Graphics Reference
In-Depth Information
Candidates for important features are silhouettes, contours on geometric mod-
els, apparent contours, suggestive contours, and places where the light field can
be condensed to one line. All of these fit under the general category of
edges,
as
the term is used in computer vision, that is, places where the brightness changes
rapidly. Such edges can exist at multiple scales, in that something that presents a
gradual change in brightness, seen up close, may represent a rapid transition when
seen from farther away. There's some evidence [Eld99] that edges, considered at
all scales, completely characterize an image. This idea, in reverse, is at the heart of
recent work on gradient-based expressive rendering techniques, which we discuss
in Section 34.7.
An alternative to reasoning about where lines
should
be drawn is to observe
where they actually
are
drawn. Cole et al. [CGL
+
12] have performed a carefully
constructed experiment to see where artists draw lines in single-object illustra-
tions, given several views of the object to look at during the drawing process. They
find that occluding contours and places with large image gradients are strongly
favored, but these do not by any means account for all the lines that are drawn.
There are larger-scale issues in expressive rendering as well. In drawing a pic-
ture of two people standing on a bridge in Paris, we're likely to concentrate on
the bridge and the people, sketch the general shapes of the buildings in the back-
ground, and perhaps include some added detail on the Eiffel Tower. These choices
represent the features in the scene that are
salient
to us, but there's no way to algo-
rithmically determine saliency from the image data without an understanding of
the full scene; in larger-scale imagery, expressive rendering at present must rely on
additional user input to determine the saliency of even details that may be strongly
significant in terms of perception.
Silhouette
P
Crease
Cusp
Because geometric characteristics of objects, like their boundaries, arise in expres-
sive rendering, and because these have also often been studied in geometry, there's
a well-defined vocabulary in place; unfortunately, usages differ between mathe-
matics and graphics. We'll adhere to the mathematical conventions.
First, when an object sits in front of a background, the
silhouette
is the bound-
ary between the object's image and the background (see Figure 34.9). For a
smooth object like a sphere, if
S
is a silhouette point, then the tangent plane at
S
contains the ray from the eye to
S
; points where the tangent contains the view
direction are called
contour points
; the set of all contour points is called the
contour.
Thus, for a smooth object, every silhouette point is a contour point, or,
equivalently, the silhouette is a subset of the contour. But there may be many other
contour points as well, as seen in Figure 34.9 (bottom) where the contour extends
into the interior of the surface.
Figure 34.9: (Top) The silhouette
separates foreground from back-
ground. (Top middle) P is on a
contour if the ray from the eye
to P is tangent to the surface
at P. (Lower middle) A crease
is a point at which nearby tan-
gent planes converge to two dif-
ferent limits; the definition can be
weakened to give a notion of a
crease at a certain scale. (Bot-
tom) A cusp is a point Q of a con-
tour curve C at which the tangent
line to C is the same as the line
from the eye to Q.
The condition for a point
P
of a smooth surface to be a contour point, as viewed
from an eyepoint
C
, is that
n
(
P
)
·
(
P
−
C
)=
0,
(34.1)
that is, that the surface normal be orthogonal to the view vector.
Unfortunately, contour points have been called silhouettes in several graphics
papers, blurring the distinction between the two notions. Note that a contour point
S
may be visible or not: All that's required is that the ray from the eye to
S
be
