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I have difficulty in understanding what is Hue and Saturation. please explain what is hue and saturation to me with an example or analogy.

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Hue is the main indication of color. It is the value actually telling you which color it is or the value that lets you go "red" when you see a red object.

Saturation is the perceived intensity. In other words it is a value of how dominant the color is, or how colorful the object looks.

Practical example: Regardless of the color, shadows generally happen to have low saturation values.

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If you draw a intensity on wavelength curve for each pixel in the image, hue refers to the peak of the curve, i.e., at the visible wavelength with the greatest energy from the output. Saturation is the relative bandwidth of the curve. As saturation increases, colors appear more "pure." As saturation decreases, colors appear more "washed-out."

The aim that we convert RGB to HSV is to separate the information from color space with the other information such as the brightness, pureness, and saturation.

The conversion from RGB to HSV is shown in this page with both mathematical formulas and the numerical look-up.

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If the density of photons is equal at all frequencies in the visual range, then a typical human would usually see just gray, and the color saturation would be said to be zero. For RGB image data, the same if R == G == B. The hue would be indeterminate.

If all the photons are of identical frequency at the red end of the human visual range, then the saturation would be 100%, and the hue would be at the red end of the hue range. Or R = 255, G = 0, B = 0 for 8-bit RGB images.

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this comes from Wikipedia (but is consistent with my old 1970s communications textbook):

$$R, G, B, Y \in \left[ 0, 1 \right], \quad I \in \left[-0.5957, 0.5957\right], \quad Q \in \left[-0.5226, 0.5226\right]$$

$$ \begin{bmatrix} Y \\ I \\ Q \end{bmatrix} = \begin{bmatrix} 0.299 & 0.587 & 0.114 \\ 0.595716 & -0.274453 & -0.321263 \\ 0.211456 & -0.522591 & 0.311135 \end{bmatrix} \begin{bmatrix} R \\ G \\ B \end{bmatrix} $$

$$ \begin{bmatrix} R \\ G \\ B \end{bmatrix} = \begin{bmatrix} 1 & 0.9563 & 0.6210 \\ 1 & -0.2721 & -0.6474 \\ 1 & -1.1070 & 1.7046 \end{bmatrix} \begin{bmatrix} Y \\ I \\ Q \end{bmatrix} $$

the $Y$ signal is the monochrome intensity. about the same as B&W. a B&W TV would need only that. the $I$ and $Q$ signals are the chroma or color signals. as their names suggest, consider them as the "in-phase" and "quadrature" components of a single complex-valued modulated signal which is how the old NTSC standard used to do it. $I$ is the real part, $Q$ is the imaginary part.

color "saturation" would be the magnitude of $I+jQ$ and color "hue" would be the complex angle of $I+jQ$.

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enter image description here

When we are on the HSL (Hue, Saturation, Luminosity) color system in windows, if we move the white cursor vertically, only the Saturation tab varies as it controls the intensity of the specific color one is on.

However, if we move horizontally, only the Hue tab varies as it indicates the actual color we are in. From this, we can see that the Luminosity tab controls the whiteness (upper limit) or blackness (lower limit) of any color.

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