Doppler Time-of-Flight Rendering

TL;DR

This paper introduces a novel simulation method for Doppler time-of-flight cameras in dynamic scenes, enabling accurate and efficient modeling of their measurements with an open-source simulator.

Contribution

It derives path integral expressions for D-ToF measurements and develops a tailored sampling technique, significantly improving simulation accuracy and efficiency.

Findings

Sampling technique reduces variance by up to two orders of magnitude

Provides an open-source simulator for D-ToF imaging system analysis

Enables investigation of modulation, materials, and illumination effects

Abstract

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.