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In this paper, we present our minimal 4-point and linear 8-point algorithms to estimate the relative pose of a multi-camera system with known vertical directions, i.e. known absolute roll and pitch angles. We solve the minimal 4-point algorithm with the hidden variable resultant method and show that it leads to an 8-degree univariate polynomial that gives up to 8 real solutions. We identify a degenerated case from the linear 8-point algorithm when it is solved with the standard Singular Value Decomposition (SVD) method and adopt a simple alternative solution which is easy to implement. We show that our proposed algorithms can be efficiently used within RANSAC for robust estimation. We evaluate the accuracy of our proposed algorithms by comparisons with various existing algorithms for the multi-camera system on simulations and show the feasibility of our proposed algorithms with results from multiple real-world datasets.

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