Dynamic grain models via fast heuristics for diagram representations

Abstract

ABSTRACT The present paper introduces a mathematical model for analysing dynamic grain growth. In particular, we show how the characteristic measurements grain volumes, centroids, and central second-order moments at discrete moments in time can be quickly turned into a continuous description of the grain growth process in terms of geometric diagrams (which largely generalize the well-known Voronoi and Laguerre tessellations). We give a theoretical analysis of common optimization-free heuristics in terms of discriminant analysis and evaluate the computational behaviour of our algorithm on real-world data.