Tag Archives: 3×3

Color, Perceptual, Sharpness

Cone Fundamentals & the LMS Color Space

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In the last article we showed how a digital camera’s captured raw data is related to Color Science.  In my next trick I will show that CIE 2012 2 deg XYZ Color Matching Functions \bar{x}, \bar{y}, \bar{z} displayed in Figure 1 are an exact linear transform of Stockman & Sharpe (2000) 2 deg Cone Fundamentals \bar{\rho}, \bar{\gamma}, \bar{\beta} displayed in Figure 2

(1)   \begin{equation*} \left[ \begin{array}{c} \bar{x}} \\ \bar{y} \\ \bar{z} \end{array} \right] = M_{lx} * \left[ \begin{array} {c}\bar{\rho} \\ \bar{\gamma} \\ \bar{\beta} \end{array} \right] \end{equation*}

with CMFs and CFs in 3xN format, M_{lx} a 3×3 matrix and * matrix multiplication.  Et voilà:[1]

Figure 1.  Solid lines: CIE (2012) 2° XYZ “physiologically-relevant” Colour Matching Functions and photopic Luminous Efficiency Function (V) from cvrl.org, the Colour & Vision Research Laboratory at UCL.  Dotted lines: The Cone Fundamentals in Figure 2 after linear transformation by 3×3 matrix Mlx below.  Source: cvrl.org.

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