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

Zhu, Yuteng and Finlayson, Graham D. (2020) A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric. Sensors, 20 (23). ISSN 1424-8220

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Abstract

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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 07 Jan 2021 01:01
Last Modified: 08 Jan 2021 01:06
URI: https://ueaeprints.uea.ac.uk/id/eprint/78079
DOI: 10.3390/s20236882

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