  In this investigation we focus on the problem of mapping the ground
reflectivity with multiple laser scanners mounted on mobile robots/vehicles.
The problem originates because regions of the ground become populated with a
varying number of reflectivity measurements whose value depends on the observer
and its corresponding perspective. Here, we propose a novel automatic,
data-driven computational mapping framework specifically aimed at preserving
edge sharpness in the map reconstruction process and that considers the sources
of measurement variation. Our new formulation generates map-perspective
gradients and applies sub-set selection fusion and de-noising operators to
these through iterative algorithms that minimize an $\ell_1$ sparse regularized
least squares formulation. Reconstruction of the ground reflectivity is then
carried out based on Poisson's formulation posed as an $\ell_2$ term promoting
consistency with the fused gradient of map-perspectives and a term that ensures
equality constraints with reference measurement data. We demonstrate our new
framework outperforms the capabilities of existing ones with experiments
realized on Ford's fleet of autonomous vehicles. For example, we show we can
achieve map enhancement (i.e., contrast enhancement), artifact removal,
de-noising and map-stitching without requiring an additional reflectivity
adjustment to calibrate sensors to the specific mounting and robot/vehicle
motion.
