Probabilistic Modeling of Disparity Uncertainty for Robust and Efficient Stereo Matching

TL;DR

Uncertainty estimation in stereo matching is critical for safety but remains underexplored, with prior work failing to disentangle data (aleatoric) and model (epistemic) uncertainty. The paper proposes an uncertainty-aware stereo framework based on Bayes risk, using ordinal regression to model the disparity distribution for data uncertainty and a post-hoc kernel regression on OR embeddings to estimate model uncertainty without retraining. It defines $U_t$, $U_d$, and $U_m$, estimates $U_d$ via the variance of the disparity distribution $\mathrm{Var}[Y|X]$, and estimates $U_m$ with a kernel-regression excess-risk approximation, demonstrating reliable uncertainty quantification across four benchmarks and enabling data filtering to improve accuracy. The approach yields robust, data-efficient disparity estimation with practical impact for autonomous driving and robotics.

Abstract

Stereo matching plays a crucial role in various applications, where understanding uncertainty can enhance both safety and reliability. Despite this, the estimation and analysis of uncertainty in stereo matching have been largely overlooked. Previous works struggle to separate it into data (aleatoric) and model (epistemic) components and often provide limited interpretations of uncertainty. This interpretability is essential, as it allows for a clearer understanding of the underlying sources of error, enhancing both prediction confidence and decision-making processes. In this paper, we propose a new uncertainty-aware stereo matching framework. We adopt Bayes risk as the measurement of uncertainty and use it to separately estimate data and model uncertainty. We systematically analyze data uncertainty based on the probabilistic distribution of disparity and efficiently estimate model uncertainty without repeated model training. Experiments are conducted on four stereo benchmarks, and the results demonstrate that our method can estimate uncertainty accurately and efficiently, without sacrificing the disparity prediction accuracy.

Figures (15)

• Figure 1: (a)(b): inputs of stereo matching. (c)(d): disparity ground truth and prediction. (e): disparity prediction error. (f)(g)(h): Our estimation of data, model and total uncertainty. The estimated uncertainty aligns well with prediction error.
• Figure 2: Pipeline of the proposed stereo matching and uncertainty quantification method. Ordinal regression model is adopted to estimate PMF of disparity. Prediction is the expectation of PMF, and data uncertainty is PMF's variance. The model is supervised by the ordinal label, using ordinal regression loss. Model uncertainty is estimated with a kernel regression model, which is fitted on the embeddings of OR model.
• Figure 3: Experimental results of KITTI kitti and Virtual KITTI vk2. Red box: Large error, small uncertainty—model fails to predict large errors. Orange box: Small error, large uncertainty—model is overly cautious. Green box: uncertainty aligns well with error.
• Figure 4: Experimental results of Scene Flow sceneflow and DrivingStereo drivingstereo. Red box: Large error, small uncertainty—model fails to predict large errors. Orange box: Small error, large uncertainty—model is overly cautious. Green box: uncertainty aligns well with error.
• Figure 5: (a) GwcNet gwcnet variance as uncertainty. (b) Our uncertainty. (c) Errormap.