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Surface normal estimation from a single image is an important task in 3Dscene understanding. In this paper, we address two limitations shared by theexisting methods: the inability to estimate the aleatoric uncertainty and lackof detail in the prediction. The proposed network estimates the per-pixelsurface normal probability distribution. We introduce a new parameterizationfor the distribution, such that its negative log-likelihood is the angular losswith learned attenuation. The expected value of the angular error is then usedas a measure of the aleatoric uncertainty. We also present a novel decoderframework where pixel-wise multi-layer perceptrons are trained on a subset ofpixels sampled based on the estimated uncertainty. The proposeduncertainty-guided sampling prevents the bias in training towards large planarsurfaces and improves the quality of prediction, especially near objectboundaries and on small structures. Experimental results show that the proposedmethod outperforms the state-of-the-art in ScanNet and NYUv2, and that theestimated uncertainty correlates well with the prediction error. Code isavailable at https://github.com/baegwangbin/surface_normal_uncertainty.

Estimating and Exploiting the Aleatoric Uncertainty in Surface Normal Estimation