A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/20/23/6882 |
| _version_ | 1797545973576105984 |
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| author | Yuteng Zhu Graham D. Finlayson |
| author_facet | Yuteng Zhu Graham D. Finlayson |
| author_sort | Yuteng Zhu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T14:23:33Z |
| format | Article |
| id | doaj.art-a7c858b7e688401f9012085ad4ccc738 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T14:23:33Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-a7c858b7e688401f9012085ad4ccc7382023-11-20T23:11:57ZengMDPI AGSensors1424-82202020-12-012023688210.3390/s20236882A Mathematical Investigation into the Design of Prefilters That Make Cameras More ColorimetricYuteng Zhu0Graham D. Finlayson1School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UKSchool of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UKBy 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.https://www.mdpi.com/1424-8220/20/23/6882filter designoptimization methodcamera sensorscolorimetry |
| spellingShingle | Yuteng Zhu Graham D. Finlayson A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric Sensors filter design optimization method camera sensors colorimetry |
| title | A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric |
| title_full | A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric |
| title_fullStr | A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric |
| title_full_unstemmed | A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric |
| title_short | A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric |
| title_sort | mathematical investigation into the design of prefilters that make cameras more colorimetric |
| topic | filter design optimization method camera sensors colorimetry |
| url | https://www.mdpi.com/1424-8220/20/23/6882 |
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