Perspective Reconstruction of a Spheroid from an Image Plane Ellipse

The perspective reconstruction of a spheroid’s position and orientation from a single image plane ellipse is derived, by direct inversion of the projection equations, assuming the semi-major and semi-minor axes are known. Attention is paid to the geometric interpretation of the reconstruction. The reconstruction is formulated and reduced to an eigenvalue problem, to yield 2 solutions for the spheroid’s position and orientation. The symmetry of the polar planes for these solutions are then deduced.

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