This paper focuses on real-time all-frequency image-based rendering using an innovative solution for run-time computation of light transport. The approach is based on new results derived for non-linear phase shifting in the Haar wavelet domain. Although image-based methods for real-time rendering of dynamic glossy objects have been proposed, they do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements and real-time rendering when both varying light and viewpoint changes are required together with high sampling rates for high frequency lighting of glossy material. On the other hand, current methods cannot handle object rotation, which is one of the paramount issues for all PRT methods using wavelets. This latter problem arises because the precomputed data are defined in a global coordinate system and encoded in the wavelet domain, while the object is rotated in a local coordinate system. At the root of all the above problems is the lack of efficient run-time solution to the nontrivial problem of rotating wavelets (a non-linear phase-shift), which we solve in this paper.
One of the oldest and most straightforward approaches for solving the light integral equation is to approximate the solution using the Monte Carlo method @cite_173 @cite_87 @cite_85 . Global illumination algorithms based on Monte Carlo are general enough to allow estimation of the integral for any material type and light distribution.
@cite_85 @cite_173 @cite_87
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We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated. We present a closed-form expression for the irradiance at a point on a surface due to an arbitrary polygonal Lambertian luminaire with linearly-varying radiant exitance. The solution consists of elementary functions and a single well-behaved special function that can be either approximated directly or computed exactly in terms of classical special functions such as Clausen’s integral or the closely related dilogarithm. We first provide a general boundary integral that applies to all planar luminaires and then derive the closed-form expression that applies to arbitrary polygons, which is the result most relevant for global illumination. Our approach is to express the problem as an integral of a simple class of rational functions over regions of the sphere, and to convert the surface integral to a boundary integral using a generalization of irradiance tensors. The result extends the class of available closed-form expressions for computing direct radiative transfer from finite areas to differential areas. We provide an outline of the derivation, a detailed proof of the resulting formula, and complete pseudo-code of the resulting algorithm. Finally, we demonstrate the validity of our algorithm by comparison with Monte Carlo. While there are direct applications of this work, it is primarily of theoretical interest as it introduces much of the machinery needed to derive closed-form solutions for the general case of luminaires with radiance distributions that vary polynomially in both position and direction. The problem of the global solution of Fredholm integral equations is studied. This means that one seeks to approximate the full solution function (as opposed to the local problem, where only the value of the solution in a single point or a functional of the solution is sought). The Monte Carlo complexity, i.e., the complexity of the stochastic solution of this problem, is analyzed. The framework for this analysis is provided by information-based complexity theory. The investigations complement previous ones on the stochastic complexity of the local solution and on deterministic complexity of both local and global solutions. The results show that even in the global case Monte Carlo algorithms can perform better than deterministic ones, although the difference is not as large as in the local case. This paper describes a new method for estimating the illumination distribution of a real scene from a radiance distribution inside shadows cast by an object in the scene. First, the illumination distribution of the scene is approximated by discrete sampling of an extended light source. Then the illumination distribution of the scene is estimated from a radiance distribution inside shadows cast by an object of known shape onto another object in the scene. Instead of assuming any particular reflectance properties of the surface inside the shadows, both the illumination distribution of the scene and the reflectance properties of the surface are estimated simultaneously, based on iterative optimization framework. In addition, this paper introduces an adaptive sampling of the illumination distribution of a scene. Rather than using a uniform discretization of the overall illumination distribution, we adaptively increase sampling directions of the illumination distribution based on the estimation at the previous iteration. Using the adaptive sampling framework, we are able to estimate overall illumination more efficiently by using fewer sampling directions. The proposed method is effective for estimating an illumination distribution even under a complex illumination environment.