Poisson and multinomial mixture models for multivariate SIMS image segmentation.

Multivariate statistical methods have been advocated for analysis of spectral images, such as those obtained with imaging time-of-flight secondary ion mass spectrometry (TOF-SIMS). TOF-SIMS images using total secondary ion counts or secondary ion counts at individual masses often fail to reveal all salient chemical patterns on the surface. Multivariate methods simultaneously analyze peak intensities at all masses. We propose multivariate methods based on Poisson and multinomial mixture models to segment SIMS images into chemically homogeneous regions. The Poisson mixture model is derived from the assumption that secondary ion counts at any mass in a chemically homogeneous region vary according to the Poisson distribution. The multinomial model is derived as a standardized Poisson mixture model, which is analogous to standardizing the data by dividing by total secondary ion counts. The methods are adapted for contextual image segmentation, allowing for spatial correlation of neighboring pixels. The methods are applied to 52 mass units of a SIMS image with known chemical components. The spectral profile and relative prevalence for each chemical phase are obtained from estimates of model parameters.