Bachelor-Arbeit

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 stratification.

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 absorbed.
• 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.

Literature:

• [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 33-41
• [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. 1441-1450

Student tasks:

• 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 account stratification
• Study of the 1D, 2D (surface illumination) and 3D (volumetric effects) cases

Requirements

• Strong background in Mathematics / Statistics

Aufgabensteller:
Prof. Dr. D. Kranzlmüller

Dauer der Bachelor-Arbeit: 3 Monate

Anzahl Bearbeiter: 1

Betreuer:


• Ruben García-Hernández (LRZ)

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