Robust Confidence Intervals in Stereo Matching using Possibility Theory

TL;DR

The paper tackles estimating the magnitude and locus of disparity estimation errors in stereo matching by producing confidence intervals derived from possibility theory. It converts cost curves into possibility distributions and uses alpha-cuts to obtain interval estimates, with a regularization step for low-confidence regions and a post-processing framework that preserves consistency with the disparity map. The approach achieves at least $90\%$ interval accuracy on Middlebury and satellite datasets, without requiring training, and provides interpretable, white-box uncertainty suitable for propagation into elevation intervals in 3D reconstruction. Overall, the method offers an explainable alternative to black-box confidence measures that can be integrated into traditional cost-volume pipelines and GIS-enabled Earth Observation workflows.

Abstract

We propose a method for estimating disparity confidence intervals in stereo matching problems. Confidence intervals provide complementary information to usual confidence measures. To the best of our knowledge, this is the first method creating disparity confidence intervals based on the cost volume. This method relies on possibility distributions to interpret the epistemic uncertainty of the cost volume. Our method has the benefit of having a white-box nature, differing in this respect from current state-of-the-art deep neural networks approaches. The accuracy and size of confidence intervals are validated using the Middlebury stereo datasets as well as a dataset of satellite images. This contribution is freely available on GitHub.

Figures (8)

• Figure 1: Example of intervals on a image of the city of Montpellier, France. \ref{['fig:fig1a']} presents the left image, colored pixels indicate wrong interval locations. \ref{['fig:fig1b']} contains confidence intervals along a section of the dashed line in \ref{['fig:fig1a']}
• Figure 2: Example of three MC-CNN cost curves with different confidences from ambiguity.
• Figure 3: The possibility distributions obtained from the cost curves of \ref{['fig:ambiguity']}. The arrows and vertical lines indicate the disparity intervals obtained with $\alpha=0.9$.
• Figure 4: Low confidence areas with $l=2$.
• Figure 5: Intervals without (\ref{['fig:no_reg']}) and with (\ref{['fig:reg']}) regularization from Middlebury's $cones$. CENSUS cost function is used. Areas with low confidence are indicated in gray.