  Haptic feedback is important to make robots more dexterous and effective in
unstructured environments. High-resolution haptic sensors are still not widely
available, and their application is often bound by the resolution-robustness
dilemma. A route towards high-resolution and robust skin embeds a few sensor
units (taxels) into a flexible surface material and uses signal processing to
achieve sensing with super-resolution accuracy. We propose a theory for
geometric super-resolution to guide the development of haptic sensors of this
kind and link it to machine learning techniques for signal processing. This
theory is based on sensor isolines and allows us to predict force sensitivity
and accuracy in contact position and force magnitude as a spatial quantity. We
evaluate the influence of different factors, such as elastic properties of the
material, structure design, and transduction methods, using finite element
simulations and by implementing real sensors. We empirically determine sensor
isolines and validate the theory in two custom-built sensors with barometric
units for 1D and 2D measurement surfaces. Using machine learning methods for
the inference of contact information, our sensors obtain an unparalleled
average super-resolution factor of over 100 and 1200, respectively. Our theory
can guide future haptic sensor designs and inform various design choices.
