional measurements performed on the surfaces determined from each single-gray-value model provide insight on the effect of uncertainty in the instrument geometry. The proposed approach requires significantly less computations and data storage per Monte Carlo trial and provides a straight-forward way to relate uncertainties in reconstructed gray values to uncertainties in subsequent dimensional measurements. This, in turn, facilitates the practical application of the Monte Carlo Method in X-ray CT. We implement MCR to determine uncertainty distributions in the simulated X-ray CT measurement of a simple cube and an impeller due to uncertainties in the instrument geometry. Possible extension of MCR to other sources of uncertainty in the X-ray CT measurement process is discussed in the conclusions.
CIRP Journal of Manufacturing Science and Technology


computed tomography, measurement uncertainty, geometrical calibration, probability distributions, Monte Carlo


Ferrucci, M. , Ametova, E. and Dewulf, W. (2021), Monte Carlo Reconstruction: a concept for propagating uncertainty in computed tomography, CIRP Journal of Manufacturing Science and Technology, [online], (Accessed April 22, 2024)
Created July 19, 2021, Updated December 9, 2022