We propose an unbiased and efficient rendering algorithm for Doppler time-of-flight cameras. Compared to naive sampling algorithms (left two columns), ours uses antithetic sampling with path correlation, and results in rendered images with orders of magnitude lower variance (top row). This makes it feasible to use rendering to evaluate radial velocity reconstruction algorithms (bottom row).


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.

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        title={Doppler Time-of-Flight Rendering},
        author={Kim, Juhyeon and Jarosz, Wojciech and Gkioulekas, Ioannis and Pediredla, Adithya},
        journal={ACM Transactions on Graphics (TOG)},
        publisher={ACM New York, NY, USA}