A Fast Metric Based on Marching Cubes and Hausdorff Distance for the Quality Assessment of 3D Volume Data for Computed Tomography Measurement Technology

Inline X-ray Computed Tomography (xCT) offers a promising approach for the quality assurance and control of various workpieces during production. This is due to its capability to non-destructively inspect both internal and external structures. However, the typical duration of measurements, which extends to several hours, remains a limiting factor in practical applications. The sparse view xCT method, which limits the number of necessary projection images, can reduce this duration to a few minutes. Nonetheless, this reduction in time increases the overall measurement uncertainty, primarily due to streak artifacts. Therefore, the ability to efficiently quantify a quality measure sensitive to the number of projections captured during xCT measurement is crucial for determining the reliability of conducted measurements. This paper introduces a quality metric sensitive to streak artifacts, which uses a rapid surface determination algorithm known as marching cubes, followed by the computation of the Hausdorff distance between a reference surface and the extracted surface. An experimental study correlating the Hausdorff distance to the measurement uncertainty as a function of the utilized number of projections is conducted. The findings show that the Hausdorff distance increases for surfaces extracted from measurements taken with fewer projections. Additionally, by analyzing the correlation between the Hausdorff distance and the measurement uncertainty, quantified through the standard deviation of multiple extracted geometrical features from the measured test workpiece, a strong positive correlation is observed.