Page 240 -

4.2 Edges 219

Figure 4.38 Changing the character of a curve without affecting its sweep (Finkelstein and Salesin 1994) c
1994 ACM: higher frequency wavelets can be replaced with exemplars from a style library to effect different local
appearances.

on itself (Figure 4.37a). Lowe (1989) and Taubin (1995) describe techniques that compensate
for this shrinkage by adding an offset term based on second derivative estimates or a larger
smoothing kernel (Figure 4.37b). An alternative approach, based on selectively modifying
different frequencies in a wavelet decomposition, is presented by Finkelstein and Salesin
(1994). In addition to controlling shrinkage without affecting its “sweep”, wavelets allow the
“character” of a curve to be interactively modified, as shown in Figure 4.38.
The evolution of curves as they are smoothed and simplified is related to “grassfire” (dis-
tance) transforms and region skeletons (Section 3.3.3)(Tek and Kimia 2003), and can be used
to recognize objects based on their contour shape (Sebastian and Kimia 2005). More local de-
scriptors of curve shape such as shape contexts (Belongie, Malik, and Puzicha 2002) can also
be used for recognition and are potentially more robust to missing parts due to occlusions.
The field of contour detection and linking continues to evolve rapidly and now includes
techniques for global contour grouping, boundary completion, and junction detection (Maire,
Arbelaez, Fowlkes et al. 2008), as well as grouping contours into likely regions (Arbel´ aez,
Maire, Fowlkes et al. 2010) and wide-baseline correspondence (Meltzer and Soatto 2008).

4.2.3 Application: Edge editing and enhancement

While edges can serve as components for object recognition or features for matching, they
can also be used directly for image editing.
In fact, if the edge magnitude and blur estimate are kept along with each edge, a visually
similar image can be reconstructed from this information (Elder 1999). Based on this princi-
ple, Elder and Goldberg (2001) propose a system for “image editing in the contour domain”.
Their system allows users to selectively remove edges corresponding to unwanted features
such as specularities, shadows, or distracting visual elements. After reconstructing the image
from the remaining edges, the undesirable visual features have been removed (Figure 4.39).
Another potential application is to enhance perceptually salient edges while simplifying
the underlying image to produce a cartoon-like or “pen-and-ink” stylized image (DeCarlo and
Santella 2002). This application is discussed in more detail in Section 10.5.2.