Generalization of hue in the RGB cube space

Abstract

The general formulation of hue is continually being established throughout the study of the RGB (red, green, blue) cube space. This paper proposes a formulation that consists of a forward RGB to hue transform and its inverse for perfect RGB color reproduction. The proposed formulation is defined independently of the saturation and brightness, which can be considered fixed as constants. Our study indicates that the hue angle monotonically changes with the increments and decrements of intensity in the median of RGB channels. Furthermore, the formulation has simplified the hue definitions using median channel as the shift for hue angle. As a result, the forward transform produces a new set of hue angular information which significantly improves the performance of the existing hue models in terms of perceptual uniformity, visual quality and efficiency. The proposed formulation is beneficial to machine vision related studies, essentially the image segmentation and image classifications. Keywords-Hue; RGB cube space; chromatic plane; color difference; color image analysis; color segmentation I. HUE TRANSFORMATIONColors are the transformed rays of dispersed white light and they are visible to human perception. Today, the color display technologies are based on the RGB cube to represent pictures. Each of the RGB channels has a certain levels of color depth, d computed in bits. However, each RGB channel only shows the addition and subtraction of the primary colors. These representations make no sense for human to distinguish the colors quantitatively. Among the broad range of colors, hue colors are most sensitive to the human perception. Fig. 1 shows the band of hue colors with 100% saturated by the white light. For standardization, hue is defined in angular information, h with red axis as the origin [1]. The degree of the hue angle, h increases while moving towards the yellow, followed by green axis and eventually goes back to red axis again, as shown in Fig. 1. Figure 1. Pure hue encoded in the RGB space.A number of models have been established to quantify and approximate the hue angle in the CIELAB color space [2]. In 1953, Preucil [3] first explained the theory of the chromatic plane using a hexagon shape. The shape has been extended by Smith [4] in his hexcone model to represent the hue, saturation and value (HSV) color space. In his study, hue, saturation and lightness (HSL) color space is also created based on a triangular model. This model is made similar to the shape of the non-linear CIE chromaticity diagram in [5]. The HSV and HSL color spaces are defined both in the form of piecewise and trigonometric functions [6].The hue transform in hue, saturation and intensity (HSI) color space is an expression which is widely used in color image processing and can be found in [7]. The hue in HSI is formulated by assuming that the chromatic plane has the shape of an equilateral triangle. Gonzalez and Woods provide both the forward and inverse hue transforms in [8]. Kender's hue transform is a faster version of HSI mode...

Wavescapes: A visual hierarchical analysis of tonality using the discrete Fourier transform

“…Given the periodic nature of the phase, it can be assigned to a color through a circular hue. We choose the hue function h : [0,2 [ [0,1] 3 π → that maps φ k to a triple ( , , ) r g b , representing the strengths of the red, green and blue components of the color (Ong & Khoo, 2014):…”