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Restoration of Deformed Lattice Patterns

Published online by Cambridge University Press:  05 September 2017

Ulf Grenander
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Abstract

The restoration of crystal lattices which have been jittered presents some problems that do not seem to have been previously studied. This is true especially in the multi-dimensional case. It is shown that a statistic suggested by Bartlett can be used for this purpose, and this is done both for Gaussian and general deformation mechanisms. The results are accompanied by some numerical experiments.

Type
Part VII — Probability Models in the Physical Sciences
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 275 - 293
Copyright
Copyright © 1975 Applied Probability Trust 

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References

Bartlett, M. S. (1964) The spectral analysis of two-dimensional point processes. Biometrika 51, 299–311.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Grenander, U et al. Reports Nos. 1–32 on pattern analysis. Division of Applied Mathematics, Brown University, Providence, Rhode Island.Google Scholar
Mcclure, D. E. (1973) Personal communication.Google Scholar