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Statistical shape analysis of images of the human brain and its use in the criminal justice system and beyond

Summary of impact
Methods developed in Leeds for statistical shape analysis have been used on brain images to assess the extent of brain damage in people suffering from fetal alcohol syndrome disorders (FASD) and as a method of diagnosis. 

The research has also been used to present expert witness testimony over the past 15 years in 25 death-penalty court cases in the US, 15 of them since 2008. In such cases, the guilt of the defendant is not in question, but evidence of FASD can be used as a mitigating circumstance when sentencing. 

Overall, success has been achieved in about two-thirds of the cases. Away from the justice system, a positive diagnosis of FASD, using the statistical shape analysis developed at Leeds, enabled a baby to receive state-funded specialist medical care.

Underpinning research 
The field of statistical shape analysis seeks to quantify in a statistical sense the differences between shapes of geometrical objects. There is now an established body of methodology, much of it developed at Leeds. 

Below is a summary of the relevant key research achievements at Leeds and how these methods have been used to diagnose FASD.

  • A consolidation of the research in shape analysis up to 1998 is given in the research monograph, which was awarded the Statistics Book of the Year prize in 1999 from Wiley. This monograph unified and extended several disparate strands of development and demonstrated the power of shape analysis through a variety of case studies in morphometrics and image analysis.
  • A key ingredient in modern shape methodology is the use of Procrustes tangent coordinates, sometimes called Procrustes residuals, for landmark data. Improving on earlier approaches to Procrustes analysis, the Leeds group developed the fundamental representation of Procrustes tangent coordinates as a tangent-plane projection. This coordinate system transforms the problem of shape comparisons into a version of multivariate analysis and enables the statistical analysis of complex and subtle differences in shape space to be reduced to a familiar setting using existing statistical tools. 
  • Another view of shape change is through continuous deformations of two- or three-dimensional space, typically using thin-plate splines, which are related to the theory of self-similar intrinsic random fields. The implications of this theory for multi-scale metric comparisons between images were set out in a 2006. Methods were given to estimate the self-similarity parameter and to assess goodness-of-fit with an application to medical images.
  • An extension of landmark-based shape analysis to include directions along the outline of an object was developed in a 2004 paper, in which outline data are summarized in terms of key landmarks together with tangent vectors. This work provides more powerful tools for the analysis of image data.
  • In 2013 the use of shape analysis, building on the earlier Leeds work, began to be used to assess brain damage in fetal alcohol syndrome disorders.