Graphics Reference
In-Depth Information
The 2001 paper by Liu et al. was significant in that it described the first use
of BTF synthesis for actual rendering. Also the algorithm for constructing the
reference image is useful in itself, as it provides a method for obtaining a usable
BTF sample from a sparse set of captured BTF images. However, the synthesis
method described in the paper has some limitations. For example, the geometry
of the BTF is limited by the height-field representation. Also it did not consider
mapping the BTF over surfaces having complex geometry. These problems are
solved by the method introduced in the next section.
9.2.2 3D Textons
The notion of a
texton
was proposed by neuroscientist Bela Julesz in 1981 as a
kind of elementary “atom” of human texture perception. According to Julesz's
Texton Theory
, textons are “the putative units of pre-attentive human texture per-
ception.” The idea is that a few simple visual structures known as textons (ele-
ments such as crosses, bars, and terminators) together with orientation indicators,
provide a kind of basis for image recognition. Textons were only loosely de-
fined until 2001, when Thomas Leung and Jitendra Malik formalized the notion
of 2D and 3D textons in the paper entitled “Representing and Recognizing the
Visual Appearance of Materials using Three-dimensional Textons” [Leung and
Malik 01].
Textons come about from analyzing the results of filtering a pixel in a texture
image by a “bank” of filters. Leung and Malik's filter bank had 48 filters in to-
tal, including elongated Gaussian filters, simple scaling filters, and phase-shifting
filters. The filter response of a pixel is the collection of results of applying each
filter to the pixel; this is a 48-dimensional vector in Leung and Malik's work. Of
course, there is a great deal of redundancy in the filter-response vectors, which can
be reduced by clustering the set of filter-response vectors. The
k
-means algorithm
can be employed (see Section 7.2.2) to cluster the filter-response vectors for all the
pixels in 48-dimensional space. All the vectors in a cluster are regarded as being
essentially the same. The center of each cluster is the texton; the filter-response
vector for the cluster is the
appearance vector
.
Three-dimensional textons are a generalization to textured surfaces that have
notable geometric mesostructure. Mesostructures were originally defined as “lo-
cal structures in the scale that human eyes can perceive,” so in capturing filter
responses at this scale, similar responses may be clustered together and consid-
ered the same response. The idea of 3D textons is that rough understanding of
how responses are distributed in a small area, rather than considering differences
in response, enables more efficient representation of the characteristics of the
surface.
