Three-dimensional Bayesian image analysis and confocal microscopy

Abstract

We report methods for tackling a challenging three-dimensional (3D) deconvolution problem arising in confocal microscopy. We fit a marked point process model for the set of cells in the sample using Bayesian methods; this produces automatic or semi-automatic segmentations showing the shape, size, orientation and spatial arrangement of objects in a sample. Importantly, the methods also provide measures of uncertainty about size and shape attributes. The 3D problem is considerably more demanding computationally than the two-dimensional analogue considered in Al-Awadhi et al. [2] due to the much larger data set and higher-dimensional descriptors for objects in the image. In using Markov chain Monte Carlo simulation to draw samples from the posterior distribution, substantial computing effort can be consumed simply in reaching the main area of support of the posterior distribution. For more effective use of computation time, we use morphological techniques to help construct an initial typical image under the posterior distribution.

Keywords:

• Bayesian statistics
• confocal microscopy
• image analysis
• Markov chain Monte Carlo methods
• mathematical morphology
• object recognition
• stochastic simulation
• three-dimensional deconvolution

Acknowledgements

The authors are grateful to Dr Nick White of Oxford University for providing the data set. The authors acknowledge, with appreciation, the comments of the referee and associate editor which improved the manuscript.