Title:

Optimising spectral calibration

Spectral calibration is the problem of recovering colour device sensitivities (e. g. of
a digital camera or scanner) given measured spectral data and the corresponding
RGBs recorded by the device. Spectral calibration is useful because if we know how
a color device responds to light then we can colourimetrically calibrate (map RGBs
to perceptually relevant coordinates) using mathematical means.
Unfortunately, spectral calibration is a hard problem. Device sensitivities are
continuous functions of wavelength and so there are many degrees of freedom to be
recover. This intrinsic high dimensional recovery problem is confounded by the fact
that typical spectra colour signals are low dimensional. Specifically, though they are
continuous functions of wavelength, the spectra can be parameterised by say 5 or 6
numbers. Spectral calibration then is an ill posed problem where we try to recover
more parameters than we have degrees of freedom. One way to work with this ill
posedness is to regularise the recovery (for example we might impose a constraint
on the smoothness of the recovered sensor).
This thesis makes 4 main contributions to spectral calibration. First, we undertake
an in depth analysis of spectral calibration in general and regularisation techniques
in particular. We show that existing approaches can be usefully combined to improve recovery performance. Second, we present a new and radically different
approach to ill posedness. Rather than applying a constraint such as smoothness,
we set forth methods to solve for all spectral sensitivities consistent with a given
set of data (color signal spectra and corresponding RGBs). Given this feasible set,
we show how we can calculate the most representative sensor and quantify its uncertainty.
We can now evaluate the feasibility of regularised solutions and estimate
their uncertainty.
In the third part of this thesis we consider the practical hardness of spectral
calibration. Measuring many colour signal spectra is a time consuming task and so
we wondered how many colour signal spectra we had to measure to arrive at a good
solution. Mathematical and experimental results show that spectral calibration,
which previously involved 100s of measurements, can be replicated with just 6 or 7
spectra. Finally, we present a new method for estimating the support of a sensor (the
part of the visible spectrum over which a sensor is sensitive) and incorporate this
into our spectral calibration methods. This is shown to be a surprisingly powerful
constrain for spectral calibration.
