NDLI: From the Rendering Equation to Stratified Light Transport Inversion

Content Provider	Springer Nature Link
Author	Ng, Tian Tsong Pahwa, Ramanpreet Singh Bai, Jiamin Tan, Kar Han Ramamoorthi, Ravi
Copyright Year	2011
Abstract	Recent advances in fast light transport acquisition have motivated new applications for forward and inverse light transport. While forward light transport enables image relighting, inverse light transport provides new possibilities for analyzing and cancelling interreflections, to enable applications like projector radiometric compensation and light bounce separation. With known scene geometry and diffuse reflectance, inverse light transport can be easily derived in closed form. However, with unknown scene geometry and reflectance properties, we must acquire and invert the scene’s light transport matrix to undo the effects of global illumination. For many photometric setups such as that of a projector-camera system, the light transport matrix often has a size of 10$^{5}$×10$^{5}$ or larger. Direct matrix inversion is accurate but impractical computationally at these resolutions.In this work, we explore a theoretical analysis of inverse light transport, relating it to its forward counterpart, expressed in the form of the rendering equation. It is well known that forward light transport has a Neumann series that corresponds to adding bounces of light. In this paper, we show the existence of a similar inverse series, that zeroes out the corresponding physical bounces of light. We refer to this series solution as stratified light transport inversion, since truncating to a certain number of terms corresponds to cancelling the corresponding interreflection bounces. The framework of stratified inversion is general and may provide insight for other problems in light transport and beyond, that involve large-size matrix inversion. It is also efficient, requiring only sparse matrix-matrix multiplications. Our practical application is to radiometric compensation, where we seek to project patterns onto real-world surfaces, undoing the effects of global illumination. We use stratified light transport inversion to efficiently invert the acquired light transport matrix for a static scene, after which interreflection cancellation is a simple matrix-vector multiplication to compensate the input image for projection.
Starting Page	235
Ending Page	251
Page Count	17
File Format	PDF
ISSN	09205691
Journal	International Journal of Computer Vision
Volume Number	96
Issue Number	2
e-ISSN	15731405
Language	English
Publisher	Springer US
Publisher Date	2011-06-07
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Inverse light transport Projector radiometric compensation Matrix inversion Inter-reflection cancellation Rendering equation Computer Imaging, Vision, Pattern Recognition and Graphics Image Processing and Computer Vision Pattern Recognition Artificial Intelligence (incl. Robotics)
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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