ISSN:
1573-7683
Keywords:
structure from motion
;
algebraic geometry
;
upper semicontinuity
;
observer theory
;
Poinsot motion
;
visual motion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01250527
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