human visual system | Strolls with my Dog

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.

Continue reading Cone Fundamentals & the LMS Color Space →

Is MTF50 a good proxy for perceived sharpness? In this article and those that follow MTF50 indicates the spatial frequency at which the Modulation Transfer Function of an imaging system is half (50%) of what it would be if the system did not degrade detail in the image painted by incoming light.

It makes intuitive sense that the spatial frequencies that are most closely related to our perception of sharpness vary with the size and viewing distance of the displayed image.

For instance if an image captured by a Full Frame camera is viewed at ‘standard’ distance (that is a distance equal to its diagonal), it turns out that the portion of the MTF curve most representative of perceived sharpness appears to be around MTF90. On the other hand, when pixel peeping the spatial frequencies around MTF50 look to be a decent, simple to calculate indicator of it, assuming a well set up imaging system in good working conditions. Continue reading MTF50 and Perceived Sharpness →

Musings about Photography