Communications in Mathematical Sciences
Volume 17 (2019)
$3D$ crystal image analysis based on fast synchro-squeezed transforms
Pages: 2113 – 2140
We propose an efficient algorithm to analyze $3D$ crystal structure at the individual particle level based on a fast $3D$ synchro-squeezed wave packet transform. The proposed algorithm can automatically extract microscopic information from $3D$ atomic/particle resolution crystal images, e.g., crystal orientation, defects, and deformation, which are important information for characterizing material properties as well as potentially understanding the underlying formation processes. The effectiveness of our algorithms is illustrated by experiments of synthetic datasets and real $3D$ microscopic colloidal images.
crystal defect, elastic deformation, crystal rotation, $3D$ general wave shape, $3D$ band-limited synchro-squeezed transforms
2010 Mathematics Subject Classification
65T99, 74B20, 74E15, 74E25
H. Yang thanks the support of the start-up grant of the Department of Mathematics at the National University of Singapore and the Ministry of Education in Singapore under the grant MOE2018-T2- 2-147. L. Li gratefully acknowledges the Department of Mechanical Engineering at Virginia Tech for the start-up support.
Received 30 January 2019
Accepted 4 July 2019
Published 3 February 2020