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In an HSV model, the Hue is the color model. So when we split the image or remove H, should we get an image without rgb colors?

Similarly, saturation is the gray shade. I read that images become more grey and faded in this case. So what should happen when we remove both, hue and saturation, leaving only the vue component behind?

Any example images would be nice.

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Removing hue and saturation ("desaturating") leads to a grayscale image with the same luminance as the original colors, for instance:

original image grayscale image
(source: my own photo)

It is not possible to remove hue alone without removing saturation, as any saturated color must be saturated in some direction (hue). Nor is it possible to "split" the image into HSV "components" in quite the way you can split into RGB components. Hue works like an angle of rotation around the "color wheel", while saturation is the radius from the center:

hue/saturation color wheel
(image from here)

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https://alloyui.com/examples/color-picker/hsv.html - it would be the best for you to play a little with HSV color picker.

Problem of color picking with HSV boils down to 2D coordinates (H, S) with additional parameter V. Therefore, you are using H as x-axis value ans S as y-axis value. If you drop H and S (set them to 0), you basically have white color and with V, you can choose grey scale lying between white and black.

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