7.1 Density Estimation

The photon map represents incoming flux in the model. Each photon transports a fraction of the light source power, and a photon hit in a region indicates that this region is receiving some illumination from the light source either directly or indirectly. However, based on a single photon we cannot say how much light the region receives. This is given by the photon density, d ? /dA, and to estimate the irradiance for a given region we therefore need to compute the density of the photons.

The first methods using photon tracing [2, 87] used illumination maps (similar to texture maps, but storing illumination instead of color) to bin the photons. Later approaches used a tessellated version of the geometry to store the photons [74]. In all of these approaches the individual photons are not stored explicitly. Instead the power carried by the photons is accumulated for some local region. Knowing the area of this region immediately gives an estimate of the photon density. This approach can be seen as a histogram approach to density estimation.

Density estimation is a research area in statistics, and...