On the relationship between hidden Markov models and convex functional transforms for simulating scanning probe microscopy

Omolabake A. Adenle; William J. Fitzgerald

doi:10.1117/12.824187

22 May 2009 On the relationship between hidden Markov models and convex functional transforms for simulating scanning probe microscopy

Omolabake A. Adenle, William J. Fitzgerald

Author Affiliations +

Proceedings Volume 7378, Scanning Microscopy 2009; 737814 (2009) https://doi.org/10.1117/12.824187
Event: SPIE Scanning Microscopy, 2009, Monterey, California, United States

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.

Citation Download Citation

Omolabake A. Adenle and William J. Fitzgerald "On the relationship between hidden Markov models and convex functional transforms for simulating scanning probe microscopy", Proc. SPIE 7378, Scanning Microscopy 2009, 737814 (22 May 2009); https://doi.org/10.1117/12.824187

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