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A SVD BASED IMAGE COMPLEXITY MEASURE
David Gustavsson, Kim Steenstrup Pedersen and Mads Nielsen
Department of Computer Science, University of Copenhagen , Universitetsparken 1, DK-2100 Copenhagen, Denmark
Keywords:
Image complexity measure, Geometry, Texture, Singular value decomposition, SVD, Truncated singular value
decomposition, TSVD, Matrix norm.
Abstract:
Images are composed of geometric structures and texture, and different image processing tools - such as
denoising, segmentation and registration - are suitable for different types of image contents. Characterization
of the image content in terms of geometric structure and texture is an important problem that one is often faced
with. We propose a patch based complexity measure, based on how well the patch can be approximated using
singular value decomposition. As such the image complexity is determined by the complexity of the patches.
The concept is demonstrated on sequences from the newly collected DIKU Multi-Scale image database.
1 INTRODUCTION
Images contain a mix of different types of informa-
tion, from highly stochastic textures such as grass and
gravelto geometric structures such as houses and cars.
Different image processing tools are suitable for dif-
ferent type of image contents and most tools are very
image content dependent. The definition of what is
texture and geometry is not particularly agreed upon
in the computer vision community. Our hypothesis
is that the separation between geometry and texture
is defined through the purpose of the method and the
scale of interest. What may be considered an unim-
portant structure / texture in one application may be
considered important in another.
For example, segmentation of an image contain-
ing objects with clear geometric structures forming
boundaries calls for edge-based or geometry-based
methods such as watersheds (Olsen and Nielsen,
1997), the Mumford-shah model (Mumfordand Shah,
1985), level sets (Sethian, 1999), or snakes (Kass
et al., 1988). While segmentation of an image con-
taining objects only discernable by differences in tex-
ture calls for texture based segmentation methods
(Randen and Husoy, 1999). That is, the type of ob-
jects we are attempting to segment defines our scale
of interest, i.e. what type and scale of structure we
include in the model of a segment.
In denoising an image containing geometric struc-
tures calls for e.g. an edge preserving method such as
anisotropic diffusion (Weickert, 1998) or total varia-
tion image decomposition (Rudin et al., 1992). For
images containing small scale texture, a patch based
denoising method such as non-local mean filtering
may be more appropriate (Buades et al., 2008). Again
we see that depending on the purpose we include
structures at finer scales into the model of the prob-
lem as needed.
As a final example, we mention that total varia-
tion (TV) image decomposition, and other functional
base methods, are very successful for inpainting im-
ages containing geometric structures (Chan and Shen,
2005). Unfortunately the functional based methods
fails to faithfully reconstruct regions containing small
scale structures, however texture based methods man-
age to reconstruct such images (Efros and Leung,
1999; Criminisi et al., 2004; Gustavsson et al., 2007;
Cuzol et al., 2008). In the functional approaches the
focus is solely on large scale structures or geometry,
whereas in the texture methods small scale texture is
included in the model.
Prior knowledge about the methods and the image
content are therefore essential for successfully solv-
ing a task. A natural question is: ”For a given type of
images, which type of methods are suitable?” Often
one wants to characterize the methods by analyzing
the type of images that it is (un)suitable for. To be
able to characterize the methods in this way, the im-
ages must be characterized with respect to the image
contents. An image complexity measure is needed,
i.e. a measure that quantify the image contents with
respect to geometric structure and texture or scale of
interest.
A patch based complexity measure using Singular
34
Gustavsson D., Steenstrup Pedersen K. and Nielsen M. (2009).
A SVD BASED IMAGE COMPLEXITY MEASURE.
In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, pages 34-39
DOI: 10.5220/0001785400340039
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