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Title: Optimising spectral calibration
Author: Alsam, Ali.
Awarding Body: University of East Anglia
Current Institution: University of East Anglia
Date of Award: 2004
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available