2010/09/25 by Dimitrios Giannakis, Giannakis, Dimitrios, Peter Schwander +4 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Data Analysis #FOS: Physical sciences #Fractal and DNA sequence analysis #Statistics and Probability (physics.data-an) #physics.comp-ph #physics.data-an
paper · pdf · doi:10.48550/arxiv.1009.5035
16 pages, 65 references, 3 figures, 3 tables. Movies available at http://www.cims.nyu.edu/~dimitris
openalex publication_date 2010/09/25 · arxiv created 2011/09/24 · arxiv updated 2011/09/27 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe. Here, we deduce for the first time the fundamental symmetries underlying image formation. Intriguingly, these are similar to those of the anisotropic "Taub universe"' of general relativity, with eigenfunctions closely related to spinning tops in quantum mechanics. This opens the possibility to apply the powerful arsenal of tools developed in two major branches of physics to new problems. We augment these tools with graph-theoretic means to recover the three-dimensional structure of objects from random snapshots of unknown orientation at four orders of magnitude higher complexity than previously demonstrated. Our theoretical framework offers a potential link to recent observations on face perception in higher primates. In a later paper, we demonstrate the recovery of structure and dynamics from ultralow-signal random sightings of systems with no orientational or timing information.