Artifacts due to imperfect determination of the scanner geometry, beam hardening and diffuse Compton scattering, limit the quantitative exploitation of radiographs or tomographies for non-destructive evaluation. Exploiting the CAD model of an industrial part, a methodology is proposed to refine the estimation of the CT-scanner geometry up to a scale factor, to correct or account for artifacts, and to assess the metrology of the part. A projective model describing the formation of X-ray images in CT-scanners is first introduced. The optimal parameters of the projective model are identified using a novel CAD-based calibration method that relies on the registration of simulated projections onto experimental ones. A metrological analysis based on the comparison between acquired and simulated X-ray images is proposed. A turbine blade, for which an automatic inspection procedure from few views is under development, is used as an example to illustrate the proposed methodology. The parametrization accounts for the refinement of the projection geometry, the calibration of beam hardening and the estimation of scattering. It is shown that, using the proposed procedure, the differences between acquired and simulated radiographic images are significantly reduced, indicating that the optimal parameters are properly identified. These differences are then exploited to detect flaws of the part.

The number [Formula: see text] of colorings of a knot [Formula: see text] by a finite quandle [Formula: see text] has been used in the literature to distinguish between knot types. In this paper, we suggest a refinement [Formula: see text] to this knot invariant involving any computable functor [Formula: see text] from finitely presented groups to finitely generated abelian groups. We are mainly interested in the functor [Formula: see text] that sends each finitely presented group [Formula: see text] to its abelianization [Formula: see text]. We describe algorithms needed for computing the refined invariant and illustrate implementations that have been made available as part of the HAP package for the GAP system for computational algebra. We use these implementations to investigate the performance of the refined invariant on prime knots with [Formula: see text] crossings.