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

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.