Uncertainty Quantification in Depth Estimation via Constrained Ordinal Regression

Abstract

Monocular Depth Estimation (MDE) is a task to predict a dense depth map from a single image. Despite the recent progress brought by deep learning, existing methods are still prone to errors due to the ill-posed nature of MDE. Hence depth estimation systems must be self-aware of possible mistakes to avoid disastrous consequences. This paper provides an uncertainty quantification method for supervised MDE models. From a frequentist view, we capture the uncertainty by predictive variance that consists of two terms: error variance and estimation variance. The former represents the noise of a depth value, and the latter measures the randomness in the depth regression model due to training on finite data. To estimate error variance, we perform constrained ordinal regression (ConOR) on discretized depth to estimate the conditional distribution of depth given image, and then compute the corresponding conditional mean and variance as the predicted depth and error variance estimator, respectively. Our work also leverages bootstrapping methods to infer estimation variance from re-sampled data. We perform experiments on both simulated and real data to validate the effectiveness of the proposed method. The results show that our approach produces accurate uncertainty estimates while maintaining high depth prediction accuracy.