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5.6 Additional reading 269

Arbel´ aez, Maire, Fowlkes et al. (2010) provide a good review of automatic segmentation
techniques and also compare their performance on the Berkeley Segmentation Dataset and
Benchmark (Martin, Fowlkes, Tal et al. 2001). 12 Additional comparison papers and databases
include those by Unnikrishnan, Pantofaru, and Hebert (2007); Alpert, Galun, Basri et al.
(2007); Estrada and Jepson (2009).
The topic of active contours has a long history, beginning with the seminal work on
snakes and other energy-minimizing variational methods (Kass, Witkin, and Terzopoulos
1988; Cootes, Cooper, Taylor et al. 1995; Blake and Isard 1998), continuing through tech-
niques such as intelligent scissors (Mortensen and Barrett 1995, 1999; P´ erez, Blake, and
Gangnet 2001), and culminating in level sets (Malladi, Sethian, and Vemuri 1995; Caselles,
Kimmel, and Sapiro 1997; Sethian 1999; Paragios and Deriche 2000; Sapiro 2001; Osher and
Paragios 2003; Paragios, Faugeras, Chan et al. 2005; Cremers, Rousson, and Deriche 2007;
Rousson and Paragios 2008; Paragios and Sgallari 2009), which are currently the most widely
used active contour methods.
Techniques for segmenting images based on local pixel similarities combined with ag-
gregation or splitting methods include watersheds (Vincent and Soille 1991; Beare 2006;
Arbel´ aez, Maire, Fowlkes et al. 2010), region splitting (Ohlander, Price, and Reddy 1978),
region merging (Brice and Fennema 1970; Pavlidis and Liow 1990; Jain, Topchy, Law et al.
2004), as well as graph-based and probabilistic multi-scale approaches (Felzenszwalb and
Huttenlocher 2004b; Alpert, Galun, Basri et al. 2007).
Mean-shift algorithms, which find modes (peaks) in a density function representation of
the pixels, are presented by Comaniciu and Meer (2002); Paris and Durand (2007). Parametric
mixtures of Gaussians can also be used to represent and segment such pixel densities (Bishop
2006; Ma, Derksen, Hong et al. 2007).
The seminal work on spectral (eigenvalue) methods for image segmentation is the nor-
malized cut algorithm of Shi and Malik (2000). Related work includes that by Weiss (1999);
Meil˘ a and Shi (2000, 2001); Malik, Belongie, Leung et al. (2001); Ng, Jordan, and Weiss
(2001); Yu and Shi (2003); Cour, B´ en´ ezit, and Shi (2005); Sharon, Galun, Sharon et al.
(2006); Tolliver and Miller (2006); Wang and Oliensis (2010).
Continuous-energy-based (variational) approaches to interactive segmentation include Leclerc
(1989); Mumford and Shah (1989); Chan and Vese (1992); Zhu and Yuille (1996); Tabb and
Ahuja (1997). Discrete variants of such problems are usually optimized using binary graph
cuts or other combinatorial energy minimization methods (Boykov and Jolly 2001; Boykov
and Kolmogorov 2003; Rother, Kolmogorov, and Blake 2004; Kolmogorov and Boykov 2005;
Cui, Yang, Wen et al. 2008; Vicente, Kolmogorov, and Rother 2008; Lempitsky and Boykov
2007; Lempitsky, Blake, and Rother 2008), although continuous optimization techniques fol-
lowed by thresholding can also be used (Grady 2006; Grady and Ali 2008; Singaraju, Grady,
and Vidal 2008; Criminisi, Sharp, and Blake 2008; Grady 2008; Bai and Sapiro 2009; Cou-
prie, Grady, Najman et al. 2009). Boykov and Funka-Lea (2006) present a good survey of
various energy-based techniques for binary object segmentation.

12 http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench/.