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From Information Scaling of Natural Images to Regimes
of Statistical Models
Ying Nian Wu
Departments of Statistics, UCLA
Computer vision can be considered a highly specialized
data collection and data analysis problem. We need to understand
the special properties of image data in order to construct
statistical models for representing the wide variety of image
patterns. One special property of vision that distinguishes itself
from other sensory data is that distance or scale plays a crucial
role in image data. More specifically, visual objects and patterns
can appear at a wide range of distances or scales, and the same visual
pattern appearing at different distances or scales produces different
image data with different statistical properties, thus entails
different regimes of statistical models. In particular, we show
that the entropy rate of the image data changes over viewing distance (as
well as the camera resolution). Moreover, the inferential uncertainty
changes with viewing distance too. We call these changes
information scaling. From this perspective, we examine both
empirically and theoretically two prominent and yet largely
isolated research themes in image modeling literature, namely,
wavelet sparse coding and Markov random fields. Our results
indicate that the two models are appropriate on two different
entropy regimes: sparse coding targets the low entropy regime,
whereas the random fields are suitable for the high entropy
regime. Because of information scaling, both models are necessary for representing and interpreting image intensity patterns in the whole entropy range, and information scaling triggers transitions between these two regimes of models. This motivates us to propose a full-zoom primal sketch model that integrates both sparse coding and Markov random fields.
Based on the joint work with Song-Chun Zhu and Cheng-en Guo.
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