Reinhard Global Tone Mapping

1. Background Knowledge

In HDR imaging, scenes often have luminance values that span several orders of magnitude, while typical displays (and 8-bit images) can only show a limited dynamic range (e.g., 0–255). Tone mapping operators (TMOs) compress this large dynamic range into a smaller, displayable range while trying to preserve important visual properties like contrast and detail. Global TMOs apply the same mapping to every pixel based only on its luminance value; local TMOs consider spatial neighborhoods.

Reinhard’s global tone mapping operator is a classic, simple TMO. The idea is to first normalize scene (world) luminance by a “key” value that controls overall brightness, then pass it through a nonlinear curve:

• Key scaling: $L = \dfrac{a}{\bar{L}} \cdot L_w$
• Tone mapping: $L_d = \dfrac{L}{1 + L}$

Here $\bar{L}$ is the log-average luminance of the scene, which is more robust than a simple arithmetic mean for HDR data. The final $L_d$ is in $(0,1)$ and can be mapped to display intensities.

2. Algorithm / Approach

The general pattern for this problem:

1. Extract luminance from the HDR RGB image to get $L_w(x,y)$.
2. Compute log-average luminance $\bar{L}$ over all pixels.
3. Apply key scaling with a given parameter $a$ (e.g., 0.18) to get scaled luminance $L$.
4. Apply Reinhard curve $L_d = \frac{L}{1 + L}$ to compress dynamic range.
5. Re-apply color: scale original RGB channels so that their new luminance matches $L_d$.
6. Clamp and convert to the desired output range (e.g., 0–255 uint8).

This is a straightforward per-pixel mapping with an initial global statistic ($\bar{L}$).

3. Step-by-Step Strategy

Assume input is an HDR image img_hdr in floating point RGB.

1. Compute luminance channel Use standard Rec.709 coefficients:

R = img_hdr[..., 0]
G = img_hdr[..., 1]
B = img_hdr[..., 2]
Lw = 0.2126 * R + 0.7152 * G + 0.0722 * B