A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Prefiltering Strategies <s> In this work, we investigate the visual appearance of real-world surfaces and the dependence of appearance on imaging conditions. We present a BRDF (bidirectional reflectance distribution function) database with reflectance measurements for over 60 different samples, each observed with over 200 different combinations of viewing and source directions. We fit the BRDF measurements to two recent models to obtain a BRDF parameter database. These BRDF parameters can be directly used for both image analysis and image synthesis. Finally, we present a BTF (bidirectional texture function) database with image textures from over 60 different samples, each observed with over 200 different combinations of viewing and source directions. Each of these unique databases has important implications for a variety of vision algorithms and each is made publicly available. <s> BIB001 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Prefiltering Strategies <s> We present an extension to texture mapping that supports the representation of 3-D surface details and view motion parallax. The results are correct for viewpoints that are static or moving, far away or nearby. Our approach is very simple: a relief texture (texture extended with an orthogonal displacement per texel) is mapped onto a polygon using a two-step process: First, it is converted into an ordinary texture using a surprisingly simple 1-D forward transform. The resulting texture is then mapped onto the polygon using standard texture mapping. The 1-D warping functions work in texture coordinates to handle the parallax and visibility changes that result from the 3-D shape of the displacement surface. The subsequent texture-mapping operation handles the transformation from texture to screen coordinates. <s> BIB002 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Prefiltering Strategies <s> In this paper we present a new form of texture mapping that produces increased photorealism. Coefficients of a biquadratic polynomial are stored per texel, and used to reconstruct the surface color under varying lighting conditions. Like bump mapping, this allows the perception of surface deformations. However, our method is image based, and photographs of a surface under varying lighting conditions can be used to construct these maps. Unlike bump maps, these Polynomial Texture Maps (PTMs) also capture variations due to surface self-shadowing and interreflections, which enhance realism. Surface colors can be efficiently reconstructed from polynomial coefficients and light directions with minimal fixed-point hardware. We have also found PTMs useful for producing a number of other effects such as anisotropic and Fresnel shading models and variable depth of focus. Lastly, we present several reflectance function transformations that act as contrast enhancement operators. We have found these particularly useful in the study of ancient archeological clay and stone writings. <s> BIB003 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Prefiltering Strategies <s> We propose a new technique for efficiently rendering bidirectional texturefunctions (BTFs). A 6D BTF describes the appearance of a material as a texture that depends on the lighting and v iewing directions. As such, a BTF accommodates self-shadowing, interreflection, and masking effects of acomplex material without needing an explicit representation of the small scale geometry. Our method represe nts the BTF as a set of spatially varying apparent BRDFs, that each encode the reflectance field of a single pixe l in the BTF. Each apparent BRDF is decomposed into a product of three or more two-dimensional positive fac tors using a novel factorization technique, which we call chained matrix factorization (CMF). The proposed factorizatio n technique is fully automatic and suitable for both BRDFs and apparent BRDFs (which typically exhibit off-sp ecular peaks and non-reciprocity). The main benefit of CMF is that it delivers factors well suited for the limited dyna mic range of conventional texture maps. After factorization, an efficient representation of the BTF is o btained by clustering the factors into a compact set of 2D textures. With this compact representation, BTFs ca n be rendered on recent consumer level hardware with arbitrary viewing and lighting directions at interactive rates. <s> BIB004 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Prefiltering Strategies <s> This paper presents a new technique for rendering bidirectional texture functions (BTFs) at different levels of detail (LODs). Our method first decomposes each BTF image into multiple subbands with a Laplacian pyramid. Each vector of Laplacian coefficients of a texel at the same level is regarded as a Laplacian bidirectional reflectance distribution function (BRDF). These vectors are then further compressed by applying principal components analysis (PCA). At the rendering stage, the LOD parameter for each pixel is calculated according to the distance from the viewpoint to the surface. Our rendering algorithm uses this parameter to determine how many levels of BTF Laplacian pyramid are required for rendering. Under the same sampling resolution, a BTF gradually transits to a BRDF as the camera moves away from the surface. Our method precomputes this transition and uses it for multiresolution BTF rendering. Our Laplacian pyramid representation allows real-time anti-aliased rendering of BTFs using graphics hardware. In addition to provide visually satisfactory multiresolution rendering for BTFs, our method has a comparable compression rate to the available single-resolution BTF compression techniques. <s> BIB005 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Prefiltering Strategies <s> An ever-growing number of real-world computer vision applications require classification, segmentation, retrieval, or realistic rendering of genuine materials. However, the appearance of real materials dramatically changes with illumination and viewing variations. Thus, the only reliable representation of material visual properties requires capturing of its reflectance in as wide range of light and camera position combinations as possible. This is a principle of the recent most advanced texture representation, the bidirectional texture function (BTF). Multispectral BTF is a seven-dimensional function that depends on view and illumination directions as well as on planar texture coordinates. BTF is typically obtained by measurement of thousands of images covering many combinations of illumination and viewing angles. However, the large size of such measurements has prohibited their practical exploitation in any sensible application until recently. During the last few years, the first BTF measurement, compression, modeling, and rendering methods have emerged. In this paper, we categorize, critically survey, and psychophysically compare such approaches, which were published in this newly arising and important computer vision and graphics area. <s> BIB006 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Prefiltering Strategies <s> Bidirectional texture functions (BTFs) represent the appearance of complex materials. Three major shortcomings with BTFs are the bulky storage, the difficulty in editing and the lack of efficient rendering methods. To reduce storage, many compression techniques have been applied to BTFs, but the results are difficult to edit. To facilitate editing, analytical models have been fit, but at the cost of accuracy of representation for many materials. It becomes even more challenging if efficient rendering is also needed. We introduce a high-quality general representation that is, at once, compact, easily editable, and can be efficiently rendered. The representation is computed by adopting the stagewise Lasso algorithm to search for a sparse set of analytical functions, whose weighted sum approximates the input appearance data. We achieve compression rates comparable to a state-of-the-art BTF compression method. We also demonstrate results in BTF editing and rendering. <s> BIB007
A first prefiltering strategy is to store precomputed or measured values of A ðl; vÞ in (4), for a large number of view and light directions, and for many footprints A of different sizes covering the coarse mesh. The values can then be stored in a 6D table called a Bidirectional Texture Function, or BTF BIB001 . Since this approach is directly based on the general prefiltering equation, it automatically takes into account the parallax offset and the correlation effects that are modeled by this equation. It can also take self-interreflections and subsurface scattering effects into account, although they were neglected in (4). The main drawback of this approach is that it requires a lot of memory: an uncompressed BTF represents gigabytes of data. Several methods have been proposed to acquire a BTF from real measurements BIB001 , to create a BTF from Monte-Carlo simulations on a geometric surface model BIB004 , and to compress BTFs into manageable representations, in particular for interactive rendering BIB004 , BIB005 , BIB007 . A survey of these methods can be found in BIB006 . We do not discuss them here, nor the closely related image-based rendering methods assuming a fixed light or view direction such as in BIB002 and BIB003 . They are out of our scope because they do not propose algorithms to prefilter maps used in a nonlinear way for rendering. Another prefiltering strategy is to assume that the surface colors, normals, visibility, and shadows are uncorrelated, which is sometimes really the case (we discuss the validity of this hypothesis in Section 8). This hypothesis allows one to replace the A term in (4) with a product of simpler terms. Indeed, if two variables a and b are uncorrelated in the sense that R wða À aÞðb À bÞ ¼ 0, with  In practice, most methods use the following hypothesis, most often implicitly. We discuss its validity in Section 8.