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Statistics and the Life and Death of Pixels

This project would be supervised jointly with my colleague Julia Brettschneider.

The EPSRC-funded grant Inside-Out: Statistical methods for Computed Tomography validation of complex structures in Additive Layer Manufacturing
(EP/K031066/1: 2013-2016) was held jointly by Warwick Statistics and Warwick Manufacturing Group (WMG), involving a multidisciplinary team, namely Julia Brettschneider, Wilfrid Kendall (PI), Audrey Kueh (Statistics), and Tom Nichols (Statistics/WMG) and Greg Gibbons, Jay Warnett, and Mark Williams (co-PI) (WMG). The overall aim of the project was to investigate the use of advanced statistical methods to determine the best ways in which to use computed tomography (CT) to assess quality of short production runs of objects produced by Additive Layer Manufacturing ("3D printing"). The challenge here is that CT is necessarily a slow process when applied to high density objects, so careful methodological thought is required to consider the most effective ways to determine quality on a short time-scale. We have established regular industrial collaboration with Nikon UK, Renishaw, and EOS.

In the course of our work, we have identified a number of possible PhD projects. Here is one.

Digital flat detector panels are used, for example, in computed tomography [1,2]. The signals are detected by pixels arranged in a rectangular grid. Over time some pixels become dysfunctional compromising the quality of the resulting images. Eventually, the detector needs to be refurbished or replaced at high cost.Using pilot data from bad pixel maps generated by our collaborators at the Warwick Manufacturing Group, we have completed an initial round of data analysis [3]. We have given particular attention to visualising and modelling spatial arrangement of dead pixels. Our taxonomy of damages includes corner/edge damages, dead lines, several types of clusters and lines. Keen on extending this analysis to fitting spatio-temporal models, we have been collecting a series of daily test images taken first thing in the morning. Our most pressing question concerns the lines. We are hoping to get more insight into the way in which these lines develop over time. This will likely help to confirm or reject common physical explanations about them. Another question concerns the process a pixel might undergo until it ends up being classified as "dead", presumably an absorbing state. Which other states, likely transitional, are available? Can a pixel recover from being dysfunctional and return to normal rather then proceeding to death? These and other questions form the basis of a spatio-temporal analysis of the new data set. Practical applications include devising monitoring schedules for these detectors to ensure consistent image quality. We expect that this would lead very naturally to a full PhD project involving careful spatio-temporal analysis of the development of defects. This work has attracted significant interest from our industrial collaborators, who are keenly aware of the cost savings that might arise from a better understanding of the process of defect development: an initial paper is now being prepared which we hope to use to attract a diversity of data sources to help us investigate these issues. A prerequisite for this project is experience with data analysis and programming in R.

  1. Angela Cantatore and Pavel Mueller. Introduction to computed tomography.
    Technical report, DTU Mechanical Engineering, 2011.
    Available at
  2. Maire E. and Withers P. J. Quantitative X-ray tomography. International Materials Reviews, 59(1):1–43, 2013.
  3. Brettschneider J, Thornby J, Nichols TE and Kendall WS. Spatial analysis of dead pixels, CRiSM Working Paper Series No. 14-24, 2014
    Available at