Estimating microstructural feature distributions from image data using a Bayesian framework

Many microstructural characterizations methods collect data on a regular pixelized grid. This method of discretization introduces a form of measurement error which can be shown to be proportional to the resolution at which they are collected. Intuitively, measurements made from low-resolution data are associated with higher error, but quantification of this error is typically not performed. This is reflected in international standards for measurements of grain size, which only provide a recommended minimum number of sample points per microstructural component to ensure each component is sufficiently resolved. In this work, a new method for quantifying the relative uncertainty of such pixelized measurements is presented. Using a Bayesian framework and simulated data collection on features collected from a Voronoi tessellation, the distribution of true geometric properties given a particular set of measurements is computed. This conditional feature distribution provides a quantitative estimate for the relative uncertainty associated with measurements made at difference resolutions. The approach is applied to measurements of size, aspect ratio and perimeter of given microstructural components. Size distributions are shown to be the least sensitive to sampling resolution, and evidence is presented which shows that the international standards provide an overly conservative minimum resolution for grain size measurement in microstructures represented by a Voronoi tessellation.