The Symmetries of Image Formation by Scattering. I. Theoretical Framework

TL;DR

This paper develops a theoretical framework revealing fundamental symmetries in image formation by scattering, linking physics and image analysis, and demonstrating advanced methods for 3D structure recovery from complex, random data.

Contribution

It introduces the first deduction of the fundamental symmetries in scattering-based image formation, connecting physics with computational imaging, and enhances 3D structure recovery techniques.

Findings

Identified symmetries similar to those in general relativity's Taub universe.

Developed graph-theoretic methods for 3D structure reconstruction.

Achieved high-complexity structure recovery from random, unknown orientations.

Abstract

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.