Abstract
Monocular observers perceive as three-dimensional (3D) many displays that depict three points rotating rigidly in space but rotating about an axis that is itself tumbling. No theory of structure from motion currently available can account for this ability. We propose a formal theory for this ability based on the constraint of Poinsot motion, i.e., rigid motion with constant angular momentum. In particular, we prove that three (or more) views of three (or more) points are sufficient to decide if the motion of the points conserves angular momentum and, if it does, to compute a unique 3D interpretation. Our proof relies on an upper semicontinuity theorem for finite morphisms of algebraic varieties. We discuss some psychophysical implications of the theory.
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This work was supported by National Science Foundation grants IRI-8700924 and DIR-9014278 and by Office of Naval Research contract N00014-88-K-0354.
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Bennett, B.M., Hoffman, D.D., Kim, J.S. et al. Inferring 3D structure from image motion: The constraint of Poinsot motion. J Math Imaging Vis 3, 143–166 (1993). https://doi.org/10.1007/BF01250527
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DOI: https://doi.org/10.1007/BF01250527