Decoy and disclosure radii of invariant shape descriptors
Researchers measure how rotation-invariant shape descriptors both leak enrolled surfaces and admit distant decoy matches.
The paper measures the orbit-distance radius of rotation-invariant shape descriptors: a large radius admits distant decoy matches, while a small one discloses the enrolled surface. For star-shaped surfaces limited to spherical harmonics of degree at most L, band powers, even bispectra, and three degree-three invariants leave decoy families of dimension 5, 13, and 20 at L=4, 6, and 8, and a mirror decoy persists at every L. Odd bispectra remove that mirror decoy generically for L at least 4. At L=6 a decoy matches all 32 invariants to relative precision 2e-18 at orbit distance at least 0.87 times the enrolled norm; on asteroid Bennu the pool recovers volume, misses handedness, and leaves keep-out radius uncertain by more than 7 meters.
- Generic fibers have dimension n-3-r modulo rotations.
- Decoy-family dimensions are 5, 13, and 20 at L=4, 6, and 8.
- Descriptor rank first reaches n-3 at L=16; a mirror decoy remains.
- Odd bispectra generically remove the mirror decoy for L at least 4.
- Bennu model recovers volume, misses handedness, and keep-out radius errs by over 7 m.
From the original article
1 min read at arxiv.orgA recognizer that compares rotation-invariant descriptors sees a surface only up to the fiber of the descriptor. We measure this fiber by its radius in the orbit distance from the enrolled surface. A large radius admits decoys, that is, distant shapes that pass the matcher.
By Tanush Shaska · arxiv.org
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