Inner Product of RGB Unit Vectors for Simple and Versatile Detection of Color Transition

Naoya Kakiuchi; Junya Ochiai; Masaki Takeuchi; Hideji Tanaka

doi:10.2116/analsci.20C015

Inner Product of RGB Unit Vectors for Simple and Versatile Detection of Color Transition

Anal Sci. 2021 Jan 10;37(1):3-5. doi: 10.2116/analsci.20C015. Epub 2020 Dec 4.

Authors

Naoya Kakiuchi¹, Junya Ochiai², Masaki Takeuchi^{1

2

3}, Hideji Tanaka^{4

5

6}

Affiliations

¹ Graduate School of Pharmaceutical Sciences, Tokushima University, 1-78-1, Shomachi, Tokushima, 770-8505, Japan.
² Faculty of Pharmaceutical Sciences, Tokushima University, 1-78-1, Shomachi, Tokushima, 770-8505, Japan.
³ Institute of Biomedical Sciences, Tokushima University, 1-78-1, Shomachi, Tokushima, 770-8505, Japan.
⁴ Graduate School of Pharmaceutical Sciences, Tokushima University, 1-78-1, Shomachi, Tokushima, 770-8505, Japan. h.tanaka@tokushima-u.ac.jp.
⁵ Faculty of Pharmaceutical Sciences, Tokushima University, 1-78-1, Shomachi, Tokushima, 770-8505, Japan. h.tanaka@tokushima-u.ac.jp.
⁶ Institute of Biomedical Sciences, Tokushima University, 1-78-1, Shomachi, Tokushima, 770-8505, Japan. h.tanaka@tokushima-u.ac.jp.

PMID: 33281134
DOI: 10.2116/analsci.20C015

Abstract

We propose a novel concept for detecting color transition by the inner product (IP) of RGB unit vectors. A digital microscope-based detector and a Visual Basic program were developed in-house. The concept is applied to indicator-based flow titration. The IP is 1 or < 1 if the vector's direction is the same or different, respectively. The IP's change can be used as a criterion for the indicator's color transition. The present IP-based approach is simple, economical, and versatile because it is applicable to any color transition without selecting an analytical wavelength.

Keywords: Image-based colorimetry; RGB; digital microscope; flow ratiometry; flow titration; inner product.