Forming light paths connecting two points in a scene, so called direct connections, is a key building block of modern Monte Carlo rendering algorithms. For example, path tracing forms direct connections between each point on a traced path and a light source; and bidirectional path tracing forms direct connections between all pairs of vertices on two traced paths. Forming direct connections through one or multiple specular or refractive surfaces is particularly challenging: Any such connection must satisfy the laws of specular reflection or refraction at each of its vertices; as a result, valid direct connections occupy a very low-dimensional manifold within the space of all possible light paths, motivating the name manifold direct connections.

Existing works on forming manifold direct connections treat this as an optimization problem: They use gradient descent to search for points on specular reflective or refractive surfaces that, when used to form a direct connection, the resulting path satisfies the laws of specular reflection or refraction, respectively. All of these works take advantage of the fact that these laws are efficiently differentiable, and thus lend themselves to search through gradient-based optimization.

We adopt the optimization approach for forming manifold direct connections, with an important difference: Instead of optimizing over surface points such as in previous works, we optimize over the initial direction of the direct path. This reparameterized optimization problem offers a number of advantages. First, it makes it possible to form direct connections through multiple specular reflective and refractive surfaces. Furthermore, it allows forming direct connections through different surface representations, including explicit (e.g., polygonal mesh), implicit (e.g., signed distance function, neural network), and point cloud representations. Finally, it provides a continuous parameterization of the search space (space of directions), which helps accelerate the convergence of gradient-based optimization.

47 pages

Thesis Committee:
Ioannis Gkioulekas (Chair)
Matthew O'Toole

Srinivasan Seshan, Head, Computer Science Department
Martial Hebert, Dean, School of Computer Science

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