Vaibhav Rathod's Notes

PathTracer Learning - Concept - Russian Roulette

2 min read

  • The Problem

    • Path tracing is recursive — paths can bounce infinitely
    • Truncating at fixed depth introduces bias (misses long light paths)
    • Need an unbiased way to terminate paths

  • How Russian Roulette Works

    • At each bounce, randomly decide to continue or terminate
    • Survival probability: q (typically based on path throughput)
    • If random() < q: continue, divide contribution by q
    • If random() >= q: terminate, return 0
    • This is unbiased because: E[contribution] = q * (true_contribution / q) + (1-q) * 0 = true_contribution

  • Choosing the Survival Probability

    • Common choice: q = max(throughput.r, throughput.g, throughput.b)
      • Throughput = product of BRDF weights along the path
      • As path gets darker, more likely to terminate
      • Prevents wasting computation on paths that contribute little
    • Clamp: q = clamp(q, 0.05, 0.95)
      • Minimum 5%: prevents infinite loops (q=0 would never terminate)
      • Maximum 95%: prevents very bright paths from being over-weighted
    • Alternative: q = luminance(throughput) — single value, perceptually weighted

  • Implementation

  • Effect on Variance

    • Russian roulette does NOT reduce variance — it can increase it
    • Paths that survive get boosted by 1/q → higher individual contribution
    • But: eliminates wasted computation on low-contribution paths
    • Net effect: same expected value, potentially higher variance, but faster convergence per unit time

  • Splitting (Opposite of Russian Roulette)

    • When throughput is HIGH: spawn multiple child rays
    • Reduces variance for bright paths at the cost of more computation
    • Rarely used in real-time (too expensive)
    • Used in offline rendering for caustics and other difficult paths

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