Please note: This PhD defence will take place in DC 2314 and online.
Xiaochun Tong, PhD candidate
David R. Cheriton School of Computer Science
Supervisor: Professor Toshiya Hachisuka
Monte Carlo integration underlies most algorithms in both forward and inverse rendering. The practicality of these methods rests on a structural assumption: a complex problem can be broken into small pieces—light paths, branches of a program, statements of a sampler—that are handled independently and whose results are simply aggregated. This thesis studies three problems in Monte Carlo rendering where these pieces are coupled, so that treating them independently leads to exponential cost, unstable gradients, or the rejection of valid samplers. For each, we propose an algorithm that explicitly accounts for the coupling.
First, we study nonlinear Monte Carlo integration in stylized rendering. Traditional Monte Carlo rendering relies on the linearity of the rendering equation, which allows its recursion to be expanded into light transport paths that are sampled independently. Stylization applies a nonlinear function to the radiance at every bounce and breaks this expansion, so a conventional path tracer produces significant bias. Rather than sampling paths in isolation, we solve the nonlinear integral equation jointly by reusing and caching radiance estimates across paths. Our method reduces the cost from exponential to linear in path depth.
Second, we study gradient-based optimization of programs with control-flow discontinuities, as found in inverse rendering, shader optimization, and physics simulation. Existing relaxations and straight-through estimators treat each discontinuity independently, which yields unstable gradients once conditions are enclosed inside nonlinear operations. We instead smooth the program as a probabilistic mixture over all of its control-flow paths, and estimate the gradient by Monte Carlo sampling with variance reduction. Our method converges more robustly across a wide range of tasks while requiring little modification to existing programs.
Finally, we study sampling programs, which construct an invertible mapping from uniform random numbers to a target distribution; inverting this mapping yields the probability density required for Monte Carlo integration. Existing methods require the mapping to be written as a composition of individually invertible steps, which limits expressiveness and excludes many real-world samplers. We introduce an invertible domain-specific language with flexible syntax and control flow. Its compiler uses a graph-based analysis to decompose a program into smaller subprograms that are easier to invert, while keeping track of the dependencies between them. Our method can express many real-world Monte Carlo samplers and can be used to synthesize new samplers with lower variance and smaller memory footprint.
To attend this PhD defence in person, please go to DC 2314. You can also attend virtually on MS Teams.