Geometric Tools for Exploring Manifolds of Light Transport Paths

Photorealistic images created using physical simulations of light have become a ubiquitous element of our everyday lives. The most successful techniques for producing such images replicate the key physical phenomena in a detailed software simulation, including the emission of light by sources, transport through space, and scattering in the atmosphere and at the surfaces of objects. Mathematically, this computation involves the approximation of many highdimensional integrals, one for each pixel of the image, usually using Monte Carlo methods. Although a great deal of progress has been made on rendering algorithms, so that physically based rendering is now routinely used in many applications, commonly occurring situations can still cause these algorithms to become impractically slow, forcing users to make unrealistic scene modifications to obtain satisfactory results. Light transport is complex because light can flow along a great variety of different paths through a scene, though only a subset of these makes relevant contributes to the final image. The simulation becomes ineffective when it is difficult to find the important paths. Commonly occurring materials like smooth metal or glass surfaces can easily lead to such situations, where only very few lighting paths participate, leading to spiky integrands and poor convergence. How to efficiently handle such cases in general has been a long-standing problem. In this paper, we provide a geometric solution to this problem by representing light paths as points in an abstract high-dimensional configuration space that is defined by a system of constraint equations. This configuration space is a differentiable manifold, which can be locally parameterized in the neighborhood of an existing path. Building on this framework, we propose Manifold Exploration, a rendering technique that efficiently explores the integration domain by taking geometrically informed steps on the manifold of light paths.