  Conventional SVM-based image coding methods are founded on independently
restricting the distortion in every image coefficient at some particular image
representation. Geometrically, this implies allowing arbitrary signal
distortions in an $n$-dimensional rectangle defined by the
$\varepsilon$-insensitivity zone in each dimension of the selected image
representation domain. Unfortunately, not every image representation domain is
well-suited for such a simple, scalar-wise, approach because statistical and/or
perceptual interactions between the coefficients may exist. These interactions
imply that scalar approaches may induce distortions that do not follow the
image statistics and/or are perceptually annoying. Taking into account these
relations would imply using non-rectangular $\varepsilon$-insensitivity regions
(allowing coupled distortions in different coefficients), which is beyond the
conventional SVM formulation.
  In this paper, we report a condition on the suitable domain for developing
efficient SVM image coding schemes. We analytically demonstrate that no linear
domain fulfills this condition because of the statistical and perceptual
inter-coefficient relations that exist in these domains. This theoretical
result is experimentally confirmed by comparing SVM learning in previously
reported linear domains and in a recently proposed non-linear perceptual domain
that simultaneously reduces the statistical and perceptual relations (so it is
closer to fulfilling the proposed condition). These results highlight the
relevance of an appropriate choice of the image representation before SVM
learning.
