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

## Publication 35

### Segmentation of crystal defects via local analysis of crystal distortion

##### Authors:

Matt Elsey
Courant Institute of Mathematical Sciences
New York University

Benedikt Wirth

##### Abstract:
We propose a variational method to simultaneously detect dislocations and grain boundaries in an image of a crystal as well as the local crystal distortion. To this end we extract a distortion field $F$ from the image which is nearly curl-free except at dislocations and grain boundaries. The sparsity of the curl is promoted by an $L^1$-regularization of curl $F$ in the employed energy functional. The structure of the functional admits a fast and parallelizable minimization such that fairly large images can be analyzed in a few minutes.
##### Get the paper in its entirety
SegmentationofElsey.pdf

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