In this paper, we present a new mathematical foundation for image-based lighting. Using a simple manipulation of the local coordinate system, we derive a closed-form solution to the light integral equation under distant environment illumination. We derive our solution for different BRDF's such as lambertian and Phong-like. The method is free of noise, and provides the possibility of using the full spectrum of frequencies captured by images taken from the environment. This allows for the color of the rendered object to be toned according to the color of the light in the environment. Experimental results also show that one can gain an order of magnitude or higher in rendering time compared to Monte Carlo quadrature methods and spherical harmonics.
Some very interesting closed-form solutions have already been proposed to solve the light integral. The appeal of closed-form solutions lies in the fact that they provide complete elimination of noise. Furthermore, the availability of a closed-form solution expedites the rendering process significantly. For estimation methods such as Monte Carlo @cite_112 , many samples of the environment are required to render realistic low-noise images. On the other hand, several hours might be required to generate one single image.
@cite_112
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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. Many low-light enhancement methods ignore intensive noise in original images. As a result, they often simultaneously enhance the noise as well. Furthermore, extra denoising procedures adopted by most methods ruin the details. In this paper, we introduce a joint low-light enhancement and denoising strategy, aimed at obtaining well-enhanced low-light images while getting rid of the inherent noise issue simultaneously. The proposed method performs Retinex model based decomposition in a successive sequence, which sequentially estimates a piece-wise smoothed illumination and a noise-suppressed reflectance. After getting the illumination and reflectance map, we adjust the illumination layer and generate our enhancement result. In this noise-suppressed sequential decomposition process we enforce the spatial smoothness on each component and skillfully make use of weight matrices to suppress the noise and improve the contrast. Results of extensive experiments demonstrate the effectiveness and practicability of our method. It performs well for a wide variety of images, and achieves better or comparable quality compared with the state-of-the-art methods. Low-light image enhancement methods based on classic Retinex model attempt to manipulate the estimated illumination and to project it back to the corresponding reflectance. However, the model does not consider the noise, which inevitably exists in images captured in low-light conditions. In this paper, we propose the robust Retinex model, which additionally considers a noise map compared with the conventional Retinex model, to improve the performance of enhancing low-light images accompanied by intensive noise. Based on the robust Retinex model, we present an optimization function that includes novel regularization terms for the illumination and reflectance. Specifically, we use @math norm to constrain the piece-wise smoothness of the illumination, adopt a fidelity term for gradients of the reflectance to reveal the structure details in low-light images, and make the first attempt to estimate a noise map out of the robust Retinex model. To effectively solve the optimization problem, we provide an augmented Lagrange multiplier based alternating direction minimization algorithm without logarithmic transformation. Experimental results demonstrate the effectiveness of the proposed method in low-light image enhancement. In addition, the proposed method can be generalized to handle a series of similar problems, such as the image enhancement for underwater or remote sensing and in hazy or dusty conditions.