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