On the Instability of Relative Pose Estimation and RANSAC's Role

Abstract

In this paper we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact that relative pose estimation, based on standard 5-point or 7-point Random Sample Consensus (RANSAC) algorithms, can fail even when no outliers are present and there is enough data to support a hypothesis. We argue that these cases arise due to the intrinsic instability of the 5-and 7-point minimal problems. We apply our framework to characterize the instabilities, both in terms of the world scenes that lead to infinite condition number, and directly in terms of ill-conditioned image data. The approach produces computational tests for assessing the condition number before solving the minimal problem. Lastly synthetic and real data experiments suggest that RANSAC serves not only to remove outliers, but also to select for well-conditioned image data, as predicted by our theory.

Interactive 3D touch and gesture capable holographic light field display with automatic registration between user and content

“…Although it is possible in theory to estimate directly the 3D affine transformation, as initially proposed in Equation (), we experimentally found it to be more challenging for the RANSAC algorithm to estimate a correct transformation using 3D points, especially one that preserved an accurate position when changing the coordinate. This difficulty with the RANSAC algorithm for 3D points has been described elsewhere 27,28 . Therefore, we propose to use the RANSAC method in a set of coplanar points at a fixed distance and compute the distance from this plane to the 3D position of the user to obtain this last coordinate.…”

“…This difficulty with the RANSAC algorithm for 3D points has been described elsewhere. 27,28 Therefore, we propose to use the RANSAC method in a set of coplanar points at a fixed distance z ¼ z 0 and compute the distance from this plane to the 3D position of the user to obtain this last coordinate. The reason of the instability of RANSAC for this procedure, as well as the consideration of using a more accurate method should be the topic of future work.…”

A Review of Recurrent Neural Network Based Camera Localization for Indoor Environments

“…In analyzing the earlier relative pose regression approach based on image retrieval in [169], a new framework for computing the absolute pose was proposed, which included fundamental matrices and a modified RANSAC [170]. A matching score map for an additional regression, that is, the important matrix, was trained using the Siamese ResNet34 [130] network.…”