DARTS: Diffusion Approximated Residual Time Sampling for Time-of-flight Rendering in Homogeneous Scattering Media

TL;DR

DARTS introduces diffusion approximated residual time sampling to ToF rendering in homogeneous scattering media, jointly addressing distance and direction sampling under time-of-flight constraints. By integrating transient diffusion theory into a residual-time framework and extending ellipsoidal connections with elliptical diffusion sampling, the method enables full transient path construction with high efficiency. The approach uses RIS for distance sampling and offline tabulation for direction sampling (EDA), achieving at least a 5x reduction in MSE relative to state-of-the-art methods at equal render time and compatible with both path tracing and photon-based renderers. This yields significant improvements in time-gated and transient ToF rendering in complex scenes, while outlining clear limitations and directions for extending to varied emitters, heterogeneous media, and complex visibility settings.

Abstract

Time-of-flight (ToF) devices have greatly propelled the advancement of various multi-modal perception applications. However, achieving accurate rendering of time-resolved information remains a challenge, particularly in scenes involving complex geometries, diverse materials and participating media. Existing ToF rendering works have demonstrated notable results, yet they struggle with scenes involving scattering media and camera-warped settings. Other steady-state volumetric rendering methods exhibit significant bias or variance when directly applied to ToF rendering tasks. To address these challenges, we integrate transient diffusion theory into path construction and propose novel sampling methods for free-path distance and scattering direction, via resampled importance sampling and offline tabulation. An elliptical sampling method is further adapted to provide controllable vertex connection satisfying any required photon traversal time. In contrast to the existing temporal uniform sampling strategy, our method is the first to consider the contribution of transient radiance to importance-sample the full path, and thus enables improved temporal path construction under multiple scattering settings. The proposed method can be integrated into both path tracing and photon-based frameworks, delivering significant improvements in quality and efficiency with at least a 5x MSE reduction versus SOTA methods in equal rendering time.

Figures (12)

• Figure 1: Rendering of time-resolved transport using proposed DARTS in a scene with complex surface materials and homogeneous scattering media. DARTS integrates transient diffusion approximation into the path construction and adapts our elliptical sampling to provide path length control, enabling high quality time-of-light rendering and can be compatible with different existing frameworks. The example scene is illuminated by two non-synchronized pulse emitters with different start times of emission. Each image is rendered for 20 minutes. It can be seen that our sampling approach can greatly improve the SOTA photon based methods and provide lower overall MSE in the same rendering time.
• Figure 2: Unidirectional path tracing in a scene filled with participating media. Random walk generates a path (solid black lines) with multiple vertices and all the vertices are connected to the emitter either through direct shadow connection (dashed yellow lines) or generalized shadow connection with control vertices (dashed red lines)
• Figure 3: Recursive decomposition of indirect radiance $\tilde{L}_k$ into the direct and indirect components. Through this decomposition, the estimator can actually be written as the summation of an infinite series of direct component at each vertex. This decomposition is easier to discuss, since it only depicts the local state transition.
• Figure 4: Illustration of DA distance sampling. Samples are drawn with statistically higher contribution according to product of transmittance and approximated transient radiance: 4 candidate samples $d_i$ are depicted in (a). $d_1$ and $d_4$ are invalid. Though $d_2$ has higher transmittance, the incident contribution on vertex $\mathbf{x}_k$ is lower than that of $d_3$, due having lower estimated radiance. Note that $d_4$ is not presented in (b), since it is invalid due to non-causality.
• Figure 5: Two major sampling procedures in EDA sampling. The offline tabulation yields a 3D table for any vertex to query. This table is used for inverse transform sampling. Each value in the table is estimated via Monte Carlo integration on GPU (a). Two possible elliptical sampling cases: the equi-time ellipse does not intersect any surfaces (case I, left half); surface is encountered within the sampling range (case II, right half) (b)