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In this paper, we study the configurations of motion and structure that lead to inherent ambiguities in radial distortion estimation (or 3D reconstruction with unknown radial distortions). By analyzing the motion field of radially distorted images, we solve for critical surface pairs that can lead to the same motion field under different radial distortions and possibly different camera motions. We study the properties of the discovered critical configurations and discuss the practically important configurations that often occur in real applications. We demonstrate the impact of the radial distortion ambiguity on multi-view reconstruction with synthetic experiments and real experiments.

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