A survey of photon mapping state-of-the-art research and future challenges <s> Improved shading point generation <s> We present an extension to Hachisuka et al.'s Progressive Photon Mapping (or PPM) algorithm [Hachisuka et al. 2008] in which we estimate the radius of the density estimation kernels using frequency analysis of light transport [Durand et al. 2005]. We predict the local radiance frequency at the surface of objects, and use it to optimize the size of the density estimation kernels, in order to accelerate convergence. The key is to add frequency information to a small proportion of photons: frequency photons. In addition to contributing to the density estimation, they will provide frequency information. <s> BIB001 </s> A survey of photon mapping state-of-the-art research and future challenges <s> Improved shading point generation <s> This article introduces a novel locally adaptive progressive photon mapping technique which optimally balances noise and bias in rendered images to minimize the overall error. It is the result of an analysis of the radiance estimation in progressive photon mapping. As a first step, we establish a connection to the field of recursive estimation and regression in statistics and derive the optimal estimation parameters for the asymptotic convergence of existing approaches. Next, we show how to reformulate photon mapping as a spatial regression in the measurement equation of light transport. This reformulation allows us to derive a novel data-driven bandwidth selection technique for estimating a pixel's measurement. The proposed technique possesses attractive convergence properties with finite numbers of samples, which is important for progressive rendering, and it also provides better results for quasi-converged images. Our results show the practical benefits of using our adaptive method. <s> BIB002 </s> A survey of photon mapping state-of-the-art research and future challenges <s> Improved shading point generation <s> Progressive photon mapping solves the memory limitation problem of traditional photon mapping. It gives the ::: correct radiance with a large passes, but it converges slowly. We propose an anisotropic progressive photon mapping ::: method to generate high quality images with a few passes. During the rendering process, different from standard ::: progressive photon mapping, we store the photons on the surfaces. At the end of each pass, an anisotropic method is ::: employed to compute the radiance of each eye ray based on the stored photons. Before move to a new pass, the photons ::: in the scene are cleared. The experiments show that our method generates better results than the standard progressive ::: photon mapping in both numerical and visual qualities. <s> BIB003
Hachisuka and Jensen (2009) presented a new formulation of progressive photon mapping, called stochastic progressive photon mapping (SPPM), which makes it possible to calculate the average radiance value over a region and render distributed ray tracing effects. The difference between PPM and SPPM is that SPPM adds a new distributed ray tracing pass after each photon tracing pass. Through the distributed ray tracing pass, the algorithm can randomly generate hit-points for the average radiance value over a region of a pixel. Fig. 11 shows the process of SPPM. Knaus and Zwicker (2011) also proposed a probabilistic derivation of PPM as an expansion of SPPM. This approach does not require the maintenance of local statistics. It uses a probability value of the eye path in the first step to accumulate the illumination reconstruction to the pixel value which is computed in the same way as standard photon mapping algorithms. They presented a probabilistic analysis based on Monte Carlo sampling. This method can obtain a better result at glossy surfaces than SPPM. Improved shading point generation is a significant improvement in PPM methods. With these improvements, PPM can handle rendering an anisotropic surface, such as glossy surfaces. Fig. 12 shows the comparison of PPM and SPPM. Eye pass Photon pass Fig. 11 The process of stochastic progressive photon mapping used bias and variance estimation when describing an error estimation framework for adaptive rendering. The error estimation is the sum of constructing a bias estimator and noise estimator constructed for PPM. BIB001 extended PPM with frequency analysis of light transport to adaptively choose bandwidth in the radiance estimation kernels. They divided photons into ordinary photons and frequency photons. In addition, they traced frequency photons and accumulated frequency information which was used to update the shading points' kernel bandwidth. BIB002 combined PPM with an optimized computing kernel, through a better bandwidth selection, which can optimally balance noise and bias and speed up the convergence for progressive rendering. This method conducts an analysis of the radiance estimation and error estimation to obtain the optimal estimation parameters such as the bandwidth and an attenuation ratio of the radius. BIB003 proposed an anisotropic method to accelerate the convergence in PPM. At each rendering pass, they used the anisotropic method to compute the radiance of each shading point.