| Abstract
Two types of redundancies are contained
in images: statistical redundancy and psychovisual redundancy. Image representation
techniques for image coding should remove both redundancies in order to
obtain good results.
In order to establish an appropriate representation,
the standard approach to transform coding only considers the statistical
redundancy, whereas the psychovisual factors are introduced after
the selection of the representation as a simple scalar weighting in the
transform domain.
In this work, we take into account the
psychovisual factors in the definition of the representation together with
the statistical factors, by means of the perceptual metric and the covariance
matrix, respectively. I n general the ellipsoids described by these matrices
are not aligned. Therefore, the optimal basis for image representation
should simultaneously diagonalize both matrices. This approach to the basis
selection problem has several advantages in the particular application
of image coding. As the transform domain is Euclidean (by definition),
the quantizer design is highly simplified and at the same time, the use
of scalar quantizers is truly justified. The proposed representation is
compared to covariance-based representations such as the DCT and the KLT
or PCA using standard JPEG-like and Max-Lloyd quantizers.
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