We introduce Doppler time-of-flight (D-ToF) rendering, an extension of ToF rendering for dynamic scenes, with applications in simulating D-ToF cameras. D-ToF cameras use high-frequency modulation of illumination and exposure, and measure the Doppler frequency shift to compute the radial velocity of dynamic objects. The time-varying scene geometry and high-frequency modulation functions used in such cameras make it challenging to accurately and efficiently simulate their measurements with existing ToF rendering algorithms. We overcome these challenges in a twofold manner: To achieve accuracy, we derive path integral expressions for D-ToF measurements under global illumination and form unbiased Monte Carlo estimates of these integrals. To achieve efficiency, we develop a tailored time-path sampling technique that combines antithetic time sampling with correlated path sampling.We show experimentally that our sampling technique achieves up to two orders of magnitude lower variance compared to naive time-path sampling. We provide an open-source simulator that serves as a digital twin for D-ToF imaging systems, allowing imaging researchers, for the first time, to investigate the impact of modulation functions, material properties, and global illumination on D-ToF imaging performance.
We thank the anonymous reviewers for their feedback and especially Anonymous Reviewer 4 for the idea to use scene scaling in Sec. 6.5 to mitigate the ringing artifacts due to limited floating-point precision. We also thank the authors of Hu et al. [2022] for helpful discussions on Sec. 7, and in particular correcting an error in Fig. 25. Wojciech Jarosz was supported by NSF award 1844538, Ioannis Gkioulekas by NSF awards 1730147, 1900849, and a Sloan Research Fellowship, and Adithya Pediredla by a Burke research initiation award.
@article{kim23doppler,
author = {Kim, Juhyeon and Gkioulekas, Ioannis and Jarosz, Wojciech and Pediredla, Adithya},
title = {Doppler Time-of-Flight Rendering},
journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)},
year = {2023},
month = nov,
volume = {42},
number = {6},
doi = {10/gs82tm},
keywords = {transient, antithetic sampling}
}