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This article introduces three-filters-to-normal+ (3F2N+), an extension of ourprevious work three-filters-to-normal (3F2N), with a specific focus onincorporating discontinuity discrimination capability into surface normalestimators (SNEs). 3F2N+ achieves this capability by utilizing a noveldiscontinuity discrimination module (DDM), which combines depth curvatureminimization and correlation coefficient maximization through conditionalrandom fields (CRFs). To evaluate the robustness of SNEs on noisy data, wecreate a large-scale synthetic surface normal (SSN) dataset containing 20scenarios (ten indoor scenarios and ten outdoor scenarios with and withoutrandom Gaussian noise added to depth images). Extensive experiments demonstratethat 3F2N+ achieves greater performance than all other geometry-based surfacenormal 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 threeadditional experiments to demonstrate the effectiveness of incorporating ourproposed 3F2N+ into downstream robot perception tasks, including freespacedetection, 6D object pose estimation, and point cloud completion. Our sourcecode and datasets are publicly available at https://mias.group/3F2Nplus.

Three-Filters-to-Normal+: Revisiting Discontinuity Discrimination in Depth-to-Normal Translation