Efficient Gaussian Process-Based Modelling and Prediction of Image Time Series

  • Marco Lorenzi
  • Gabriel Ziegler
  • Daniel C. Alexander
  • Sebastien Ourselin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9123)


In this work we propose a novel Gaussian process-based spatio-temporal model of time series of images. By assuming separability of spatial and temporal processes we provide a very efficient and robust formulation for the marginal likelihood computation and the posterior prediction. The model adaptively accounts for local spatial correlations of the data, and the covariance structure is effectively parameterised by the Kronecker product of covariance matrices of very small size, each encoding only a single direction in space. We provide a simple and flexible framework for within- and between-subject modelling and prediction. In particular, we introduce the Hoffman-Ribak method for efficient inference on posterior processes and its uncertainty. The proposed framework is applied in the context of longitudinal modelling in Alzheimer’s disease. We firstly demonstrate the advantage of our non-parametric method for modelling of within-subject structural changes. The results show that non-parametric methods demonstrably outperform conventional parametric methods. Then the framework is extended to optimize complex parametrized covariate kernels. Using Bayesian model comparison via marginal likelihood the framework enables to compare different hypotheses about individual change processes of images.



Marco Lorenzi is grateful to Prof. John Ashburner, for his help in finalizing this work, and to Dr. Richard Turner, for his precious suggestions on the train toward London. Sebastien Ourselin receives funding from the EPSRC (EP/H046410/1, EP/J020990/1, EP/K005278), the MRC (MR/J01107X/1), the EU-FP7 project VPH-DARE@IT (FP7-ICT-2011-9-601055), the NIHR Biomedical Research Unit (Dementia) at UCL and the National Institute for Health Research University College London Hospitals Biomedical Research Centre (NIHR BRC UCLH/UCL High Impact Initiative- BW.mn.BRC10269). Gabriel Ziegler is supported in part by the German Academic Exchange Service (DAAD). The Wellcome Trust Centre for Neuroimaging is supported by core funding from the Wellcome Trust [grant number 091593/Z/10/Z].


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marco Lorenzi
    • 1
  • Gabriel Ziegler
    • 2
  • Daniel C. Alexander
    • 1
  • Sebastien Ourselin
    • 1
  1. 1.Centre for Medical Image Computing, CMICUCLLondonUK
  2. 2.Wellcome Trust Centre for NeuroimagingUCLLondonUK

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