Exploiting polar symmetry in designing equivariant observers for vision-based motion estimation

Accurately estimating camera motion from image sequences poses a significant challenge in computer vision and robotics. Many computer vision methods first compute the essential matrix associated with a motion and then extract orientation and normalized translation as inputs to pose estimation, reconstructing the scene scale (that is unobservable in the epipolar construction) from separate information. In this paper, we design a continuous-time filter that exploits the same perspective by using the epipolar constraint to define pseudo-measurements. We propose a novel polar symmetry on the pose of the camera that makes these measurements equivariant. This allows us to apply recent results from equivariant systems theory to estimating pose. We provide a novel explicit persistence of excitation condition to characterize observability of the full pose, ensuring reconstruction of the scale parameter that is not directly observable in the epipolar construction.Comment: Preprint for L-CS

Nonlinear constructive observer design for direct homography estimation

Feature-based homography estimation approaches rely on extensive image processing for feature extraction and matching, and do not adequately account for the information provided by the image. Therefore, developing efficient direct techniques to extract the homography from images is essential. This paper presents a novel nonlinear direct homography observer that exploits the Lie group structure of $\mathbf{SL}(3)$ and its action on the space of image maps. Theoretical analysis demonstrates local asymptotic convergence of the observer. The observer design is also extended for partial measurements of velocity under the assumption that the unknown component is constant or slowly time-varying. Finally, simulation results demonstrate the performance of the proposed solutions on real images.Comment: 11 pages, 3 figures, to appear in Proceedings of IFAC World Congress 202