A survey of photon mapping state-of-the-art research and future challenges <s> Jensen and Christensen <s> Monte Carlo (MC) photon shooting approach is becoming an important global illumination technique in research and commercial applications. In this work, we focus on the problem of lighting reconstruction for planar surfaces. Our contribution is in the development of new, efficient photon density estimation techniques. We formulate local error measures of lighting reconstruction which under some reasonable constraints (discussed below) imposed on the lighting function that behave like the actual error. The minimization of our error estimates is very fast for planar surfaces and usually leads to a better quality lighting result than traditional methods. Also, the local error estimation offers more information than global error measures usually provided by MC solvers, which are not good predictors of image quality. We compare the actual error resulting from various techniques, and evaluate the visual appearance of the reconstructed lighting. <s> BIB001 </s> A survey of photon mapping state-of-the-art research and future challenges <s> Jensen and Christensen <s> Density estimation techniques such as the photon map method rely on a particle transport simulation to reconstruct indirect illumination, which is proportional to the particle density. In the photon map framework, particles are usually located using nearest-neighbour methods due to their generality. However, these methods have an inherent tradeoff between local bias and noise in the reconstructed illumination, which depends on the density estimate bandwidth. This paper presents a bias compensating operator for nearest-neighbour density estimation which adapts the bandwidth according to the estimated bias in the reconstructed illumination. <s> BIB002 </s> A survey of photon mapping state-of-the-art research and future challenges <s> Jensen and Christensen <s> A number of popular global illumination algorithms uses density estimation to approximate indirect illumination. The density estimate is performed on finite points -- particles -- generated by a stochastic sampling of the scene. In the course of the sampling, particles, representing light, are stochastically emitted from the light sources and reflected around the scene. The sampling induces noise, which in turn is handled by the density estimate during the illumination reconstruction. Unfortunately, this noise reduction imposes a systematic error (bias), which is seen as a blurring of prominent illumination features. This is often not desirable as these may lose clarity or vanish altogether. We present an accurate method for reconstruction of indirect illumination with photon mapping. Instead of reconstructing illumination using classic density estimation on finite points, we use the correlation of light footprints, created by using Ray Differentials during the light pass. This procedure gives a high illumination accuracy, improving the trade-off between bias and variance considerable as compared to traditional particle tracing algorithms. In this way we preserve structures in indirect illumination. <s> BIB003
A similar method proposed by Myszkowski (1997) computes a bias and noise error estimate for density estimation at the shading point. It is called the enhanced nearest neighbor (ENN) method. By comparing the variance of different bandwidths, the method selects one that minimizes the error. BIB001 was one of the first to thoroughly investigate bias in density estimation. BIB002 used the same error estimate in density estimation, following up Myszkowski (1997)'s work, but Roland optimized it by using a binary search to select the optimal bandwidth. et al. (2007; 2008) and Schjøth (2009) summarized an approach using an anisotropic estimator to reduce the topological bias and noise at radiance discontinuities.  suggested an approach inspired by a shape-adaptive structure tensor in density estimation to reduce the bias along edges and structures. The structure tensor is constructed in an in-between pass after photon tracing, and computed from the first order structure of the photon map. Another accurate method was presented for reconstruction of illumination with photons BIB003 . The method uses ray differentials (Igehy, 1999) during the photon tracing pass on every photon and calculates footprints of every photon instead of using classic density estimation with a series of a specified number of photons and their total area. Then the method stores the irradiance of the photon and changes Eq. (1) using only the irradiance without the area. In this way, indirect illumination can achieve a high accuracy reconstruction. We can see the changes in the kernel in Fig. 5 . Photon differentials can obtain an accurate rendering especially in the area of feature and edge BIB003 .