Symmetric Photography: Exploiting Data-sparseness in Reflectance Fields


Gaurav Garg, Stanford University

Eino-Ville Talvala, Stanford University

Marc Levoy, Stanford University

Hendrik P. A. Lensch, Stanford University


Proceedings of EGSR 2006.






The reflectance field of a glass full of gummy bears is captured using two coaxial projector/camera pairs placed 120 degrees apart. (a) is the result of relighting the scene from the front projector, which is coaxial with the presented view, where the (synthetic) illumination consists of the letters ''EGSR''. Note that due to their sub-surface scattering property, even a single beam of light that falls on a gummy bear illuminates it completely. In (b) we simulate homogeneous backlighting from the second projector combined with the illumination used in (a). For validation, a ground-truth image (c) was captured by loading the same projector patterns into the real projectors. Our approach is able to faithfully capture and reconstruct the complex light transport in this scene. (d) shows a typical frame captured during the acquisition process with the corresponding projector pattern in the inset.




We present a novel technique called symmetric photography to capture real world reflectance fields. The technique models the 8D reflectance field as a transport matrix between the 4D incident light field and the 4D exitant light field. It is a challenging task to acquire this transport matrix due to its large size. Fortunately, the transport matrix is symmetric and often data-sparse. Symmetry enables us to measure the light transport from two sides simultaneously, from the illumination directions and the view directions. Data-sparseness refers to the fact that sub-blocks of the matrix can be well approximated using low-rank representations. We introduce the use of hierarchical tensors as the underlying data structure to capture this data-sparseness, specifically through local rank-1 factorizations of the transport matrix. Besides providing an efficient representation for storage, it enables fast acquisition of the approximated transport matrix and fast rendering of images from the captured matrix. Our prototype acquisition system consists of an array of mirrors and a pair of coaxial projector and camera. We demonstrate the effectiveness of our system with scenes rendered from reflectance fields that were captured by our system. In these renderings we can change the viewpoint as well as relight using arbitrary incident light fields.



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