Published in ACM Transactions on Graphics, Volume 29, Issue 4 (SIGGRAPH 2010)

Kernel Nystrom for Light Transport

fabrication resutls

Relighting results using the light transport matrix reconstructed by our method. Complex light transport effects, including caustics (a), complex occlusions (b), and a mixture of caustics, complex occlusions, inter-reflections, and subsurface scattering (c) are all faithfully reproduced.


We propose a kernel Nystrom method for reconstructing the light transport matrix from a relatively small number of acquired images. Our work is based on the generalized Nystrom method for low rank matrices. We introduce the light transport kernel and incorporate it into the Nystrom method to exploit the nonlinear coherence of the light transport matrix. We also develop an adaptive scheme for efficiently capturing the sparsely sampled images from the scene. Our experiments indicate that the kernel Nystrom method can achieve good reconstruction of the light transport matrix with a few hundred images and produce high quality relighting results. The kernel Nystrom method is effective for modeling scenes with complex lighting effects and occlusions which have been challenging for existing techniques.


Low-rank approximation, light transport matrix



 author = {Wang, Jiaping and Dong, Yue 
 and Tong, Xin and Lin, Zhouchen and Guo, Baining},
 title = {Kernel Nystr\öm method for light transport},
 journal = {ACM Trans. Graph.},
 issue_date = {August 2009},
 volume = {28},
 number = {3},
 month = jul,
 year = {2009},
 issn = {0730-0301},
 pages = {29:1--29:10},
 articleno = {29},
 numpages = {10},
 url = {},
 doi = {10.1145/1531326.1531335},
 acmid = {1531335},
 publisher = {ACM},
 address = {New York, NY, USA},


The authors would like to thank Yi Ma and John Wright for helpful discussions, and Matthew Callcut for proofreading the paper and dubbing the video. We also thank the anonymous reviewers for their helpful suggestions and comments.