Todor Georgiev
Sr. Research Scientist, Photoshop Group, Adobe Systems
tgeorgie at adobe dot com
Computational Photography (mathematical section)
In 2007 I taught the mathematical section of the SIGGRAPH Course on Computational Photography:
It presents complete lightfield theory that gives us the tools to solve old and new problems. For example, understanding Dappled Photography, the MERL "heterodyning" camera.
Outline
The physical quantity recored in a light-field camera is the radiance. It's well understood by science. So, if we want to build a rigorous theory of light-fields, we need to study what's already known about radiance in radiometry, optics and theoretical physics:
(1) In the course we use "plane-angle" parametrization of rays. This is a more flexible "differential" form of the familiar two plane parametrization.
(2) Ray transforms are represented in the formalism of matrix optics. Relations to Hamiltonian mechanics are shown. Rays satisfy Liouville's theorem due to conservation of a natural symplectic dot product that exists in ray space.
(3) Radiance conservation is derived. The explicit form of radiance transforms ("lightfield transforms") follows directly from that. This is shown both in spatioangular, and in frequency representation.
(4) Cameras described mathematically as examples of how the method works. This presentation is based on our Adobe Tech Report of April 2007.
- Pinhole camera (nontrivial derivation), and "2F" camera.
- Ives' camera, invented back in 1903, now presented with a new theory. Very interesting!
- Lippmann's "reversible prints" (and the plenoptic camera). His original 1908 paper: Epreuves Reversibles. Photographies Integrales. English translation (Fredo Durand): Reversible Prints. Integral Photographs.
- MERL "heterodyning" camera.
- Adobe camera (arrays of lenses and prisms). See cool presentation at macnews.de
- I showed some cool lightfield cameras and lenses. Also, watch the video of a more recent, and better demonstration of our 3D lens technology: Array of lenses and prisms
- Several examples are created with our Adobe frequency multiplexing camera ("dappled" or "heterodyning" camera in MERL terminology), and with our Adobe lens-prism camera.
(5) Additional links to very good and educational reading material:
Hamiltonian mechanics and
Liouville's theorem.
A frequency analysis of light transport
Integral history: 100 Years Light-Field
Plenoptic camera and Hand-held plenoptic camera
