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170 3 Image processing

and variational approaches (Chan, Osher, and Shen 2001; Tschumperl´ e and Deriche 2005;
Tschumperl´ e 2006; Kaftory, Schechner, and Zeevi 2007).
Good references to image morphology include (Haralick and Shapiro 1992, Section 5.2;
Bovik 2000, Section 2.2; Ritter and Wilson 2000, Section 7; Serra 1982; Serra and Vincent
1992; Yuille, Vincent, and Geiger 1992; Soille 2006).
The classic papers for image pyramids and pyramid blending are by Burt and Adelson
(1983a,b). Wavelets were first introduced to the computer vision community by Mallat (1989)
and good tutorial and review papers and books are available (Strang 1989; Simoncelli and
Adelson 1990b; Rioul and Vetterli 1991; Chui 1992; Meyer 1993; Sweldens 1997). Wavelets
are widely used in the computer graphics community to perform multi-resolution geomet-
ric processing (Stollnitz, DeRose, and Salesin 1996) and have been used in computer vision
for similar applications (Szeliski 1990b; Pentland 1994; Gortler and Cohen 1995; Yaou and
Chang 1994; Lai and Vemuri 1997; Szeliski 2006b), as well as for multi-scale oriented filter-
ing (Simoncelli, Freeman, Adelson et al. 1992) and denoising (Portilla, Strela, Wainwright et
al. 2003).
While image pyramids (Section 3.5.3) are usually constructed using linear filtering op-
erators, some recent work has started investigating non-linear filters, since these can better
preserve details and other salient features. Some representative papers in the computer vision
literature are by Gluckman (2006a,b); Lyu and Simoncelli (2008) and in computational pho-
tography by Bae, Paris, and Durand (2006); Farbman, Fattal, Lischinski et al. (2008); Fattal
(2009).
High-quality algorithms for image warping and resampling are covered both in the im-
age processing literature (Wolberg 1990; Dodgson 1992; Gomes, Darsa, Costa et al. 1999;
Szeliski, Winder, and Uyttendaele 2010) and in computer graphics (Williams 1983; Heckbert
1986; Barkans 1997; Akenine-M¨ oller and Haines 2002), where they go under the name of
texture mapping. Combination of image warping and image blending techniques are used to
enable morphing between images, which is covered in a series of seminal papers and books
(Beier and Neely 1992; Gomes, Darsa, Costa et al. 1999).
The regularization approach to computer vision problems was first introduced to the vi-
sion community by Poggio, Torre, and Koch (1985) and Terzopoulos (1986a,b, 1988) and
continues to be a popular framework for formulating and solving low-level vision problems
(Ju, Black, and Jepson 1996; Nielsen, Florack, and Deriche 1997; Nordstr¨ om 1990; Brox,
Bruhn, Papenberg et al. 2004; Levin, Lischinski, and Weiss 2008). More detailed mathe-
matical treatment and additional applications can be found in the applied mathematics and
statistics literature (Tikhonov and Arsenin 1977; Engl, Hanke, and Neubauer 1996).
The literature on Markov random fields is truly immense, with publications in related
fields such as optimization and control theory of which few vision practitioners are even
aware. A good guide to the latest techniques is the book edited by Blake, Kohli, and Rother
(2010). Other recent articles that contain nice literature reviews or experimental compar-
isons include (Boykov and Funka-Lea 2006; Szeliski, Zabih, Scharstein et al. 2008; Kumar,
Veksler, and Torr 2010).
The seminal paper on Markov random fields is the work of Geman and Geman (1984),
who introduced this formalism to computer vision researchers and also introduced the no-
tion of line processes, additional binary variables that control whether smoothness penalties
are enforced or not. Black and Rangarajan (1996) showed how independent line processes