0 1 Recall
figure 8. Categorizing artists’ lines. (a) fraction of all lines
explained by image based lines only, object based lines only, and
both. (b) fraction of all lines explained by the exterior contours,
interior occluding contours, and all other object space lines.
0.2 0.4 0.6
0.2 0.4 0.6 0.8 1
Other Interior C. Exterior C.
features of human line drawings.
Figure 9 shows a simple example of this type. Two drawings of the same prompt (twoboxcloth with Grace Cathedral
lighting) are compared by the composition of CG line
types. The colored bars indicate the fraction of the drawing made up by each line type. In this case, however, each
set of bars represents a single drawing. One immediate
difference between the drawings is that artist A drew more
lines besides the contours. Non-contour lines account for
26% of artist A’s drawing and only 13% of artist B’s drawing. The bulk of the difference between the artists is in the
use of ridge-like lines (green, yellow, and pink bars). Artist
A drew ridge-like lines along the top of the shape, while
artist B did not. This visual difference is evident from the
statistics, which show a large fraction of geometric ridges
and apparent ridges in artist A’s drawing and almost none
in artist B’s drawing.
3. 3. Can local properties explain lines?
While it is interesting to investigate the relationship between
artists’ lines and the lines commonly used in CG, a more
fundamental question is how artists’ lines relate to differential properties of images and surfaces. The analysis above
addresses this question indirectly, since each CG definition
is based on a set of local properties, but it is restricted to the
relationships suggested by the known line-drawing algorithms. To address this question, we take a classic data mining approach. For every pixel of every prompt, we compute:
( 1) a feature vector x of properties derived from the 3D surface and 2D rendered image and ( 2) an estimated probability that a line will be included at the corresponding location
in an artist’s line drawing. Our goals are to learn a function
f(x) that estimates the probability p of an artist drawing at
a point (regression) and to understand which combinations
of properties are most useful for building such a function
choosing local properties. To build the feature vector for
each pixel, we compute 15 local properties of three types
commonly used in image processing, CG, and differential
geometry. First, we consider four image-space properties
of the rendered image prompt: luminance, gradient magnitude after s = 2 pixels Gaussian blur (ImgGradMag),
and minimum and maximum eigenvalues of the image
Hessian (corresponding to extrema in second derivative of
luminance (ImgMinCurv and ImgMaxCurv, respectively).
figure 9. Comparison of two drawings by different artists.
two drawings of the same prompt show significant visual
differences. these differences are reflected in the statistics,
especially in the use of ridge-like lines (green). RV: ridges
and valleys, aR: apparent ridges, sC: suggestive contours
(see figure 2).
0.0 0.1 0.2 0.3
AR RV & AR RV
SC & AR
In general, we expect that lines are more likely near image
edges (ImgGradMag is large) and at ridges and valleys of
luminance (where ImgMinCurv and ImgMaxCurve are
Second, we consider view-independent, differential
properties of the visible point on the 3D surface, including
the maximum (k1), minimum (k2), mean ((k1+ k2)/2), and
Gaussian (k1k2) curvatures (SurfMaxCurv, SurfMinCurv,
SurfMeanCurv, and SurfGaussianCurv, respectively). In
most cases, we expect lines to occur in areas where these
expressions are large, though it has also been observed that
lines are drawn near parabolic lines (k1k2 = 0).
Third, we consider view-dependent properties that correspond to specific definitions for computer-generated
lines. Corresponding to the definition of ridges and valleys,
we take the derivative of the largest principal curvature in
the corresponding principal direction (SurfMaxCurvDeriv),
which is zero at ridges and valleys. Corresponding to occluding contours, we compute the dot product between normal
and view vectors (N · V). Corresponding to apparent ridges
and valleys, we compute the largest view-dependent principal curvature (ViewDepCurv) and its derivative in the corresponding apparent principal direction (ViewDepCurvDeriv),
which are large and zero, respectively, at apparent ridges.
Corresponding to suggestive contours, we compute the
radial curvature (RadialCurv) and its derivative in the radial
direction (RadialCurvDeriv), which are zero and large,
respectively, at suggestive contours. Finally, corresponding
to principal highlights, we compute radial torsion, which is
zero at principal highlights.
Finally, we estimate the probability, p, of an artist drawing at a pixel by averaging the registered drawings of all artists for the same prompt and blurring with a Gaussian filter
to account for tracing errors (s = 0.5 mm).
Predicting lines by regression. Several of the computed
properties clearly can be used to distinguish pixels where
artists draw from where they do not (Figure 10). However,