On the Duality of Forward and Inverse Light Transport



Inverse light transport seeks to undo global illumination effects, such as interreflections, that pervade images of most scenes. This paper presents the theoretical and computational foundations for inverse light transport as a dual of forward rendering. Mathematically, this duality is established through the existence of underlying Neumann series expansions. Physically, it can be shown that each term of our inverse series cancels an interreflection bounce, just as the forward series adds them. While the convergence properties of the forward series are well-known, we show that the oscillatory convergence of the inverse series leads to more interesting conditions on material reflectance. Conceptually, the inverse problem requires the inversion of a large light transport matrix, which is impractical for realistic resolutions using standard techniques. A natural consequence of our theoretical framework is a suite of fast computational algorithms for light transport inversion -- analogous to finite element radiosity, Monte Carlo and wavelet-based methods in forward rendering -- that rely at most on matrix-vector multiplications. We demonstrate two practical applications, namely, separation of individual bounces of the light transport and fast projector radiometric compensation to display images free of global illumination artifacts in real-world environments.


M.K. Chandraker, J. Bai, T.-T. Ng and R. Ramamoorthi
On the Duality of Forward and Inverse Light Transport [PDF]
IEEE PAMI 33(10):2122-2128, October 2011.

J. Bai, M.K. Chandraker, T.-T. Ng and R. Ramamoorthi
A Dual Theory of Inverse and Forward Light Transport [PDF] [Tech Report] [Web]
ECCV 2010, Heraklion, Greece.

Details and sample results:

Inverse light transport as dual analogue of forward rendering:

From left to right, we add more terms of our inverse series, going from full global illumination to the direct lighting inpt. This is the inverse of the forward rendering process in computer graphics, where successive bounces of the forward series take one from direct lighting input to the globally illuminated image.

photometric reconstruction

Theoretical duality of forward and inverse light transport:

photometric reconstruction

Algorithmic benefits of duality:

Our duality theory allows development of fast algorithms for light transport inversion, that mirror algorithms developed for efficient rendering in the computer graphics community. For light transport inversion, we propose dual versions of iterative finite element methods, wavelet acceleration and Monte Carlo methods developed for forward rendering. These algorithms enable novel applications such as radiometric compensation in projector-camera systems at resolutions higher than possible with a straightforward light transport inversion.

photometric reconstruction

Application: Fast Direct-Global Recovery and Bounce Separation

An application is to efficiently separate observed images into direct and global components, as well as recover each bounce of global illumination. Notice the light bouncing alternatingly off the left and right walls of the scene.

photometric reconstruction

photometric reconstruction

Application: Fast radiometric compensation in projector-camera systems

The fast algorithms presented in this paper can be used to achieve desired projector outputs, free of global illumination artifacts, even in scenes with complex geometry and reflectances. Our prototype Matlab implementation for the iterative finite element method can invert 130K x 130K light transports in 3 seconds.


Last updated May 31, 2014.