Temporally Sliced Photon Primitives for Time-of-flight Rendering

Abstract

We derive a class of new Monte Carlo estimators for volumetric time-of-flight rendering, generalizing prior work on transient photon points and beams. Conceptually, our method starts with any steady-state photon primitive – like a photon plane, parallelepiped, or parallelotope – and slices it with a temporal wavefront, producing a primitive of one dimension lower. We show how different unbiased temporally sliced primitives arise by analytically integrating any four dimensions within a novel extended spatio-temporal path space formulation. The differences between these estimators reduce to the determinant of a 4×4 Jacobian matrix, with columns dictated by the chosen dimensions. We then show how to combine the relative strengths of different sliced primitives using multiple importance sampling. Finally, we implement several of the new estimators enabled by our theory and compare them to each other as well as previous techniques.