# Diagonal Transforms Suffice for Color Constancy

## Abstract:

This paper's main result is to show that under the conditions imposed
by the Maloney-Wandell color constancy algorithm, color constancy can
in fact be expressed in terms of a simple independent adjustment of
the sensor responses - in other words as a von Kries adaptation type
of coefficient rule algorithm - so long as the sensor space is first
transformed to a new basis. Our overall goal is to present a theoretical
analysis connecting many established theories of color constancy. For
the case where surface reflectances are 2-dimensional and illuminants
are 3-dimensional, we prove that perfect colour constancy can always
be solved for by an independent adjustment of sensor responses, which
means that the colour constancy transform can be expressed as a
diagonal matrix. This result requires a prior transformation of the
sensor basis and to support it we show in particular that there exists
a transformation of the original sensor basis under which the
non-diagonal methods of Maloney-Wandell, Forsyth's MWEXT and Funt and
Drew's lightness algorithm all reduce to simpler, diagonal-matrix
theories of colour constancy. Our results are strong in the sense
that no constraint is placed on the initial sensor spectral
sensitivities. In addition to purely theoretical arguments, the paper
contains results from simulations of diagonal-matrix-based color
constancy in which the spectra of real illuminants and reflectances
along with the human cone sensitivity functions are used. The
simulations demonstrate that when the cone sensor space is transformed
to its new basis in the appropriate manner, a diagonal matrix supports
close to optimal colour constancy.

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Keywords: Color, color constancy, computer vision,
Maloney--Wandell, von Kries adaptation, coefficient rule,
Finite--Dimensional Models

copyright 1992 G.D. Finlayson, M.S. Drew and B.V. Funt