<p>Stereo Visual odometry (VO) is a well-established technique for estimating the egomotion of a stereo camera by tracking salient features across consecutive stereo pairs. VO is often combined with complementary sensor data to improve trajectory estimation, yet most sensor-fusion approaches rely on heuristics or empirical parameter tuning to jointly process heterogeneous measurements. Motivated by the need for a statistically rigorous treatment of uncertainty in stereo VO, this work presents a 3D–3D stereo VO framework on the Special Euclidean group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\textbf {SE}}\varvec{(3)}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">SE</mi> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> formulated under the Maximum Likelihood principle. The proposed method explicitly models the physical characteristics of the optical sensor and the image formation process to enable a principled propagation of measurement uncertainty from pixel scale to motion parameters. The objective is to quantitatively assess the pose accuracy achievable from stereo VO only, independent of external sensors or fusion schemes. The pipeline includes feature extraction and tracking, robust motion hypothesis generation via Sample Consensus, and on-manifold six-degree-of-freedom pose refinement. A physically grounded subpixel keypoint refinement stage yields non-isotropic, per-feature pixel covariances tied informed by local image gradients, which are analytically propagated through stereo triangulation to the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${\textbf {SE}}\varvec{(3)}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">SE</mi> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> pose updates. The resulting covariances associated with inter-frame pose increments and landmark measurements are expressed as Gaussian factors directly usable in graph-based back-ends, supporting bundle adjustment and pose-graph optimization. Experiments on the KITTI odometry benchmark and on the non-urban, Mars-analog DLR MADMAX dataset demonstrate that the proposed framework produces pose estimates whose empirical errors remain consistent with the predicted uncertainty over long sequences. Although the current system estimates inter-frame motion only, and thus accumulates drift over time, the observed error growth remains statistically aligned with the propagated uncertainty. These results establish a principled foundation for the integration of VO within learning-based or multi-sensor navigation frameworks while preserving a physically motivated, sensor-driven treatment of uncertainty.</p>

Principled Uncertainty Propagation for Stereo Visual Odometry

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2026年2月21日

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Fabio Valerio Buonomo,
Simone Andolfo,
Antonio Genova

摘要

Stereo Visual odometry (VO) is a well-established technique for estimating the egomotion of a stereo camera by tracking salient features across consecutive stereo pairs. VO is often combined with complementary sensor data to improve trajectory estimation, yet most sensor-fusion approaches rely on heuristics or empirical parameter tuning to jointly process heterogeneous measurements. Motivated by the need for a statistically rigorous treatment of uncertainty in stereo VO, this work presents a 3D–3D stereo VO framework on the Special Euclidean group ${\textbf {SE}}\varvec{(3)}$ $SE (3)$ formulated under the Maximum Likelihood principle. The proposed method explicitly models the physical characteristics of the optical sensor and the image formation process to enable a principled propagation of measurement uncertainty from pixel scale to motion parameters. The objective is to quantitatively assess the pose accuracy achievable from stereo VO only, independent of external sensors or fusion schemes. The pipeline includes feature extraction and tracking, robust motion hypothesis generation via Sample Consensus, and on-manifold six-degree-of-freedom pose refinement. A physically grounded subpixel keypoint refinement stage yields non-isotropic, per-feature pixel covariances tied informed by local image gradients, which are analytically propagated through stereo triangulation to the ${\textbf {SE}}\varvec{(3)}$ $SE (3)$ pose updates. The resulting covariances associated with inter-frame pose increments and landmark measurements are expressed as Gaussian factors directly usable in graph-based back-ends, supporting bundle adjustment and pose-graph optimization. Experiments on the KITTI odometry benchmark and on the non-urban, Mars-analog DLR MADMAX dataset demonstrate that the proposed framework produces pose estimates whose empirical errors remain consistent with the predicted uncertainty over long sequences. Although the current system estimates inter-frame motion only, and thus accumulates drift over time, the observed error growth remains statistically aligned with the propagated uncertainty. These results establish a principled foundation for the integration of VO within learning-based or multi-sensor navigation frameworks while preserving a physically motivated, sensor-driven treatment of uncertainty.