A Generalized Framework for Multi-Level Image Data via Multivariate Log Gaussian Cox Processes

Music City Center 

In microscopic images of cells, various cell populations often co-exist in a particular tissue, forming highly spatially structured communities where different taxa interact at micrometer scales. Quantifying the spatial relationships of microbes is essential for uncovering biofilm functions and biological mechanisms. Multivariate log Gaussian Cox processes are flexible models for the analysis of multivariate point patterns. However, they have so far been focused on single realizations only (i.e. single images), ignoring similarity and dissimilarity across images. We move beyond this limitation to model spatial interactions among multiple object types, integrating multi-level images from multiple subjects. Particularly, we propose a unified hierarchical multivariate log Gaussian Cox process framework for multi-level image data from multiple subjects with a global governing process, providing a comprehensive quantification of the multivariate spatial relationships among object types. The proposed framework is appealing due to the ability to quantify both within-sample and across-sample variability and to derive global and subject-level inter-type spatial relationships simultaneously.

Microbiome Biofilm Image

Cross-pair Correlation

Log Gaussian Cox Process

Multivariate Point Process

Spatial Ecology 

Biometrics Section