The state-of-the-art (SoTA) surface normal estimators (SNEs) generally
translate depth images into surface normal maps in an end-to-end fashion.
Although such SNEs have greatly minimized the trade-off between efficiency and
accuracy, their performance on spatial discontinuities, e.g., edges and ridges,
is still unsatisfactory. To address this issue, this paper first introduces a
novel multi-directional dynamic programming strategy to adaptively determine
inliers (co-planar 3D points) by minimizing a (path) smoothness energy. The
depth gradients can then be refined iteratively using a novel recursive
polynomial interpolation algorithm, which helps yield more reasonable surface
normals. Our introduced spatial discontinuity-aware (SDA) depth gradient
refinement strategy is compatible with any depth-to-normal SNEs. Our proposed
SDA-SNE achieves much greater performance than all other SoTA approaches,
especially near/on spatial discontinuities. We further evaluate the performance
of SDA-SNE with respect to different iterations, and the results suggest that
it converges fast after only a few iterations. This ensures its high efficiency
in various robotics and computer vision applications requiring real-time
performance. Additional experiments on the datasets with different extents of
random noise further validate our SDA-SNE's robustness and environmental
adaptability. Our source code, demo video, and supplementary material are
publicly available at mias.group/SDA-SNE.

本文提出了一种新颖的多方向动态规划策略来自适应性地确定内点，以便最小化光滑性能量，并使用递归多项式插值算法迭代地细化深度梯度，从而实现更合理的表面法线，进而将其运用于具有实时性能需求的各种机器人和计算机视觉应用中。最终，该论文提出的 SDA-SNE 方法在空间不连续的区域表现出极高的性能。