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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