Frequency based Kernel Estimation for Progressive Photon Mapping

彬彬

We present an extension to Hachisuka et al.’s Progressive Photon

Mapping (or PPM) algorithm [Hachisuka et al. 2008] in which

we estimate the radius of the density estimation kernels using frequency

analysis of light transport [Durand et al. 2005]. We predict

the local radiance frequency at the surface of objects, and use it to

optimize the size of the density estimation kernels, in order to accelerate

convergence. The key is to add frequency information to

a small proportion of photons: frequency photons. In addition to

contributing to the density estimation, they will provide frequency

information.

1 Algorithm Overview

Our algorithm works as follow: First, we ray trace hitpoints in the

scene from the camera. Second, we iteratively trace a proportion

of frequency photons and ”classical” photons in the scene. These

frequency photons are used to update the frequency estimate at hitpoints.

Classical progressive photon mapping progressively reduces the

size of the density estimation kernel to cancel the bias of density

estimation, at the expense of increasing variance. However, if the

radiance is smooth enough, this size can be kept constant, and additional

photons will only decrease variance of the estimate. The

role of frequency photons is precisely to conservatively predict this

phenomenon.

Consequently, we update the hitpoints’ collecting size using the following

heuristic: if the kernel size of classical PPM is greater than

our prediction we decrease the radius just as the standard progressive

photon mapping method does. Otherwise, we don’t decrease

the kernel size. We make this process iterative by always using a

fixed proportion of frequency photons to update the desired size of

all hitpoints.

tc

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