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Abstract <p>A method for estimating the relative position and orientation of a camera from corresponding image points is presented, in which the translation is eliminated from the optimization while the rotation is estimated using a spectral criterion based on the consistency of epipolar plane normals. For each point pair, a symmetric rank-1 matrix is constructed from the cross product of normalized bearing directions, and the smallest eigenvalue of the sum of these matrices is minimized over <i>R</i> ∈ <i>SO</i>(3). The translation direction is then recovered as the eigenvector associated with the minimal eigenvalue. A smooth approximation to the smallest eigenvalue via the log-sum-exp function is introduced, and iterative robust weights are employed. The implementation relies on automatic differentiation. Experiments on real data confirm the high reliability of the estimates.</p>

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Spectral Criterion for Estimating the Relative Camera Pose

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Ye. V. Goshin

摘要

Abstract

A method for estimating the relative position and orientation of a camera from corresponding image points is presented, in which the translation is eliminated from the optimization while the rotation is estimated using a spectral criterion based on the consistency of epipolar plane normals. For each point pair, a symmetric rank-1 matrix is constructed from the cross product of normalized bearing directions, and the smallest eigenvalue of the sum of these matrices is minimized over R ∈ SO(3). The translation direction is then recovered as the eigenvector associated with the minimal eigenvalue. A smooth approximation to the smallest eigenvalue via the log-sum-exp function is introduced, and iterative robust weights are employed. The implementation relies on automatic differentiation. Experiments on real data confirm the high reliability of the estimates.