The successful operation of a remote compliant tactile sensor requires that the shape of the surface membrane be accurately reconstructed from noisy data. To solve this problem, the reconstructed approximation to the shape of the membrane should depend smoothly on the data, but for an idealized fingertip, it is shown that it does not. Furthermore, experiments conducted on a prototype compliant fingertip show that a least-squares solution to the problem of determining the membrane shape behaves poorly in the presence of noise. A solution based on specific probabilistic assumptions is presented and the Bayes' theorem is used to compute a maximum a posteriori estimate. While application of this technique is problematic unless the conditional density function is unimodal, a novel condition that will guarantee unimodality, and hence a certain robustness, is presented. This result is applied to interpret tactile sensing data for the prototype fingertip.
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