We present a technique for sampling light probe images using variance minimization. The technique
modifies the median cut algorithm for light probe sampling * [Debevec 2005]* so that the variance within
each region is minimized.

The algorithm recursively divides the entire light probe image into 2^n regions as follows:

- Add the entire light probe image to the region list as a single region.
- For each region in the list, subdivide such that the maximum of the two sub-regions' variances is minimized.
- If the number of iterations is less than n, return to step 2.
- Place a light source at the centroid of each region, and set the light source color to the sum of the pixel values within the region.

The variance of each region * r* can be calculated from the following equation:

Where **L p** is the light energy weighting factor of

**Figure 3** illustrates the differences in sample placement between the Median Cut algorithm and
the proposed Variance Minimization algorithm. **Figure 4** shows a scene rendered with 64 sampled
lights from the Grace Cathedral light probe which is a close match to the ground truth
Monte-Carlo solution.

VarianceMinimization_SIG09.pdf, (366KB)

VarianceMinimization_4ftx3ft_Poster.png, (18.9MB)

Median Cut Algorithm for Light Probe Sampling, SIGGRAPH 2005 Poster