Theoretical study of photon mapping with stratification
Photon mapping is the most widely used algorithm for generating high quality,
global illumination images. It is based on simulating the light transport of
photons (formally using a MonteCarlo method). However, as it is commonly
implemented, it has a very small overestimation bias, of 1/k. The bias was
discovered by modelling the photon mapping algorithm as a stochastic process,
and noticing that the search for the nearest impacts can be modelled using Order
Statistics [Garcia12] [Garcia14]. Some photon mapping variants use
The student will work within the theoretical framework described in the
references above, and will study how stratification affects the photon maps
bias. The expected result is that the result will still be an overestimation of
1/k, possibly convolved with some stratification parameters.
Description of the photon mapping algorithm
The algorithm can be divided in the following phases
- Photon tracing from the light sources.
- The photons interact with the scene and are reflected, refracted or
- The photon interaction points are stored for later use in a data
structure called "photon map".
- Raytracing from the eye.
- For each pixel, the visible point in the scene is found.
- Multiple rays from that point are created, and the contribution of each
(see below) is integrated in a final colour
- Photon map query
- Each ray from the previous step will possibly intersect the scene
geometry at a point.
- A photon map query searchs the photon map data structure for k photon
impacts near this point, and calculates the flux density at the point.
- [Garcia12]: Description and solution of an unreported intrinsic bias in photon
mapping density estimation with constant kernel. R. García, C.
Ureña, M. Sbert. Computer Graphics Forum Volume 31 (2012), number 1, pp
- [Garcia14]: Overestimation and underestimation biases in photon mapping with
non-constant kernels. Garcia-Hernandez, R, Ureña, C, Poch, J, Sbert, M. IEEE
Transactions on Visualization and Computer Graphics, Volume 20, Issue 10. Pp.
- Study of the state of the art in the following areas: photon mapping, order
statistics, montecarlo stratified algorithms.
- Extension of the codes which calculate bias and variance for the usecases in
the references above, to include stratification
- Extension of the mathematical framework in the references above to take into
- Study of the 1D, 2D (surface illumination) and 3D (volumetric effects)
- Strong background in Mathematics / Statistics
Prof. Dr. D. Kranzlmüller
Dauer der Bachelor-Arbeit: