Nonparametric Bayesian Modelling of Spatial Fields and Images

Fluorescence cellular imaging often lends itself to modelling through a spatial Poisson point process with an unknown intensity function which can be non-parametrically modelled through a mixture model. The shape and organization of cells is then reflected in the appropriate choices of prior distributions on the base measures of the mixture models as well as background versus signal fluorescence.

The immune response to vaccines and microbial pathogens is characterized by the spatial reorganization of leukocytes into microanatomical structures such as germinal centers and granulomas. Below we show a zoomed-in image of a lymph node section stained for B220, taken from C.Ji, D.Merl, T.Kepler, and M.West. Spatial mixture modelling for unobserved point processes: examples in immunofluorescence histology. Bayesian Analysis, 4(2):297--316, 2009.
Contour plot of the populations
Data on cellular organization is often provided by immunofluorescence histology, in which antibodies against specific molecules are conjugated (directly or indirectly) to fluorophores and used to stain thin sections of tissue for subsequent microscopic imaging. We have developed statistical tools to assist in the identification and quantitative characterization of cellular aggregates in immunofluorescent images. We model the spatial distribution of cells as a heterogeneous point process; the major inferential task then is the estimation of the Poisson intensity function underlying the point process. Note that this intensity function represents cellular density, not the fluorescence intensity itself. The intensity function is itself modeled as a flexible non-parametric Gaussian mixture model and provides the basis for the computation of statistics used to characterize the state of development of germinal centers and other cellular aggregates. We describe these methods and their efficient computational implementation and illustrate their use on high-resolution images of lymph node sections stained for CD4, IgM, B220 and GL7. We identify and quantitatively characterize some of the major structural components of post-immunization lymph nodes such as B-cell follicles and germinal centers.

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