Color scales that are effective in both color and grayscale

We consider the problem of finding a color scale which performs well when converted to a grayscale. We assume that each color is converted to a shade of gray with the same intensity as the color. We also assume that the color scales have a linear variation of intensity and hue, and find scales which maximize the average chroma (or “colorfulness”) of the colors. We find two classes of solutions, which traverse the color wheel in opposite directions. The two classes of scales start with hues near cyan and red. The average chroma of the scales are 65-77% those of the pure colors. ∗Electronic address: [email protected] 1 ar X iv :1 21 1. 36 59 v1 [ cs .G R ] 1 5 N ov 2 01 2 It is often desirable to present quantitative results in both color and grayscale formats. In the black-and-white or grayscale format, an interval of numerical values maps to a scale of grays which increase uniformly in lightness. Color is usually represented as a threedimensional object, and could thus be used to represent a three-dimensional region of numerical values. More typically, a color scale is used to represent a one-dimensional interval of numerical values. Colors are usually easier to distinguish than grays because of the additional dimensions along which colors vary. Thus a color scale is generally preferable to a grayscale. However, black and white printing is less costly than color printing, so it is useful to be able to print color images in black and white and obtain readable images. Such images are also readable by those with some degree of color blindness, which includes about 10% of males and a much smaller percentage of females. A color can be defined in different ways. Here we use the common RGB color model [1, 2]. A color is defined by a three-component vector, [R,G,B], where the components represent the values of red, green, and blue in the color. The components R,G,B lie on the interval [0, 1], so a color corresponds to a point in the unit cube, [0, 1], in RGB space. For example, pure red is [1, 0, 0], pure green is [0, 1, 0], and pure blue is [0, 0, 1]. Black is [0, 0, 0], white is [1, 1, 1], and grays are of the form [g, g, g], 0 < g < 1. Colors can also be represented in terms of three other quantities: hue, chroma, and