This EPSRC-funded project is an interdisciplinary collaboration between certain members of the Statistics Department (myself, my EPSRC-funded research associate Audrey Kueh, my Statistics Department colleagues Tom Nichols and Julia Brettschneider) and colleagues in Warwick Manufacturing Group (Mark Williams and Greg Gibbons, and a sequence of EPSRC research associates funded at 50% or less namely John Thornby, Jay Warnett, David Crevillen Garcia, and Clair Barnes).
Our objective was to develop fast methods for CT analysis of artefacts produced by 3D printing. We began by making a thorough examination of the nature of typical data, including validating a variance-mean statistical model for CT images, and careful analysis of the projection images at a pixel level. In the second of these tasks we found some very interesting issues to do with dead pixels, and this spawned off into its own investigation. We are now preparing a paper on this: see Brettschneider et al, (2014) for an account of our initial investigations.

We then considered very carefully the nature of "penumbras" in projections (blurring of boundaries arising from the fact that the x-ray source is not a point). We discovered some surprising features of this, and the story is told in Kueh et al. (2016).

Finally we developed an approach enabling rapid mapping of small defects, deploying image analysis techniques, false-discovery-rate analysis, and careful mathematical stereography. We are now preparing a paper on this as well.

1. We have investigated issues of image quality for CT scanners, and published an analysis (Kueh et al, 2016) demonstrating that penumbra effects can be mitigated by careful filter design.
2. The model for the variance -mean relationship was confirmed in broad detail. However there are several significant features of interest which are now being investigated by an EPSRC-funded research student.
3. We have developed a procedure for rapid assessment and location of collections of small defects in 3D-printed objects. A paper describing this methodology is now in preparation.
4. We have developed an analysis of spatial statistics for dead pixels in detector screens. A paper describing this methodology is now in preparation (preliminary working papers: Brettschneider et al, 2014, 2017), and we hope to formulate a web-based data-collection exercise to draw together information from other users of detector screens.
5. Warnett et al. (2016) reports on ongoing investigation of industrial uses for real-time tomography devices developed in the context of airport baggage searches.
   In related work carried out during this period using nonlinear geometric mean values,
6. Kendall (2015) has developed non-parametric methods for studying hurricane trajectories.
   

Here is a list of papers or working papers which concern work funded wholly or in part by this grant:

• Brettschneider, JA, Thornby, J, Nichols, TE, Kendall, WS. (2014). Spatial analysis of dead pixels: Technology, conventions and data. University of Warwick: Department of Statistics, Centre for Research in Statistical Methodology Working Paper series Volume 14, issue 24, 21pp . Access at http://www2.warwick.ac.uk/fac/sci/statistics/crism/research/paper14-24.
  
• Brettschneider, J. A., Warnett, J. W., Nichols, T. E., & Kendall, W. S. (n.d.). Higher level spatial analysis of dead pixels on detectors based on local grid geometry Department of Statistics, Centre for Research in Statistical Methodology Working Paper series Volume 17, issue 2, 21pp. Access at http://www2.warwick.ac.uk/fac/sci/statistics/crism/research/17-02.
  
• Kendall, WS, & Kueh, A. (2015). Layered 2D ray-averaging approximation. In 60th World Statistics Congress, Rio de Janeiro (p. 6pp). Access at http://www.isi2015.org/components/com_users/views/registration/tmpl/media/uploadedFiles/paper/1990/3959/OR-B07-P2-S.pdf.
• Kendall, WS. (2015). Barycentres and Hurricane Trajectories. In I. L. Dryden & J. T. Kent (Eds.), Geometry-Driven Statistics (pp. 146–160). Chichester / New York: John Wiley & Sons Ltd. Access at arXiv:1406.7173.
• Kueh A, Warnett JM, Gibbons GJ, Brettschneider J, Nichols TE, Williams MA, & Kendall WS. (2016). Modelling the penumbra in Computed Tomography. Journal of X-ray science and technology, 24 (4), pp. 583-97. Gold Access: journal-of-x-ray-science-and-technology/xst576.
  
• Warnett, JM, Titarenko, V, Kiraci, E, Attridge, A, Lionheart, WRB, Withers, P.J, & Williams, MA. (2016). Towards in-process x-ray CT for dimensional metrology. Measurement Science and Technology, 27(3), 14pp. Open Access at http://doi.org/10.1088/0957-0233/27/3/035401.

In conclusion, here is a mindmap generated in the early stages of the project.