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3.8 Additional reading 169

the problem at hand and desired robustness and computation constraints may be required to
choose the best technique.
Perhaps the biggest advantage of CRFs and DRFs, as argued by Kumar and Hebert (2006),
Tappen, Liu, Freeman et al. (2007) and Blake, Rother, Brown et al. (2004), is that learning the
model parameters is sometimes easier. While learning parameters in MRFs and their variants
is not a topic that we cover in this book, interested readers can find more details in recently
published articles (Kumar and Hebert 2006; Roth and Black 2007a; Tappen, Liu, Freeman et
al. 2007; Tappen 2007; Li and Huttenlocher 2008).

3.7.3 Application: Image restoration

In Section 3.4.4, we saw how two-dimensional linear and non-linear filters can be used to
remove noise or enhance sharpness in images. Sometimes, however, images are degraded by
larger problems, such as scratches and blotches (Kokaram 2004). In this case, Bayesian meth-
ods such as MRFs, which can model spatially varying per-pixel measurement noise, can be
used instead. An alternative is to use hole filling or inpainting techniques (Bertalmio, Sapiro,
Caselles et al. 2000; Bertalmio, Vese, Sapiro et al. 2003; Criminisi, P´ erez, and Toyama 2004),
as discussed in Sections 5.1.4 and 10.5.1.
Figure 3.57 shows an example of image denoising and inpainting (hole filling) using a
Markov random field. The original image has been corrupted by noise and a portion of the
data has been removed. In this case, the loopy belief propagation algorithm computes a
slightly lower energy and also a smoother image than the alpha-expansion graph cut algo-
rithm.

3.8 Additional reading

If you are interested in exploring the topic of image processing in more depth, some popular
textbooks have been written by Lim (1990); Crane (1997); Gomes and Velho (1997); J¨ ahne
(1997); Pratt (2007); Russ (2007); Burger and Burge (2008); Gonzales and Woods (2008).
The pre-eminent conference and journal in this field are the IEEE Conference on Image Pro-
cesssing and the IEEE Transactions on Image Processing.
For image compositing operators, the seminal reference is by Porter and Duff (1984)
while Blinn (1994a,b) provides a more detailed tutorial. For image compositing, Smith and
Blinn (1996) were the first to bring this topic to the attention of the graphics community,
while Wang and Cohen (2007a) provide a recent in-depth survey.
In the realm of linear filtering, Freeman and Adelson (1991) provide a great introduc-
tion to separable and steerable oriented band-pass filters, while Perona (1995) shows how to
approximate any filter as a sum of separable components.
The literature on non-linear filtering is quite wide and varied; it includes such topics as
bilateral filtering (Tomasi and Manduchi 1998; Durand and Dorsey 2002; Paris and Durand
2006; Chen, Paris, and Durand 2007; Paris, Kornprobst, Tumblin et al. 2008), related itera-
tive algorithms (Saint-Marc, Chen, and Medioni 1991; Nielsen, Florack, and Deriche 1997;
Black, Sapiro, Marimont et al. 1998; Weickert, ter Haar Romeny, and Viergever 1998; Weick-
ert 1998; Barash 2002; Scharr, Black, and Haussecker 2003; Barash and Comaniciu 2004),