Odometry Without Correspondence from Inertially Constrained Ruled Surfaces

TL;DR

The paper tackles visual odometry without relying on point correspondences by leveraging ruled surfaces generated by translating straight lines in image-time space. It introduces an inertially constrained, low-dimensional parameterization TS_{X_0,V_0}(t,α) and a ruling reprojection loss solved with a closed-form inner optimization, integrated in a sliding-window framework with IMU data. The approach is validated on diverse motion patterns and scene configurations, including coplanar and non-coplanar lines, with results showing competitive trajectory estimates and robust behavior to various non-idealities, albeit with notable Z-axis drift tied to IMU biases. This work offers a path toward feature-free, edge-driven odometry with tight visual-inertial coupling and potential applicability to edge-dominated sensing and event-like processing.

Abstract

Visual odometry techniques typically rely on feature extraction from a sequence of images and subsequent computation of optical flow. This point-to-point correspondence between two consecutive frames can be costly to compute and suffers from varying accuracy, which affects the odometry estimate's quality. Attempts have been made to bypass the difficulties originating from the correspondence problem by adopting line features and fusing other sensors (event camera, IMU) to improve performance, many of which still heavily rely on correspondence. If the camera observes a straight line as it moves, the image of the line sweeps a smooth surface in image-space time. It is a ruled surface and analyzing its shape gives information about odometry. Further, its estimation requires only differentially computed updates from point-to-line associations. Inspired by event cameras' propensity for edge detection, this research presents a novel algorithm to reconstruct 3D scenes and visual odometry from these ruled surfaces. By constraining the surfaces with the inertia measurements from an onboard IMU sensor, the dimensionality of the solution space is greatly reduced.

Figures (13)

• Figure 1: (a) rulings projected to image frame and (b) ruled surfaces in image-time space.
• Figure 2: (a) Scene setup with coplanar lines and estimated rulings, and (b) the camera trajectory alongside line poses in world coordinates.
• Figure 3: Estimated trajectory of the camera and the estimated poses of the lines in the scene in world coordinates. Lines are in warm colors and the trajectory in purple. Circular motion parallel to the scene plane.
• Figure 4: Estimated trajectory of the camera and the estimated poses of the lines in the scene in world coordinates. Lines are in warm colors and the trajectory in purple. Square non-smooth motion parallel to the scene plane.
• Figure 5: (a) Scene setup with non-coplanar lines, (b) point cloud and estimated ruled surface in image-time space, and (c) the camera trajectory alongside line poses.