DIMACS TR: 2004-53
Optimal Mapping of Deep Gray Scale Images to a Coarser Scale of Gray
Authors: Solomon Borodkin, Aleksey Borodkin and Ilya Muchnik
ABSTRACT
The problem of optimal mapping of multi-level gray scale images to a coarser gray scale is formulated
and explored. A distance between images having different intensity ranges is introduced. Minimization
of such a distance can be viewed as least squares approximation of a source high range image by the
best target image with a given number of levels of gray. Following S.Lloyd [1], we proved that the latter
problem is equivalent to optimal partitioning of the source image intensity range into a given number of
intervals, provided that the sum of intra-interval variations reaches minimum. An efficient algorithm for
optimal partitioning based on dynamic programming is used, which is the same in complexity as the ones
known from literature, but better in terms of required memory. The proposed approach is applied to visualization
of deep gray scale medical images. Advantages of the method over linear mapping and histogram
equalization are demonstrated on the sample images. The other application fields may include image
optimization for printing/faxing/copying.
Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-53.pdf
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