Photon Parameterisation for Robust Relaxation Constraints

Abstract

This paper presents a novel approach to detecting and preserving fine illumination structure within photon maps. Data derived from each photon's primal trajectory is encoded and used to build a high-dimensional kd-tree. Incorporation of these new parameters allows for precise differentiation between intersecting ray envelopes, thus minimizing detail degradation when combined with photon relaxation. We demonstrate how parameter-aware querying is beneficial in both detecting and removing noise. We also propose a more robust structure descriptor based on principal components analysis that better identifies anisotropic detail at the sub-kernel level. We illustrate the effectiveness of our approach in several example scenes and show significant improvements when rendering complex caustics compared to previous methods.

A Visualization Tool Used to Develop New Photon Mapping Techniques

“…Spencer and Jones [SJ13a] discuss a scheme based solely on the primal trajectory of each photon is used to demonstrate the effectiveness of parametrized structure differentiation. This candidate was chosen because of its theoretical consistency with models of caustic ray envelopes (illustrated in Figure b), and through experimental validation using the visualization tool.…”

“…Projections of two candidate parameter spaces for the Prism scene in Figure . (a) The space of photon primal trajectories defined by Spencer and Jones [SJ13a]. (b) The amalgamation of photon path space vertices and normals creates a novel parameter space which is robust to unusual discontinuities.…”

“…The 250‐nearest neighbours to the photon at the centre of the loupe have been queried and highlighted, and three sets of attributes have been visualized: The derived orthogonal constraining basis, , for the selected photon, visualized as a pair of perpendicular arrows. These indicate by what degree and in what direction migration of this photon will be limited and are calculated using principal component analysis (PCA) [SJ13a]. The post‐relaxation drift of each neighbour. These ellipsoids represent how much each photon has moved within the confines of its constraining basis.…”

“…Among the more prominent benefits of photon relaxation is its relatively high resilience to bias [SJ13a]. Although this property has also been the goal of numerous other noise reduction algorithms, the unique way in which the algorithm redistributes individual photons allows not only for structure adaptation, but also for structure dissociation .…”

Light Beam Tracing for Multi-Bounce Specular and Glossy Transport Paths

“…Photon relaxation permits a smaller kernel to be used in the radiance estimate which reduces the bias, but due to the redistribution a low variance is maintained. Spencer and Jones [38] further improved upon photon relaxation by parameterising the photons to distinguish between neighbouring light ray envelopes. They also developed a progressive solution [39] to photon relaxation.…”