Six-Point Method for Multi-Camera Systems with Reduced Solution Space

TL;DR

Several minimal solvers that use six PCs to compute the 6DOF relative pose of multi-camera systems are presented, including a minimal solver for the generalized camera and two minimal solvers for the practical configuration of two-camera rigs.

Abstract

Relative pose estimation using point correspondences (PC) is a widely used technique. A minimal configuration of six PCs is required for two views of generalized cameras. In this paper, we present several minimal solvers that use six PCs to compute the 6DOF relative pose of multi-camera systems, including a minimal solver for the generalized camera and two minimal solvers for the practical configuration of two-camera rigs. The equation construction is based on the decoupling of rotation and translation. Rotation is represented by Cayley or quaternion parametrization, and translation can be eliminated by using the hidden variable technique. Ray bundle constraints are found and proven when a subset of PCs relate the same cameras across two views. This is the key to reducing the number of solutions and generating numerically stable solvers. Moreover, all configurations of six-point problems for multi-camera systems are enumerated. Extensive experiments demonstrate the superior accuracy and efficiency of our solvers compared to state-of-the-art six-point methods. The code is available at https://github.com/jizhaox/relpose-6pt

Figures (12)

• Figure 1: Relative pose estimation for a multi-camera system. A point is observed by perspective camera $C_i$ in view 1 and by camera $C_{i'}$ in view 2. $\{\mathbf{Q}_i, \mathbf{s}_i\}$ and $\{\mathbf{Q}_{i'}, \mathbf{s}_{i'}\}$ are extrinsic parameters for $C_i$ and $C_{i'}$, respectively. The related point correspondence is described by two-view epipolar geometry of cameras $C_i$ and $C_{i'}$.
• Figure 2: Relative pose estimation for generalized cameras. Note that points $o_i$ and $o'_i$ do not necessarily correspond to the same physical point of the generalized camera.
• Figure 3: Relative pose estimation for two-camera rigs. Specifically, our goal is to determine the 6DOF relative pose while six PCs are observable by two views of a two-camera rig. (a) inter-camera case, (b) intra-camera case.
• Figure 4: Relative pose estimation error with varying image noise for a generalized camera. We design a simulated multi-camera system comprising 12 omnidirectional cameras. The extrinsic parameters, including orientation and position, are totally random. The three rows correspond to the generic, inter-camera, and intra-camera cases, respectively. The 6pt-Our solver in the three rows represent 6pt-Our-generic, 6pt-Our-inter, and 6pt-Our-intra, respectively.
• Figure 5: Application of the six-point method to the generalized camera model.

Theorems & Definitions (1)

• proof