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Importance sampling is a common and effective technique for
reducing the rendering time of standard Monte Carlo-based
global-illumination algorithms. For measured (or tabular) surface
reflectance functions (e.g. BRDFs), however, it is unclear how to
efficiently generate samples of incident direction consistent with
the distribution of energy of these functions. In a SIGGRAPH 2004
paper, we propose a new factored model of the BRDF that is
designed to support efficient importance sampling within
physically-based rendering systems. This is achieved by
reparameterizing the BRDF domain before factoring the
high-dimensional function using the Non-Negative Matrix
Factorization (NMF) algorithm. Our final representation reduces
rendering times by a factor of 4-10 for scenes that contain a
variety of measured materials.
Although matrix factorization is appropriate for compressing BRDFs,
not all functions are separable. We introduce a more general
representation of high-dimensional measured data (again, in the
context of physically-based rendering) optimized to provide
compression and efficient importance sampling. Our approach is
based on the Douglas-Peucker polyline approximation algorithm and
achieves significant compression ratios of multi-dimensional
datasets while providing a final representation that can be
directly sampled. In our experiments, we show this representation
provides ~4x decrease in the time it takes to render scenes with
both complex materials and illumination.
Existing data-driven representations of appearance functions are
compact, accurate and easy to use for rendering. Another crucial
goal, which has so far received little attention, is
editability: for practical use, we must be able to change
both the directional and spatial behavior of surface reflectance
(e.g., making one material shinier, another more anisotropic, and
changing the spatial ``texture maps'' indicating where each
material appears). We introduce the Inverse Shade Tree
framework that provides a general approach to estimating the
``leaves'' of a user-specified shade tree from high-dimensional
measured datasets of appearance. These leaves are sampled 1- and
2-dimensional functions that capture both the directional behavior
of individual materials and their spatial mixing patterns. In
order to compute these shade trees automatically, we map the
problem to matrix factorization and introduce a flexible new
algorithm that allows for constraints such as non-negativity,
sparsity, and energy conservation.
Unlike (quasi-)homogeneous materials, the spatial component of
heterogeneous subsurface scattering can be arbitrarily
complex. Storing the spatial component outright results in
impractically large datasets. We address the problem of acquiring
and compactly representing the spatial component of heterogeneous
subsurface scattering functions. A material model based on matrix
factorization is proposed that can be mapped onto arbitrary
geometry and, due to its compact form, can be incorporated into
most visualization systems with little overhead. We use a
projector and digital video camera to acquire several real-world
datasets. We evaluate our representation in terms of both its
qualitative and numerical accuracy.
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