We present a novel algorithm for light source estimation in scenes reconstructed with a RGB-D camera based on an analytically-derived formulation of path-tracing. Our algorithm traces the reconstructed scene with a custom path-tracer and computes the analytical derivatives of the light transport equation from principles in optics. These derivatives are then used to perform gradient descent, minimizing the photometric error between one or more captured reference images and renders of our current lighting estimation using an environment map parameterization for light sources. We show that our approach of modeling all light sources as points at infinity approximates lights located near the scene with surprising accuracy. Due to the analytical formulation of derivatives, optimization to the solution is considerably accelerated. We verify our algorithm using both real and synthetic data.
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