6 research outputs found
Lattice Identification and Separation: Theory and Algorithm
Motivated by lattice mixture identification and grain boundary detection, we
present a framework for lattice pattern representation and comparison, and
propose an efficient algorithm for lattice separation. We define new scale and
shape descriptors, which helps to considerably reduce the size of equivalence
classes of lattice bases. These finitely many equivalence relations are fully
characterized by modular group theory. We construct the lattice space
based on the equivalent descriptors and define a metric
to accurately quantify the visual similarities and
differences between lattices. Furthermore, we introduce the Lattice
Identification and Separation Algorithm (LISA), which identifies each lattice
patterns from superposed lattices. LISA finds lattice candidates from the high
responses in the image spectrum, then sequentially extracts different layers of
lattice patterns one by one. Analyzing the frequency components, we reveal the
intricate dependency of LISA's performances on particle radius, lattice
density, and relative translations. Various numerical experiments are designed
to show LISA's robustness against a large number of lattice layers, moir\'{e}
patterns and missing particles.Comment: 30 Pages plus 4 pages of Appendix. 4 Pages of References. 24 Figure