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5.1 Active contours 249

(a)

(b)

Figure 5.11 Level set segmentation (Cremers, Rousson, and Deriche 2007) c 2007 Springer: (a) grayscale
image segmentation and (b) color image segmentation. Uni-variate and multi-variate Gaussians are used to model
the foreground and background pixel distributions. The initial circles evolve towards an accurate segmentation of
foreground and background, adapting their topology as they evolve.

approach is to re-cast the problem in a segmentation framework, where the energy measures
the consistency of the image statistics (e.g., color, texture, motion) inside and outside the seg-
mented regions (Cremers, Rousson, and Deriche 2007; Rousson and Paragios 2008; Houhou,
Thiran, and Bresson 2008). These approaches build on earlier energy-based segmentation
frameworks introduced by Leclerc (1989), Mumford and Shah (1989), and Chan and Vese
(1992), which are discussed in more detail in Section 5.5. Examples of such level-set seg-
mentations are shown in Figure 5.11, which shows the evolution of the level sets from a series
of distributed circles towards the final binary segmentation.
For more information on level sets and their applications, please see the collection of
papers edited by Osher and Paragios (2003) as well as the series of Workshops on Variational
and Level Set Methods in Computer Vision (Paragios, Faugeras, Chan et al. 2005) and Special
Issues on Scale Space and Variational Methods in Computer Vision (Paragios and Sgallari
2009).

5.1.5 Application: Contour tracking and rotoscoping

Active contours can be used in a wide variety of object-tracking applications (Blake and Isard
1998; Yilmaz, Javed, and Shah 2006). For example, they can be used to track facial features
for performance-driven animation (Terzopoulos and Waters 1990; Lee, Terzopoulos, and Wa-