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Technical Perspective: The Path to Light Transport

The interaction of light with materials results in a rich visual experience that can bring wonder and puzzlement to children and adults alike. Light can follow a complex path before reaching our eyes, reflecting off objects or bending to yield shiny reflections, rainbows, or the bewildering patches of light known as caustics. Physically based rendering seeks to faithfully simulate this complex process through numerical integration and the modeling of light-matter interaction. But it offers more than a formidable technical challenge, it also provides us with a fascinating behind-the-scenes perspective on the genesis of our visual experience.

The difficulty of light simulation stems from the very complexity of the physical process. While the simulation of light reaching objects directly from a light source is simple enough, it only accounts for a fraction of the light illuminating our world. Much light bounces off objects in a recursive way, and can have a significant impact even after many bounces, especially if the objects it reflects off are very shiny or translucent. Initially, computer graphics rendering avoided this complexity and only considered direct illumination, relying on various hacks such as fake additional lights to make the results look acceptable. Most early CGI in movies such as Toy Story and Jurassic Park did not take into account indirect illumination and relied instead on the artists' ability to fake believable lighting.

Over the last two decades, the field has made tremendous progress in simulating light interreflections for relatively easy cases, in particular when materials are not too shiny. In this case light gets more and more diffuse as it bounces around, which requires limited precision to resolve. Simple forms of physically based rendering are now used in movie production. And for the majority of its catalog, Ikea has now switched to fully photorealistic 3D computer graphics rendered with global illumination.

However, with the easy aspects of indirect lighting now under control, the hard cases become salient: light reflections involving multiple shiny or transparent objects. If you have ever wondered at a dinner table where the bright patterns focused by a wine glass come from, consider that it is even harder for algorithms to find the proper light path combinations.

To better understand the difficulty of the problem, consider its formal definition. The value of a pixel is the integral of light reaching a given point of the scene after it has been reflected an arbitrary number of times. The domain of integration is the space of light paths, where each path links a series of vertices in the scene. Direct illumination corresponds to a single vertex, the visible point, between a light source and the camera. Indirect illumination can involve two, three, or more vertices. Modern solutions typically involve Monte Carlo approaches and random sampling to approximate the integral at each pixel. The first challenge comes from the high dimensionality of the domain, proportional to the number of bounces. The second challenge is caused by shiny materials, refraction, and complex scene geometry, which can make the integrand extremely complex. Current sampling solutions miss these important but hard-to-find paths. For example, caustics are formed when light reflects in just the right direction off a very shiny object, or when it is bent by a refractive material with a given curvature and index of refraction.

The paper builds on the Metropolis Light Transport, which works by performing a random walk through path space carefully engineered to linger near paths in exact proportion to their contribution to the image.

The following paper presents a technique to address these challenging problems of light transport by characterizing mathematically the narrow manifolds of high-contribution light paths within the high-dimensional path space. It builds on a Markov Chain Monte Carlo method known as Metropolis Light Transport, which works by performing a random walk through path space that is carefully engineered to linger near paths in exact proportion to their contribution to the image. The Markov chain approach replaces the problem of finding an important path starting from nothing with the problem of modifying a path to explore high-contribution areas.

The key idea of this paper is to characterize the path-space geometry of these high-contribution areas and to walk in the direction of the ridge (or manifold), not across it. For this, the authors have had to characterize the complex geometry of multi-bounce specular paths, where changes in one vertex location affect the incoming direction of light from the previous vertex as well as outgoing direction to the next one, which means the problem is correlated across a full set of bounces. They have derived equations that enable efficient walks, and the results speak for themselves.

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Frédo Durand ( is a professor of electrical engineering and computer science at the Massachusetts Institute of Technology, Cambridge, MA.

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To view the accompanying paper, visit

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