Concept: Temporal Accumulation

• Parent: PathTracer Learning - Phase 5 - Advanced Topics

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

Ghosting

• When reprojection is wrong: old samples from wrong location persist
• Causes: disocclusion, fast motion, lighting changes
• Appears as: blurry trails, smearing, incorrect colors
• Solution: PathTracer Learning - Concept - Temporal Rejection

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

Related

• PathTracer Learning - Concept - Temporal Rejection
• PathTracer Learning - DLSS and Denoising