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Section 6.6 Notes 192

Texture Synthesis
Texture synthesis exhausted us long before we could exhaust it. Patch based texture
synthesis is due to Efros and Freeman (2001); this paper hints at a form of con-
ditional texture synthesis. Hertzmann et al. (2001) demonstrate that conditional
texture synthesis can do the most amazing tricks. Vivek Kwatra and Li-Yi Wei
organized an excellent course on texture synthesis at SIGGRAPH 2007; the notes
are at http://www.cs.unc.edu/ ~ kwatra/SIG07_TextureSynthesis/index.htm.

Denoising
Early work on image denoising relied on various smoothness assumptions—such as
Gaussian smoothing, anisotropic filtering (Perona and Malik 1990c), total varia-
tion (Rudin et al. 2004), or image decompositions on fixed bases such as wavelets
(Donoho & Johnstone 1995; Mallat 1999), for example. More recent approaches
include non-local means filtering (Buades et al. 2005), which exploits image self-
similarities, learned sparse models (Elad & Aharon 2006; Mairal et al. 2009), Gaus-
sian scale mixtures (Portilla et al. 2003), fields of experts (Agarwal and Roth May
2002), and block matching with 3D filtering (BM3D) (Dabov et al. 2007). The idea
of using self-similarities as a prior for natural images exploited by the non-local
means approach of Buades et al. (2005) has in fact appeared in the literature in
various guises and under different equivalent interpretations, e.g., kernel density es-
timation (Efros and Leung 1999), Nadaraya-Watson estimators (Buades et al. 2005),
mean-shift iterations (Awate and Whitaker 2006), diffusion processes on graphs
(Szlam et al. 2007), and long-range random fields (Li and Huttenlocher 2008).
We have restricted our discussion of sparsity-inducing regularizers to the 1 norm
here, but the 0 pseudo-norm, which counts the number of nonzero coefficients
in the code associated with a noisy signal can be used as well. Chapter 22 dis-
cusses 0 -regularized sparse coding and dictionary learning in some detail. Let
us just note here that simultaneous sparse coding is also relevant in that case,
the 1,2 norm being replaced by the 0,∞ pseudo-norm, which directly counts the
number of nonzero rows. See (Mairal et al. 2009) for details. An implemen-
tation of non-local means is available at: http://www.ipol.im/pub/algo/bcm_
non_local_means_denoising/, and BM3D is available at http://www.cs.tut.
fi/ ~ foi/GCF-BM3D/. An implementation of LSSC is available at http://www.di.
ens.fr/ ~ mairal/denoise_ICCV09.tar.gz.

Shape from Texture

We have assumed that textures are albedo marks on smooth surfaces. This really
isn’t true, as van Ginneken et al. (1999) point out; an immense number of textures
are caused by indentations on surfaces (the bark on a tree, for example, where the
main texture effect seems to be dark shadows in the grooves of the bark), or by
elements suspended in space (the leaves of a tree, say). Such textures still give
us a sense of shape—for example, in Figure 6.1, one has a sense of the free space
in the picture where one could move. The resulting changes in appearance as the
illumination and view directions change are complicated (Dana et al. 1999, Lu et
al. 1999, Lu et al. 1998, Pont and Koenderink 2002). We don’t discuss this case