Proxy Tracing: Unbiased Reciprocal Estimation for Optimized Sampling in BDPT

TL;DR

This work targets the longstanding challenge BDPT faces with specular and glossy paths by introducing proxy sampling and a novel unbiased reciprocal estimator. By dropout of problematic light-sub-path vertices and retracing a proxy segment, the approach expands feasible sampling directions while preserving unbiasedness via a carefully derived reciprocal PDF estimator. The method is embedded within a probabilistic BDPT framework (SPCBPT) and leverages subspace modeling, MIS weighting, and light-sub-path reuse to manage complex sampling distributions efficiently. Empirical results across multiple scenes show robust improvements in convergence speed and image quality for difficult paths, with strong compatibility with path guiding and CMIS frameworks. The approach offers a practical, scalable path sampling tool that can augment existing BDPT families and potentially advance state-of-the-art rendering of caustics and specular-dominant transport.

Abstract

Robust light transport algorithms, particularly bidirectional path tracing (BDPT), face significant challenges when dealing with specular or highly glossy involved paths. BDPT constructs the full path by connecting sub-paths traced individually from the light source and camera. However, it remains difficult to sample by connecting vertices on specular and glossy surfaces with narrow-lobed BSDF, as it poses severe constraints on sampling in the feasible direction. To address this issue, we propose a novel approach, called \emph{proxy sampling}, that enables efficient sub-path connection of these challenging paths. When a low-contribution specular/glossy connection occurs, we drop out the problematic neighboring vertex next to this specular/glossy vertex from the original path, then retrace an alternative sub-path as a proxy to complement this incomplete path. This newly constructed complete path ensures that the connection adheres to the constraint of the narrow lobe within the BSDF of the specular/glossy surface. Unbiased reciprocal estimation is the key to our method to obtain a probability density function (PDF) reciprocal to ensure unbiased rendering. We derive the reciprocal estimation method and provide an efficiency-optimized setting for efficient sampling and connection. Our method provides a robust tool for substituting problematic paths with favorable alternatives while ensuring unbiasedness. We validate this approach in the probabilistic connections BDPT for addressing specular-involved difficult paths. Experimental results have proved the effectiveness and efficiency of our approach, showcasing high-performance rendering capabilities across diverse settings.

Figures (16)

• Figure 1: Motivation of Proxy tracing. (a) When the end vertex of a light sub-path lies on a glossy surface, the probability of connecting it to the eye sub-path within the narrow BSDF lobe is very low. (b) To address this, our method modifies the light sub-path by introducing a proxy vertex instead of the original one, which satisfies the narrow lobe constraint on the glossy surface, thereby enabling us to handle difficult specular-involved paths by improving the connection probabilities.
• Figure 2: Semantic illustration of proxy sampling. (a) An original path, sampled from the initial distribution, often includes poorly distributed vertices, reducing the overall contribution of the full path; (b) our approach discards the problematic vertices, resulting in an incomplete path. The PDF for an incomplete path requires integrating over all potential problematic paths that could lead to the identical incomplete path; (c) proxy vertices are then traced to merge with the incomplete path and construct a new path. The data from the incomplete sub-path assists in tracing these proxy vertices, providing a more favorable conditional distribution for constructing a full path with a higher contribution.
• Figure 3: Illustration of the sampling distribution $p(t,x)$ alongside the target function $f(x)$. Parameters $\alpha$ and $\beta$ in the graph correspond to the PDF in this region. Different $t$ associates with different sampling techniques $p(x|t)$. SMIS works by first sampling $n$ techniques $t_1,t_2,...,t_n$, then performing MIS between $p(x|t_1),p(x|t_2),...,p(x|t_n)$.
• Figure 4: Two failure cases in SMIS. (a) In handling this $L_{DD}SS$ type light sub-path, our proxy sampling designates the $L_{DD}S$ as the dropout vertices, represented by $\bar{g}_o$, while the residual $S$ forms the incomplete path $\bar{h}$. Within SMIS framework, $\bar{g}_o$ is associated with technique $t$, and $p(\bar{h}|t)$ is proportional to the PDF that traces from $\bar{g}_o$'s last vertex to the first vertex (denote as $h$ without the bar) following $\bar{g}_o$ in $\bar{h}$. The probabilities $p(h_2|t_1)$ and $p(h_1|t_2)$, signified by yellow dashed lines, are nearly zero. (b) In scenario where visibility varies significantly, different techniques in SMIS primarily sample separate regions of $f(x)$. This leads to an inherent bias in SMIS because there is a positive probability that the combined sampling distribution cannot cover $f(x)$'s support.
• Figure 5: A light sub-path can be segmented into several components: the path to be dropped out $\bar{g}$, the residual path $\bar{h}^*$, and the terminal specular vertex $y_{s-1}$ located on a specular surface. The control vertex $h_c$ represents the terminal of $\bar{h}^*$ and the control direction $\omega_c$ is the incident direction at $h_c$. Reciprocal estimation is determined by these elements: the control vertex $h_c$, control direction $\omega_c$, specular vertex $y_{s-1}$, and $u$, which is the vertex count of $\bar{g}$.