Centered pyramids
Brigger, P.; Muller, F.; Illgner, K.; Unser, M.
Image Processing, IEEE Transactions on
Volume 8, Issue 9, Sep 1999 Page(s):1254 - 1264
Digital Object Identifier 10.1109/83.784437
Summary:Quadtree-like pyramids have the advantage of re-suiting in a
multiresolution representation where each pyramid node has four
unambiguous parents. Such a centered topology guarantees a clearly
defined up-projection of labels. This concept has been successfully and
extensively used in applications of contour detection, object
recognition and segmentation. Unfortunately, the quadtree-like type of
pyramid has poor approximation powers because of the employed
piecewise-constant image model. This paper deals with the construction
of improved centered image pyramids in terms of general approximation
functions. The advantages of the centered topology such a symmetry,
consistent boundary conditions and accurate up-projection of labels are
combined with a more faithful image representation at coarser pyramid
levels. We start by introducing a general framework for the design of
least squares pyramids using the standard filtering and decimation
tools. We give the most general explicit formulas for the computation of
the filter coefficients by any (well behaving) approximation function in
both the continuous (L2) and the discrete (l2)
norm. We then define centered pyramids and provide the filter
coefficients for odd spline approximation functions. Finally, we compare
the centered pyramid to the ordinary one and highlight some applications
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