The structure of light fields of natural scenes is highly complex due to high frequencies in the radiance distribution function. However it is the low-order properties of light that determine the appearance of common matte materials. We describe the local light field in terms of spherical harmonics and analyze the qualitative properties and physical meaning of the low-order components. We take a first step in the further development of Gershun's classical work on the light field by extending his description beyond the 3D vector field, toward a more complete description of the illumination using tensors. We show that the three first components, namely, the monopole (density of light), the dipole (light vector), and the quadrupole (squash tensor) suffice to describe a wide range of qualitatively different light fields. In this paper we address a related issue, namely, the spatial properties of light fields within natural scenes. We want to find out to what extent local light fields change from point to point and how different orders behave. We found experimentally that the low-order components of the light field are rather constant over the scenes whereas high-order components are not. Using very simple models, we found a strong relationship between the low-order components and the geometrical layouts of the scenes.
] of natural scenes are highly complex and vary within a scene from point to point. However, in many applications complex lighting can be successfully replaced by its low-order approximation [J. Opt. Soc. Am. A 18, 2448 Appl. Opt. 46, 7308 (2007)]. The purpose of this research is to investigate the structure of light fields in natural scenes. We describe the structure of light fields in terms of spherical harmonics and analyze their spatial variation and qualitative properties over scenes. We consider several types of natural scene geometries. Empirically and via modeling, we study the typical behavior of the first-and second-order approximation of the local light field in those scenes. The first-order term is generally known as the "light vector" and has an immediate physical meaning. The quadrupole component, which we named "squash tensor," is a useful addition as we show in this paper. The measurements were done with a custom-made device of novel design, called a "Plenopter," which was constructed to measure the light field in terms of spherical harmonics up to the second order. In different scenes of similar geometries, we found structurally similar light fields, which suggests that in some way the light field can be thought of as a property of the geometry. Furthermore, the smooth variation of the light field's low-order components suggests that, instead of specifying the complete light field of the scene, it is often sufficient to measure the light field only in a few points and rely on interpolation to recover the light field at arbitrary points of the scene.
We present a method for measurement and reconstruction of light fields in finite spaces. Using a custommade device called a plenopter, we can measure spatially and directionally varying radiance distribution functions from a real-world scene up to their second-order spherical harmonics approximations. Interpolating between measurement points, we can recover this function for arbitrary points of a scene. We visualized the global structure of the light field using light tubes, which gives an intuitive description of the flux propagation throughout three-dimensional scenes and provides information about the quality of light in the scenes. Our second-order reconstructions are sufficient to render convex matte objects and therefore have a direct interest for computer graphics applications.
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