Geometry Depth Consistency in RGBD Relative Pose Estimation

TL;DR

This work tackles RGBD relative pose estimation by identifying that a single veridical RGBD correspondence imposes strong depth-consistency constraints on all other potential matches. It introduces Geometric Depth Consistency (GDC), which constrains correspondences to lie on nested curves in the image domains, and pairs it with Filtered RANSAC to prune outliers efficiently. The authors further enhance robustness and speed with Nested RANSAC, biasing selections toward high-confidence top-ranked matches. Comprehensive experiments on TUM-RGBD, ICL-NUIM, and RGBD Scene v2 show substantial runtime savings and competitive pose accuracy, especially under high outlier ratios. The combination of GDC and nested strategies yields scalable, robust RGBD pose estimation suitable for VO/SLAM pipelines and 3D reconstruction tasks.

Abstract

Relative pose estimation for RGBD cameras is crucial in a number of applications. Previous approaches either rely on the RGB aspect of the images to estimate pose thus not fully making use of depth in the estimation process or estimate pose from the 3D cloud of points that each image produces, thus not making full use of RGB information. This paper shows that if one pair of correspondences is hypothesized from the RGB-based ranked-ordered correspondence list, then the space of remaining correspondences is restricted to corresponding pairs of curves nested around the hypothesized correspondence, implicitly capturing depth consistency. This simple Geometric Depth Constraint (GDC) significantly reduces potential matches. In effect this becomes a filter on possible correspondences that helps reduce the number of outliers and thus expedites RANSAC significantly. As such, the same budget of time allows for more RANSAC iterations and therefore additional robustness and a significant speedup. In addition, the paper proposed a Nested RANSAC approach that also speeds up the process, as shown through experiments on TUM, ICL-NUIM, and RGBD Scenes v2 datasets.

Figures (18)

• Figure 1: (Top) 50 potential matches selected from a rank-ordered list of correspondences between a pair of RGBD images. (Bottom) A pair of correspondence which is manually determined to be veridical is selected (white square tokens). Each remaining correspondence is probed as to whether the pair falls on corresponding curves using the proposed geometric depth consistency constraint. Those potential matches that fail this test are shown in black tokens and excluded as nonviable correspondences.
• Figure 1: The geometric depth consistency constrains a correspondence $(\gamma_i,\rho_i)$ and $(\overline{\gamma}_i,\overline{\rho}_i)$ to lie on the corresponding level-sets of $\phi$ and $\overline{\phi}$ constructed with respect to a reference point correspondence $(\gamma_0,\rho_0)$ and $(\overline{\gamma}_0,\overline{\rho}_0)$. Due to noise in feature location and depth measurement, the observed correspondence $\overline{\gamma}_i$ is a perturbation of the true corresponding point $\overline{\gamma}_i^{*}$ which must lie on the level-set $\overline{\phi}$. The distance $\overline{d}$ is the extent of this perturbation.
• Figure 2: A veridical correspondence $(\gamma_i,\overline{\gamma}_i)$ partitions the space of correspondences $(\gamma_j,\overline{\gamma}_j)$ into a nested set of curves (identified by a common color) so that if $\gamma_j$ falls on a curve in image one, $\overline{\gamma}_j$ must fall on the corresponding curve in image two.
• Figure 2: Distribution of outlier ratio $e$ for pairs of images from the (a) TUM-RGBD TUMRGBD_Dataset, (b) ICL-NUIM handa2014benchmark, and (c) RGBD Scene v2 RGBD_Scenes_v2_Dataset datasets. Number of image pairs are 132,946, 38,085, and 39,325 image pairs, respectively. The bin size used in this histogram is 0.05.
• Figure 3: A scene surface $S$ viewed by two cameras. Assume the correspondence $\gamma_i$ and $\overline{\gamma}_i$ both coming from 3D point $\Gamma_i$, a sphere of radius $r$ centered at $\Gamma_i$ (shown in red), and $S$ intersect at a curve ${\mathcal{\mathbf{\widehat{C}}}}$ (shown in green). The curve ${\mathcal{\mathbf{\widehat{C}}}}$ projects to 2D curves $C$ and $\overline{C}$ in image $i$ and image $j$, respectively. This shows any feature $\gamma_j$ lying on curve $C$ must have its correspondence on curve $\overline{C}$.

Theorems & Definitions (4)

• Definition 1
• Proposition 1
• Proposition 1
• proof