Concept: Tone Mapping

• Parent: PathTracer Learning - Phase 5 - Advanced Topics

Why Tone Mapping?

• Path tracing computes HDR radiance values (can be 0 to thousands of nits)
• Displays can only show LDR values in [0, 1] (or [0, 1000 nits for HDR displays)
• Tone mapping compresses the HDR range to the display range
• Also applies a “filmic” look — mimics how film responds to light

Exposure

• First step: scale radiance by exposure
• exposed = radiance * exposure
• exposure = 2^EV where EV is exposure value (stops)
• Auto-exposure: compute average luminance of the scene, adjust exposure
  • avg_lum = exp(average(log(luminance(pixel) + 0.001)))
  • exposure = key_value / avg_lum where key_value ≈ 0.18 (18% gray)

Reinhard Tone Mapping

• Simple, classic operator
• L_out = L_in / (1 + L_in)
• Extended Reinhard (preserves white point):
  • L_out = L_in * (1 + L_in / L_white²) / (1 + L_in)
  • L_white — luminance that maps to pure white
• Pros: simple, never clips
• Cons: desaturates highlights, not filmic

ACES Filmic Tone Mapping

• Academy Color Encoding System — industry standard for film
• Approximation by Krzysztof Narkowicz (widely used in games):

  vec3 ACESFilm(vec3 x) {
      float a = 2.51;
      float b = 0.03;
      float c = 2.43;
      float d = 0.59;
      float e = 0.14;
      return clamp((x * (a * x + b)) / (x * (c * x + d) + e), 0.0, 1.0);
  }

• Better approximation by Stephen Hill (more accurate to full ACES):
  • Applies an input transform (RRT) and output transform (ODT)
  • Requires color space conversion to ACEScg first
• Pros: filmic look, good highlight rolloff, industry standard
• Cons: slightly desaturates, not physically accurate

AgX Tone Mapping

• Troy Sobotka 2022 — used in Blender since 3.x
• Designed to handle highly saturated colors without hue shifts
• Better than ACES for path-traced content (less “orange and teal” look)

// AgX (simplified)
vec3 agx(vec3 val) {
    const mat3 agx_mat = mat3(
        0.842479062253094,  0.0423282422610123, 0.0423756549057051,
        0.0784335999999992, 0.878468636469772,  0.0784336,
        0.0792237451477643, 0.0791661274605434, 0.879142973793104
    );
    val = agx_mat * val;
    val = clamp(val, 1e-10, 1.0);
    val = log2(val);
    // ... sigmoid curve ...
    return val;
}

Gamma Correction

• After tone mapping: apply gamma correction for display
• sRGB gamma: approximately pow(x, 1/2.2) but with a linear segment near 0
• Exact sRGB transfer function:

  vec3 linearToSRGB(vec3 x) {
      return mix(
          12.92 * x,
          1.055 * pow(x, vec3(1.0/2.4)) - 0.055,
          step(0.0031308, x)
      );
  }

• Always work in linear space, convert to sRGB only at final output
• Common mistake: applying gamma twice (once in tone mapper, once in display)

Color Space Pipeline

• Correct pipeline for path tracing:
  • 1. Compute radiance in linear scene-referred space (ACEScg or sRGB linear)
  • 2. Apply exposure
  • 3. Apply tone mapping operator
  • 4. Apply gamma correction (linear → sRGB)
  • 5. Output to display
• Textures: load as sRGB (gamma-encoded), convert to linear before use
  • In Vulkan: use VK_FORMAT_R8G8B8A8_SRGB — GPU auto-converts on sample

Luminance

• Perceptual luminance from RGB: lum = dot(rgb, vec3(0.2126, 0.7152, 0.0722))
• These weights are the Rec. 709 luminance coefficients
• Used for: auto-exposure, tone mapping, denoiser guidance

Related

• PathTracer Learning - Concept - Environment Map
• PathTracer Learning - Phase 5 - Advanced Topics