Zhu, Yuteng
(2021)
*Designing a Colour Filter for Making Cameras more Colorimetric.*
Doctoral thesis, University of East Anglia.

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## Abstract

If a camera were to capture colour like a human observer, fundamentally, it should sense the light information as the way the human visual system does. It is necessary to either replicate the human visual sensitivity responses or reproduce the three-number colour representations - e.g. CIE XYZ tristimulus values - to obtain an accurate colour measurement. In practice, however, the camera sensors generally deviate from the ideal sensitivities of the human visual system. Consequently, the colour triplets a camera records are device-dependent, which generally differ from the standard observer tristimulus values. The colorimetric performance can be improved by either correcting camera responses to the reference ground-truth values using sophisticated mathematical transformations or using more imaging sensors/filters to capture more information about the incident light. These methods have their disadvantages: the former increases the computational complexity and the latter increases the system complexity and the overall cost.

In this thesis, we aim to make the digital camera capture colours more like the human visual perception by placing a colour filter in front of the camera so as to alter its spectral sensitivity functions as desired. The central contribution of this study is to carefully design a colour filter for a given camera so that the ‘filter+camera’ setting having the new sensitivities becomes almost colorimetric, i.e. recording the colour triplets that can be linearly transformed to the ground-truth XYZ tristimulus values.

The starting point for this thesis is to design the filter that makes the filtered camera best achieve the Luther condition, i.e. the new effective camera sensitivity functions after filtering are a linear combination of the colour matching function of the human visual system. Under this condition, the camera can capture any incoming colour signal accurately in the sense that the captured RGBs are almost a linear transform from the XYZ tristimuli.

Next, we reformulate the problem formulation for finding the optimal filter that targets the more generalised Vora-Value goodness measure. The Vora-Value, by definition, measures the similarity between the vector spaces spanned by the spectral sensitivities of a camera and the XYZ colour matching functions underpinning the human visual system. The Vora-Value has the advantage that the best filter is related to the target human visual space and not fixed coordinates (e.g. the XYZ and RGB colour matching functions have different coordinate values but are in the same vector space).

As well as developing a method that finding a filter maximises the Vora-Value (makes the vector spaces most similar), we examine the relationship between the Vora-Value and Luther condition optimisations. We show that the Luther-condition optimisation also maximises the Vora-Value if we find the filter that makes a linear combination of the camera sensitivities most similar to a linear transform of XYZ (that is orthonormal). This is an important result as the Luther optimisation is much simpler to implement and faster to execute. So we can use the simpler Luther-condition formulation to maximise the Vora-Value measure using a more straightforward algorithm.

A strength and weakness of the Luther and Vora-Vora optimisations is that they assume - as an explicit part of their formulations - that all spectra are equally likely. But, this is not the case in real imaging applications. So we extend our filter design algorithms in a data-driven manner that it optimises for the best colorimetric estimates given a collection of illuminants and surface reflectance data. Our extended method uses quadratic programming that allows us to add linear inequality constraints into the problem formulation. We show how to find filters that have smooth distribution and bounded transmittance (e.g. transmit at least 50% of the light) across the spectrum. Constraints like these make the filters more useful and feasible could make the filters easier to manufacture. We show that we can find smooth and highly transmissive colour filters that when placed in front of a digital camera can make the camera significantly more colorimetric and hence can be used for colour measurement applications with high demand in colour accuracy.

Item Type: | Thesis (Doctoral) |
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Faculty \ School: | Faculty of Science > School of Computing Sciences |

Depositing User: | Chris White |

Date Deposited: | 15 Dec 2021 13:47 |

Last Modified: | 15 Dec 2021 13:47 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/82695 |

DOI: |

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