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Section 6.2 Pooled Texture Representations by Discovering Textons 171

Rectified Summarized

Vertical stripes
Light stripes
Positive response Dark background

Image
Dark stripes
Light background
Negative response

Horizontal stripes
Light stripes
Positive response Dark background

Dark stripes
Negative response Light background

FIGURE 6.7: Filter-based texture representations look for pattern subelements such as
oriented bars. The brick image on the left is filtered with an oriented bar filter (shown as
a tiny inset on the top left of the image at full scale) to detect bars, yielding stripe responses
(center left; negative is dark, positive is light, mid-gray is zero). These are rectified (here
we use half-wave rectification) to yield response maps (center right; dark is zero, light
is positive). In turn, these are summarized (here we smoothed over a neighborhood twice
the filter width) to yield the texture representation on the right. In this, pixels that have
strong vertical bars nearby are light, and others are dark; there is not much difference
between the dark and light vertical structure for this image, but there is a real difference
between dark and light horizontal structure.

the steerable pyramid of Simoncelli and Freeman (1995a). Code for these filters is
available at http://www.cns.nyu.edu/ ~ eero/steerpyr/.

6.2 POOLED TEXTURE REPRESENTATIONS BY DISCOVERING TEXTONS

A texture is a set of textons that repeat in some way. We could find these textons
by looking for image patches that are common. An alternative is to find sets of
texton subelements—that is, vectors of filter outputs—that are common (if textons
are repeated, then so are their subelements). There are two important difficulties
in finding image patches or vectors of filter outputs that commonly occur together.
First, these representations of the image are continuous. We cannot simply count
how many times a particular pattern occurs, because each vector is slightly different.
Second, the representation is high dimensional in either case. A patch around a