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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
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  4:15 p.m., Tuesday, January 10, 2006\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Ying Nian Wu} \\
UCLA Department of Statistics\\
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  \textbf{Information Scaling and Cartoonlets}
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\noindent
Cartoons and textures are two ubiquitous classes of patterns in images of
natural scenes. Mathematically, cartoons are modeled by piecewise smooth
functions with smooth boundaries, whereas textures are modeled by spatial
statistics or random fields. We show that the two classes of patterns can
be physically unified by what we call information scaling, that is, the
change of statistical properties of image data over the scaling or zooming
process. In particular, we show that the entropy rate of the image data
changes over the scaling process, which transforms cartoons to textures
and eventually to white noise. Pursuing the entropy in image data, we come
up with a class of image descriptors that we call cartoonlets. Cartoonlets
arise from the alignment of phases and orientations of Gabor wavelets in
the frequency domain. The concept provides a unified modeling perspective
for describing both cartoons and textures, and it is closely connected to
three statistical principles in vision, namely, sparse coding, meaningful
alignment, and minimum entropy.  The talk is based on two papers: Wu, Zhu,
and Guo (2005) and Liu, Li, and Wu (2005).




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