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Article

A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric

School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK
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The paper is an extended version of the following conference papers: (1) Finlayson G.D. and Zhu Y. Unifying Optimization Methods for Color Filter Design. In Proceedings of the 10th Colour and Visual Computing Symposium, CEUR Workshop Proceedings, Gjøvik, Norway, 16–17 September 2020 (online open access: http://ceur-ws.org/Vol-2688/). (2) Zhu Y. and Finlayson G.D. Designing a Color Filter via Optimization of Vora-Value for Making a Camera more Colorimetric. In Proceedings of the 28th Color and Imaging Conference, pp. 181–186, 2020.
Sensors 2020, 20(23), 6882; https://doi.org/10.3390/s20236882
Received: 1 October 2020 / Revised: 27 November 2020 / Accepted: 29 November 2020 / Published: 2 December 2020
(This article belongs to the Special Issue Color & Spectral Sensors)
By placing a color filter in front of a camera we make new spectral sensitivities. The Luther-condition optimization solves for a color filter so that the camera’s filtered sensitivities are as close to being linearly related to the XYZ color matching functions (CMFs) as possible, that is, a filter is found that makes the camera more colorimetric. Arguably, the more general Vora-Value approach solves for the filter that best matches all possible target spectral sensitivity sets (e.g., any linear combination of the XYZ CMFs). A concern that we investigate here is that the filters found by the Luther and Vora-Value optimizations are different from one another. In this paper, we unify the Luther and Vora-Value approaches to prefilter design. We prove that if the target of the Luther-condition optimization is an orthonormal basis—a special linear combination of the XYZ CMFs which are orthogonal and are in unit length—the discovered Luther-filter is also the filter that maximizes the Vora-Value. A key advantage of using the Luther-condition formulation to maximize the Vora-Value is that it is both simpler to implement and converges to its optimal answer more quickly. Experiments validate our method. View Full-Text
Keywords: filter design; optimization method; camera sensors; colorimetry filter design; optimization method; camera sensors; colorimetry
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Figure 1

  • Externally hosted supplementary file 1
    Link: https://arxiv.org/abs/2009.13696
    Description: Mathematical derivation for Vora-Value based filter design method: Gradient and Hessian
MDPI and ACS Style

Zhu, Y.; Finlayson, G.D. A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric. Sensors 2020, 20, 6882. https://doi.org/10.3390/s20236882

AMA Style

Zhu Y, Finlayson GD. A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric. Sensors. 2020; 20(23):6882. https://doi.org/10.3390/s20236882

Chicago/Turabian Style

Zhu, Yuteng, and Graham D. Finlayson 2020. "A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric" Sensors 20, no. 23: 6882. https://doi.org/10.3390/s20236882

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