  This article introduces three-filters-to-normal+ (3F2N+), an extension of our
previous work three-filters-to-normal (3F2N), with a specific focus on
incorporating discontinuity discrimination capability into surface normal
estimators (SNEs). 3F2N+ achieves this capability by utilizing a novel
discontinuity discrimination module (DDM), which combines depth curvature
minimization and correlation coefficient maximization through conditional
random fields (CRFs). To evaluate the robustness of SNEs on noisy data, we
create a large-scale synthetic surface normal (SSN) dataset containing 20
scenarios (ten indoor scenarios and ten outdoor scenarios with and without
random Gaussian noise added to depth images). Extensive experiments demonstrate
that 3F2N+ achieves greater performance than all other geometry-based surface
normal estimators, with average angular errors of 7.85$^\circ$, 8.95$^\circ$,
9.25$^\circ$, and 11.98$^\circ$ on the clean-indoor, clean-outdoor,
noisy-indoor, and noisy-outdoor datasets, respectively. We conduct three
additional experiments to demonstrate the effectiveness of incorporating our
proposed 3F2N+ into downstream robot perception tasks, including freespace
detection, 6D object pose estimation, and point cloud completion. Our source
code and datasets are publicly available at https://mias.group/3F2Nplus.
