Graphics Reference
In-Depth Information
Clusters
Concatenation
k
-means
clustering
Figure 9.7
Clustering via the
k
-means algorithm. (After [Leung and Malik 01].)
resentative vector of the cluster (the mean of all the vectors in the cluster). The
3D textons
are these individual clusters, or the centers thereof; they correspond
to common surface features in the image, such as ridges and groves, as well as
simple markings.
Leung and Malik's work had the goal of using 3D textons to represent and
analyze the appearance of 3D mesostructures. Much of the paper is devoted to
the idea of constructing a basic “vocabulary” of textons that could be used to
describe the appearance of
any
material. The relevance to computer graphics is
that the texton representationmay provide a way of rendering a surface using BTF
data from novel lighting and viewing directions; i.e., textons can be used for BTF
synthesis.
9.2.3 BTF Synthesis Using 3D Textons
The paper entitled “Synthesis of Bidirectional Texture Functions on Arbitrary
Surfaces” by Xin Tong, Jingdan Zhang, Ligang Liu, Xi Wang, Baining Guo, and
Heung-Yeung Shum presents a BTF rendering method for arbitrary surface ge-
ometry [Tong et al. 02]. The method employs the 3D texton approach: 3D textons
are constructed to represent the entire BTF data set.
The details of the texton-based BTF synthesis are rather involved, but the
basic idea is conceptually simple. Three-dimensional textons are constructed for
the entire BTF data set (although in practice, not all the images are used for all
the textons). This produces a texton “vocabulary,” which is a kind of basis for
the texton representation of the surface points under arbitrary lighting/viewing
arrangements. Each pixel in the stack of images, i.e., each surface point in the
captured BTF data, is assigned a single texton “label” from the texton vocabulary.
This label is a single texton, and is chosen by the closest match to the response
vector for the point. The correspondence between surface points and texton labels
is described as a 2D “texton surface map.” An analogous map is constructed for
the neighborhood of each point to be rendered. Then, for the distance measure,
the distance between 3D textons that does not depend on BTF geometry is used,
which enables BTF synthesis to handle the arbitrary mesostructure geometry.
