Adaptive, adversarial optimal transport for high-dimensional, spatially and dimensionally disparate
Abstract
(Approved for public release)By regarding multi-temporal, multi-spatial datasets as weighted samples drawn from unknown distribution,s, the powerful tools of optimal transport can be extended to much more general problems in data analysis. This project addresses th,e co-registration of data of different type, such as between black-and while and color photographs. These can be characterized as di,stributions over spaces describing the spatial coordinates local to the two pictures plus the shade of gray or the three RGB intensi,ties. Then a pairing is sought through data-based optimal transport.In order to implement optimal transport between different spaces,, the cost function must involve distances measured in each space separately, unlike the pairwise cost of classical optimal transpor,t. In addition, this cost function must be indifferent to global transformations such as the parallax effect and a change in luminos,ity. To address these constraints, this proposal includes the development of new formulations and tools in the mathematical theory o,f optimal transport and data analysis.The methodology extends to applications of much higher dimensionality, such as the co-registra,tion of hyperspectral images.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 05, 2022
- Source ID
- N000142212192
Entities
People
- Esteban G. Tabak
Organizations
- New York University
- Office of Naval Research
- United States Navy