Radiometric Compensation through Inverse Light Transport

Wetzstein, Gordon; Bimber, Oliver

doi:10.1109/pg.2007.47

Cited by 87 publications

(62 citation statements)

References 32 publications

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“…Inverse light transport can be computed by inverting the forward light transport matrix [10,12,16,27]. In all these works, the f-LTM is first reconstructed from the measurements before deriving the i-LTM from the f-LTM.…”

Section: Inverse Light Transport Computationmentioning

confidence: 99%

“…In all current work, an inverse light transport matrix (i-LTM) is obtained by inverting a forward light transport matrix (f-LTM). For a projector-camera setup [10,16,27], a f-LTM can easily exceed the size of 10 5 × 10 5 .…”

Section: Introductionmentioning

confidence: 99%

“…Acquiring such a large f-LTM can take hours or days while inverting the f-LTM requires various forms of approximation which compromises on the accuracy of the inverse light transport [10,16,27].…”

Section: Introductionmentioning

confidence: 99%

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Compressive Inverse Light Transport

Chu¹,

Ng²,

Pahwa³

et al. 2011

Procedings of the British Machine Vision Conference 2011

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This paper explores the possibility of acquiring inverse light transport directly. The current strategy of obtaining an inverse light transport matrix involves two steps: First, acquire the forward light transport matrix (f-LTM) and then calculate the inverse of the f-LTM. Both steps of the strategy requires considerable computational power. In addition to computational cost, the measurement error incurred at the first step inevitably propagates to or potentially gets amplified in the matrix inversion step.In this paper, we propose a sensing strategy that acquires the inverse light transport matrix (i-LTM) directly, without reconstructing the f-LTM. Our direct strategy reduces both computational error and cost of acquiring i-LTM. For that, we propose a compressive inverse theory. Following the compressible property of i-LTM, a reconstruction condition for i-LTM is introduced. This new framework implies a trade-off between two factors: condition numbers of submatrices of f-LTM and the isometry constant of the illumination pattern. Our direct i-LTM reconstruction method is then demonstrated with a 2nd-bounce separation experiment on an M-shaped panel scene. Finally by quantitatively comparing our method with the existing two-stage approach, our method shows higher accuracy with lower complexity. The proofs of main theorem/lemma are contained in the supplementary material. The compressive inverse theory is general and potentially useful for wider application.

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Section: Inverse Light Transport Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Compressive Inverse Light Transport

Chu¹,

Ng²,

Pahwa³

et al. 2011

Procedings of the British Machine Vision Conference 2011

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“…[Wetzstein and Bimber 2007] form clusters of camera-projector pixels, doing a brute-force light transport inversion within clusters, but not considering inter-cluster interactions. This method is aimed at computational efficiency, but without clear error control.…”

Section: Forward Renderingmentioning

confidence: 99%

“…10, the stratified inverses method of [Ng et al 2009] will require 1 − 2 orders of magnitude more time. Also, in contrast to the method of [Wetzstein and Bimber 2007], our algorithms are physically motivated and not contingent on any tunable parameters.…”

Section: Projector Radiometric Compensationmentioning

confidence: 99%

A Dual Theory of Inverse and Forward Light Transport

Bai

Chandraker

et al. 2010

Computer Vision – ECCV 2010

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A cornerstone of computer graphics is the solution of the rendering equation for interreflections, which allows the simulation of global illumination, given direct lighting or corresponding light source emissions. This paper lays the foundations for the inverse problem, whereby a dual theoretical framework is presented for inverting the rendering equation to undo interreflections in a real scene, thereby obtaining the direct lighting. Inverse light transport is of growing importance, enabling a variety of new applications like separation of individual bounces of the light transport, and projector radiometric compensation to display images free of global illumination artifacts in real-world environments that exhibit complex geometric and reflectance properties. However, solving the inverse problem involves the inversion of a large light transport matrix (acquired by measurement on real scenes). While straightforward matrix inversion is intractable for most realistic resolutions, there is scant prior work on either theoretical foundations or fast computational algorithms to meet the objectives of inverse light transport.In this paper, we develop a mathematical theory that exposes the duality of forward and inverse light transport. Forward rendering also formally involves a matrix or operator inversion, which is conceptually equivalent to a multi-bounce Neumann series expansion. We show the existence of an analogous series for the inverse problem. However, the convergence is oscillatory in the inverse case, with more interesting conditions on material reflectance. Importantly, we give physical meaning to this duality, by showing that each term of our inverse series cancels an interreflection bounce, just as the forward series adds them.In algorithmic terms, we develop the analog of iterative finite element methods like forward radiosity to efficiently solve light transport inversion. Our iterative inverse light transport algorithm is very fast, requiring only matrix-vector multiplications, and follows directly from the dual theoretical formulation. We also explore the connections to forward rendering in terms of Monte Carlo and wavelet-based techniques. As an initial practical application, we first acquire the light transport of a real static scene, and then demonstrate iterative inversion for radiometric compensation on high-resolution datasets, as well as rapid separation of the bounces of global illumination. *

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Projector-Camera Systems in Entertainment and Art

Bimber

Yang

2009

Handbook of Multimedia for Digital Entertainment and Arts

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Radiometric Compensation through Inverse Light Transport

Cited by 87 publications

References 32 publications

Compressive Inverse Light Transport

Compressive Inverse Light Transport

A Dual Theory of Inverse and Forward Light Transport

Projector-Camera Systems in Entertainment and Art

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