Vaibhav Rathod's Notes

PathTracer Learning - Concept - Temporal Accumulation

2 min read

  • Core Idea

    • Reuse samples from previous frames to increase effective sample count
    • Frame N has 1 spp, but after 64 frames: 64 effective spp
    • Free quality improvement — no extra ray tracing cost

  • Basic Algorithm

    • Exponential moving average (EMA)
      • accumulated[t] = lerp(accumulated[t-1], current[t], α)
      • α = 1/N where N = number of accumulated frames
      • α = 1.0 → no accumulation (current frame only)
      • α = 0.1 → blend 10% new, 90% old (slow to respond to changes)
    • Running average (exact)
      • accumulated[t] = (accumulated[t-1] * (N-1) + current[t]) / N
      • Exact average of all N frames
      • Problem: N grows unboundedly — old frames from different scene state

  • Motion Vector Reprojection

    • Camera and objects move between frames
    • Must find where current pixel was in the previous frame
    • Motion vector: mv = current_uv - previous_uv
    • Reprojection: prev_uv = current_uv - motion_vector
    • Sample previous accumulation buffer at prev_uv
    • Bilinear interpolation for sub-pixel accuracy
    • Computing motion vectors
      • For static objects: only camera motion
        • prev_clip = prev_view_proj * world_pos
        • mv = (current_ndc - prev_ndc) / 2 (in UV space)
      • For dynamic objects: object transform also changes
        • Store previous frame’s transform per object
        • prev_world_pos = prev_transform * local_pos

  • Blend Factor Tuning

    • High blend factor (α = 0.5): responsive but noisy
    • Low blend factor (α = 0.05): smooth but slow to update, ghosting
    • Adaptive blend factor: increase α when rejection detects stale samples
    • Typical: α = 0.1 for stable regions, α = 1.0 for rejected pixels

  • Variance Estimation

    • Track variance of accumulated samples for denoiser guidance
    • Online variance: var = E[x²] - E[x]²
    • Accumulate both sum and sum_sq over time
    • mean = sum / N, variance = sum_sq/N - mean²
    • Used by SVGF to guide spatial filtering strength

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