Because cloth is made of fibers, we need a volume scattering model that can handle the anisotropy of fibers; we
chose a modified version of the model proposed by Jakob
7 (detailed in Section 4) for this purpose. This model
requires an optical density, an albedo, and two phase function parameters: an orientation vector and a specular lobe
width. Intuitively, the optical density describes how often
light scatters within the cloth; the albedo and the phase
function respectively capture the fraction of light being
absorbed and how light changes its direction at each scattering location.
Our technique begins with a micro CT scan of a small
area of material, showing detail at the level of individual
fibers over a fraction of a square centimeter. Such scans
can readily be ordered at moderate cost (a few hundred
US dollars) from a number of facilities, and suitable desktop CT scanners are becoming available. In a sequence of
three stages (Figure 2), we process and augment this data,
ending with a volume that defines the required scattering
model parameters using density and orientation fields
derived from the CT data, plus three global parameters: the
albedo, the lobe width, and a density multiplier that scales
the density field.
The first stage (Section 5) processes the density volume
to augment it with orientation information and to remove
noise by convolving the data with 3D oriented filters to detect
oriented structures, and thresholding to separate meaningful structure from noise. This stage produces the density
and orientation fields.
This volume can be rendered only after the global optical parameters are determined. The second stage (Section 6)
makes use of a single photograph of the material under
known (but not controlled) lighting, and associates optical
properties with the oriented volume from the first stage by
matching the texture of the rendered volume to the texture
of the photograph.
The resulting volume model is good for rendering small
samples; the third stage takes this small patch and maps
it over a large surface of cloth, using randomized tiling to
replicate the material and shell mapping14 to warp it.
The resulting renderings (Section 7) show that this
4. FIBER SCATTERING MODEL
unique approach to appearance modeling, leveraging
direct information about mesoscale geometry, produces
excellent appearance from the small scale, where the
geometry itself is visible, to the large scale, where the direc-
tional scattering properties naturally emerge from the
measured 3D structure. The characteristic appearance of
difficult materials such as velvet and satin is predicted by
our rather minimal volume scattering model, even though
we use no light scattering measurements that could tell
these materials apart, because accurate geometric infor-
mation is available.
We model light transport using the anisotropic radiative
transfer equation (RTE) from Jakob et al.
7 which states that
within participating media,
where ss and st : S2 → are the anisotropic scattering and
extinction coefficients, and fp is the phase function. Spatial
dependence has been omitted for readability.
This equation can be understood as a generalization of
the isotropic RTE that adds support for a directionally varying amount of “interaction” with a medium. For instance,
the directional dependence of st(ω) is necessary to model
the effect that light traveling parallel to coherently aligned
fibers faces less obstruction than light traveling perpendicular to the fibers.
To specify the problem to be solved, we must choose
a compatible scattering model that will supply internally
consistent definitions of st, ss, and fp. For this purpose, we
use the micro-flake model proposed in the same work. This
volume analogue of microfacet models represents different
kinds of volume scattering interactions using a directional
flake distribution D(m) that describes the orientation m of
(unresolved) idealized mirror flakes at every point in space.
Similar to microfacet models, the phase function then
involves evaluating D(m) at the half-way direction between
the incident and outgoing direction. For completeness, we
reproduce the model’s definition as follows:
Figure 2. Our volume appearance modeling pipeline: (a) CT images are acquired; (b) the density field and orientation field of the volume
are created; and (c) optical parameters of the volumetric model are assigned by matching statistics of photographs with rendered images.
(d) Larger models are rendered using our acquired volumetric appearance and geometry models.
(a) Micro CT images (b) Reconstructed density field
and orientation field
(c) Appearance matching (d) Rendered results