A survey of photon mapping state-of-the-art research and future challenges <s> Photon relaxation based on k-means <s> The photon mapping method is one of the most popular algorithms employed in computer graphics today. However, obtaining good results is dependent on several variables including kernel shape and bandwidth, as well as the properties of the initial photon distribution. While the photon density estimation problem has been the target of extensive research, most algorithms focus on new methods of optimising the kernel to minimise noise and bias. In this paper we break from convention and propose a new approach that directly redistributes the underlying photons. We show that by relaxing the initial distribution into one with a blue noise spectral signature we can dramatically reduce background noise, particularly in areas of uniform illumination. In addition, we propose an efficient heuristic to detect and preserve features and discontinuities. We then go on to demonstrate how reconfiguration also permits the use of very low bandwidth kernels, greatly improving render times whilst reducing bias. <s> BIB001 </s> A survey of photon mapping state-of-the-art research and future challenges <s> Photon relaxation based on k-means <s> Blue noise sampling is an important component in many graphics applications, but existing techniques consider mainly the spatial positions of samples, making them less effective when handling problems with non-spatial features. Examples include biological distribution in which plant spacing is influenced by non-positional factors such as tree type and size, photon mapping in which photon flux and direction are not a direct function of the attached surface, and point cloud sampling in which the underlying surface is unknown a priori. These scenarios can benefit from blue noise sample distributions, but cannot be adequately handled by prior art. Inspired by bilateral filtering, we propose a bilateral blue noise sampling strategy. Our key idea is a general formulation to modulate the traditional sample distance measures, which are determined by sample position in spatial domain, with a similarity measure that considers arbitrary per sample attributes. This modulation leads to the notion of bilateral blue noise whose properties are influenced by not only the uniformity of the sample positions but also the similarity of the sample attributes. We describe how to incorporate our modulation into various sample analysis and synthesis methods, and demonstrate applications in object distribution, photon density estimation, and point cloud sub-sampling. <s> BIB002
The photon relaxation method BIB001 ) is intended to improve caustic rendering by directly removing noise from the photon distribution. With photon relaxation, background noise can be reduced dramatically, and the uniform illumination can be calculated after reconstruction. The algorithm adds an intermediate pass between photon tracing and illumination reconstruction, i.e., iterative point repulsion which uses vector computing through the position information of neighbors (Fig. 6 ). Feature detection should be analyzed in advance to isolate those points that lie near boundaries and other important visual cues. After a sufficient number of iterations, noise is diffused away in the photon distribution, and high-frequency details are kept by feature detection and inhibiting motion in the direction of migration when photons relax. The resulting distribution has a blue noise spectral signature, which has been shown to be an optimal sample pattern in many areas of computer graphics (Ulichney, 1988), including photon mapping BIB001 ). BIB002 proposed an improved blue noise sampling which can be applied in photon relaxation. Arbitrary attributes of samples can be considered as a similarity measure like sample position. For photon mapping, photon flux and photon direction as properties decide the displacement vector during the relaxation pass, together with photon position. What is more, the new bilateral blue noise sampling strategy enables photon relaxation to produce a better performance in keeping sharp features.