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Proceedings Paper

On the relationship between hidden Markov models and convex functional transforms for simulating scanning probe microscopy
Author(s): Omolabake A. Adenle; William J. Fitzgerald
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Paper Abstract

Models for simulating Scanning Probe Microscopy (SPM) may serve as a reference point for validating experimental data and practice. Generally, simulations use a microscopic model of the sample-probe interaction based on a first-principles approach, or a geometric model of macroscopic distortions due to the probe geometry. Examples of the latter include use of neural networks, the Legendre Transform, and dilation/erosion transforms from mathematical morphology. Dilation and the Legendre Transform fall within a general family of functional transforms, which distort a function by imposing a convex solution. In earlier work, the authors proposed a generalized approach to modeling SPM using a hidden Markov model, wherein both the sample-probe interaction and probe geometry may be taken into account. We present a discussion of the hidden Markov model and its relationship to these convex functional transforms for simulating and restoring SPM images.

Paper Details

Date Published: 22 May 2009
PDF: 8 pages
Proc. SPIE 7378, Scanning Microscopy 2009, 737814 (22 May 2009); doi: 10.1117/12.824187
Show Author Affiliations
Omolabake A. Adenle, Univ. of Cambridge (United Kingdom)
William J. Fitzgerald, Univ. of Cambridge (United Kingdom)


Published in SPIE Proceedings Vol. 7378:
Scanning Microscopy 2009
Michael T. Postek; Michael T. Postek; Michael T. Postek; Dale E. Newbury; Dale E. Newbury; Dale E. Newbury; S. Frank Platek; S. Frank Platek; S. Frank Platek; David C. Joy; David C. Joy; David C. Joy, Editor(s)

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