Estimating microstructural feature distributions from image data using a bayesian framework.

Abstract

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 it is 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. Layout Description For many materials, their structure when viewed under a microscope can tell researchers a lot about how a material will perform and under what conditions it might fail. However, in order to collect and store this information for study, special high resolution images need to be taken. For imaging at really small scales this imaging process involves scientific equipment that is both expensive and time consuming to use. The resolution, or the amount of physical area on the surface of the material each pixel represents, determines what sort of information can be collected from the image. But these images have measurement error; small differences between what is shown in the image and the material itself. This works examines the relationship between the amount of error in the image and the resolution at which is was collected. A mathematical formula is developed which tells researchers what the range of probable true size are for an object they measured. This gives researchers a better picture at what they are actually looking at. Using a computer simulations, this formula is used to study the process of collecting and analysis material data. The results help show what at resolutions images should be collected to provide accurate the meaningful results for a wide range ofmeasurments. This article is protected by copyright. All rights reserved.