  This paper introduces five new density and accuracy metrics for aerial point
clouds that address the complexity and objectives of modern, dense laser scans
of urban scenes. The five metrics describe (1) vertical surface density (points
per area on vertical surfaces); (2) vertical density as a function of
horizontal density; (3) vertical surface accuracy; and a decomposition of error
into (4) within-pass and (5) cross-pass components. Specifically considered is
vertical surface coverage and the practice of overlapping flight passes to
reduce the occlusions and achieve the vertical density needed for
twenty-first-century use cases (e.g. curb and window detection). The
application of these metrics to a quartet of recent urban flyovers demonstrates
their relevance by establishing (1) the efficacy of considering sensor position
and wall height when predicting point density on vertical surfaces; (2) that
cross-pass registration accounts for a disproportionate amount of the vertical
surface error (but not horizontal) and provides a meaningful parameter to
compare high-density, urban point clouds; and (3) that compared to horizontal
density and accuracy, the vertical counterparts are disproportionately impacted
(positively for density and negatively for accuracy) by modern, optimized
flight missions.
