[Colloquium] Bahadur Memorial Lectures: STUART GEMAN Thursday May 8, 2008 4pm Eckhart 133

[Mitzi Nakatsuka]

The University of Chicago
Department of Statistics
The Bahadur Memorial Lectures

STUART GEMAN
James Manning Professor of Applied Mathematics
Brown University


On the Peculiar Statistics of Natural Images

THURSDAY, May 8, 2008 at 4:00 PM at
133 Eckhart Hall, 5734 S. University Avenue
Refreshments will be served in Eckhart 110.

ABSTRACT

Take a digital photo of a natural outdoor scene. For simplicity, convert
the photo from color to black and white. The photo can be reduced, or
scaled, to make a new (smaller) picture, say half the size in both
dimensions. The new picture is of a scene in which each of the original
objects, and in fact every imaged point, has been relocated twice as far
from the camera. This “stretching” is artificial in that it does not
correspond to any movement of the camera in the real world. Yet the
picture looks perfectly normal, and the local spatial statistical
structure (e.g. the distribution of values of horizontal or vertical
derivatives) is largely indistinguishable from the local spatial
statistical structure of the original. “Images of natural scenes are
scale invariant.” On the other hand, mathematical models of images,
or more generally of spatial processes, are never scale invariant unless
they are trivial (constant gray level, i.e. blank pictures) or exotic
(lacking a direct definition in terms of image intensities). The source
of scale invariance in natural images is an enduring mystery. I will
propose some explanations and make some connections to perception and
image coding.