Ann Lee,  Dept. of Applied Mathematics, Brown University, 12/19/01
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The Nonlinear Statistics of Natural Images
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Recently, there has been a great deal of interest in the
statistics of natural images and many investigations of these
from both the biological and computational vision
perspectives. Despite the many advances in sparse coding and
multi-resolution analysis, we are still missing a description of
the full probability distribution (as opposed to marginals) of
small neighborhoods of pixels or filter responses.
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In this talk, I will start by exploring the state space of 3-by-3
high-contrast patches from optical and 3D range images of natural
scenes. We will see that the distribution of natural data is
extremely "sparse" with the majority of data points concentrated
in compact clusters (for range data) or along a low-dimensional
manifold that correspond to edge structures (for optical data).
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Furthermore, I will show evidence from a scale-space study of
natural images that the results (for optical data) generalize to
general filter responses and larger scales. A new picture of
natural image statistics seems to emerge, where basic primitives
in images --- such as edges, bars, blobs, and terminations ---
generate observations concentrated around low-dimensional and, in
general, non-linear structures in the state space of image
data. The study shows the importance of accounting for the local
object structures in natural scenes, without imposing such strong
assumptions on the analysis as independent components or sparse
coding by linear change of basis.