Thermal conductivity contrast images in scanning thermal microscopy (SThM) are often distorted by artifacts related to local sample topography. This is pronounced on samples with sharp topographic features, on rough samples and while using larger probes, for example, Wollaston wire-based probes. The topography artifacts can be so high that they can even obscure local thermal conductivity variations influencing the measured signal. Three methods for numerically estimating and compensating for topographic artifacts are compared in this paper: a simple approach based on local sample geometry at the probe apex vicinity, a neural network analysis and 3D finite element modeling of the probe-sample interaction. A local topography and an estimated probe shape are used as source data for the calculation in all these techniques; the result is a map of false conductivity contrast signals generated only by sample topography. This map can be then used to remove the topography artifacts from measured data or to estimate the uncertainty of conductivity measurements using SThM. The accuracy of the results and the computational demands of the presented methods are discussed.

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