# Science at the triple point between mathematics, mechanics and materials science

## Publication 33

### Fast Automated Detection of Crystal Distortion and Crystal Defects in Polycrystal Images

##### Authors:

Matt Elsey
Courant Institute of Mathematical Sciences
New York University

Benedikt Wirth

##### Abstract:
Given an image of an atomic crystal, we propose a variational method which at each image location determines the local crystal state and which localizes and characterizes crystal defects. In particular, the local crystal orientation and elastic distortion are detected, as well as dislocations, and grain and twin boundaries. To this end an energy functional is devised whose minimization yields a tensor field describing the local crystal strain at each point. The desired information about the local crystal state can then be read o from this tensor fi eld; in particular, its curl provides information about grain boundaries and dislocations. As is typical for variational image processing, the energy functional is composed of a fidelity and a regularization term. It has a simple $L^2-L^1$ type structure so that its minimization can be performed via a split Bregman iteration. GPU parallelization results in short computing times.
##### Get the paper in its entirety
FastautomoatedElsey.pdf

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