SPACE-VARIANT IMAGES

SPACE-VARIANT means the resolution is variable over the extent of the image.
-- (Inverse) Logmap images are the prime examples.
-- Logmap images have many interesting and useful properties for image processing purposes [Rojer].
-- [Bederson, Ong, Schwartz and Wallace] investigates a very general (discrete) class of space variant images.

MULTI-FOVEATED IMAGES
-- We focus on a class of space-variant images that generalizes logmap images.
-- Foveated images refers to images with one compact region of maximal resolution (called the ``fovea''), and with resolution falling away from this center.
-- Parameters for specifying a foveated image:

• foveal geometry (e.g., disk or square)
• rate of falling resolution (e.g. inversely proportional to distance from foveal center)
• foveal resolution.

-- We then define multifoveated images to be the the "blending" of several foveated images (the maximum resolution blending).

FOVEATION PROBLEM:
``GIVEN A UNIFORM IMAGE, AND FOVEATION PARAMETERS, TO CONSTRUCT THE FOVEATED IMAGE''
-- More generally, if we are given a sequence of these parameters, we want to construct a sequence of such images.
-- Why would we want to do this? because foveated images low data density!
-- So, instead of sending a uniform image, it may be sufficient to send a foveated version.
-- The standard approach is to construct a fixed super-pixel geometry (which can be implemented as a "table lookup") and to assume averaging for the super-pixel values.
-- SHOW EXAMPLES FROM [Schwartz-Rojer, Geissler-Kortum]

MORE FLEXIBLE METHOD BASED ON WAVELETS:
-- Quick tour of Wavelet Theory
-- Haar Wavelet Transforms
-- How to foveate using wavelets.

MATHEMATICAL FORMULATION OF FOVEATION OPERATOR:
-- Need a scaling function s(.) and a weight function w(.).
-- Let I(x) be a 1-dim image.
Then the foveation of I(x) relative to s(.) and w(.) is defined as
-- standard weight functions: $w(t) = b |x-c| + a$.
-- How good is the wavelet approach for approximating this operator? [Eechien-Thesis]