Symmetric Photography: Exploiting Data-sparseness in

Figure 1: The reflectance field of a glass full of gummy bears is captured using two coaxial projector/camera pairs placed 120 ◦ 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, although unevenly. 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 factorization