P2-T2 — RGB, Grayscale and HSV

Learning objectives

After this lesson, you should be able to:

• Describe a colour in RGB, grayscale and HSV and convert between them with the standard formulas.
• Explain why hue is more stable than the RGB channels when the illumination changes.
• Define a hue range for a colour, including the wrap-around of red.
• Name the conditions where HSV and grayscale mislead.

The idea: describe colour the way the question is asked

Ask a person “is this red?” and they will not compare three numbers. They think of a colour, then how vivid it is, then how light or dark. HSV is built on the same split. Hue is the position on the colour circle: red, orange, yellow, green and so on. Saturation says how far the colour is from grey: a pale pink and a deep red have the same hue, different saturation. Value is the brightness: a dark red and a bright red differ in value.

Why this matters to a robot

The camera does not measure the colour of an object. It measures the colour of the object times the colour and strength of the light on it. Dim the light by half, and a red block that was (210, 40, 40) becomes (105, 20, 20): all three channels halve. A threshold such as “red channel above 150” has stopped working, although the object has not changed. The hue is the same for both, because it depends on the ratios of the channels, which the light scaled equally.

Choose a representation in which the thing that varies (brightness) is separate from the thing you care about (colour).

Grayscale

A grayscale image keeps one number per pixel, the perceived brightness. Many algorithms (edges, corners, many feature detectors) work on grayscale because shape and texture matter more than colour and a single channel is three times cheaper. But discarding colour discards information: a red block and a green block with the same brightness become indistinguishable. Look at the last column of the table below.

The mathematics: the conversions

RGB to grayscale

The common conversion is a weighted sum that follows the eye’s greater sensitivity to green (the weights of ITU-R BT.601, used by many libraries):

R, G, B

the red, green and blue values of the pixel, 0 to 255 for an 8-bit image.

Y

the gray level, in the same range. A plain average (R + G + B)/3 is also used and treats green as much as blue, which does not match how bright colours look.

RGB to HSV

Scale the channels to 0 to 1. Let M = max(R, G, B), m = min(R, G, B) and Δ = M − m. Then

V

value: the largest channel. It is the brightness of the strongest colour component.

S

saturation: the fraction of the value that is colour, as opposed to grey. A grey pixel (R = G = B) has S = 0.

H

hue: the angle of the colour on the circle, in degrees: 0° red, 60° yellow, 120° green, 180° cyan, 240° blue, 300° magenta.

Δ

the spread of the channels. If Δ = 0 the pixel is grey and the hue has no meaning.

Scaling all three channels by a factor k (a change of light) multiplies M, m and Δ by k. So S = Δ/M and the ratios inside H are unchanged, and only V changes. That is the formal reason for hue’s robustness to a uniform change of illumination.

Hue is an angle

Hues 359° and 1° are 2° apart. A range for red must therefore wrap: “from 340° up through 360°/0° to 20°”. A test written as lo ≤ h ≤ hi works for green and blue (a range that does not cross 0°) and returns nothing for red. The circular distance between two hues is min(|a − b|, 360° − |a − b|).

Where HSV misleads

• Low saturation: for a nearly grey pixel, a small amount of noise swings the hue anywhere on the circle. Always require a minimum saturation before trusting the hue.
• Low value: for a very dark pixel the channels are small integers and the ratios are dominated by quantisation and noise. Require a minimum value too.
• Non-white light: sodium or LED lamps and sunset light multiply the channels by different factors, so the hue of an object shifts. A colour cast cannot be removed by hue; white balance has to be done first.
• Saturated pixels: if a channel is clipped at 255, the ratios are wrong, and bright highlights lose their hue.

A worked example: five pixels in three descriptions

Take the red block of the first lab, the same block in half the light, a yellow block, a green block, and a grey floor pixel.

Compute the first row by hand. Scaled to 0 to 1: R = 0.824, G = B = 0.157. So M = 0.824, m = 0.157, Δ = 0.667. V = 0.82, S = 0.667/0.824 = 0.81. The maximum is R, so H = 60° × ((G − B)/Δ mod 6) = 60° × 0 = 0°.

Now halve the light (second row, (105, 20, 20)): M = 0.412, m = 0.078, Δ = 0.333, so S = 0.81 again and H = 0°; only V falls to 0.41. The RGB values changed by half and the hue and saturation did not move.

Three more observations from the table:

• The yellow block has a hue near 53°, well separated from the red at 0° and the green near 134°. A hue range of ±20° around each is enough to tell them apart.
• The grey floor pixel has a saturation near 0.03. Its hue is computed from a tiny spread of the channels and means nothing: this is why the saturation limit is needed.
• In grayscale, the red block gives 91 and the grey floor 118, so they are not separated by a lot; with a different red and floor they could be equal. A grayscale detector cannot find a red block on a floor of the same brightness, while a hue test can.

A red range, written out

A pixel is red if its hue is within 20° of 0°, its saturation is at least 0.4 and its value at least 0.2. In code, with the wrap handled:

Lab P2-L1 asks you to write exactly this and to find out what happens when you write 340 ≤ h ≤ 20 instead.

Engineering implications and limitations

Calibrate thresholds on your own camera. Hue values depend on the sensor, the white balance and the lens. Collect images of the target under the lighting you expect, plot the hue, saturation and value histograms of the target pixels and of the background, and choose limits with a margin. Document the images they came from.

Fix white balance and exposure first. Auto white balance moves hues from frame to frame; auto exposure moves values. For a colour-coded task, lock both, or normalise (for example with a reference patch) before thresholding.

Know your channel order. OpenCV loads images as blue-green-red by default and has separate conversion codes for BGR to HSV. Using the RGB formula on a BGR image gives a hue mirrored around green. Hue in OpenCV’s 8-bit images is also stored as 0 to 179 (half degrees), which breaks thresholds copied from textbooks.

Use more than one cue. A colour test finds red things, not red blocks: a red shirt, a red sign and a red reflection pass it. Combine colour with size, shape, position or depth, and with tracking over time.

Pick grayscale deliberately. Use it when the task is about shape or texture and colour would only add variation, and convert with the luminance weights. Do not use it when colour is the signal.

Common misconceptions

Engineering takeaways

1. RGB, grayscale and HSV describe the same pixel; the right one is the one in which your question is simple.
2. Gray Y = 0.299 R + 0.587 G + 0.114 B; HSV is computed from the max, min and spread of the channels.
3. A uniform change of illumination scales R, G and B together, so hue and saturation are unchanged and only value changes.
4. Hue is an angle: red’s range wraps through 0°, and hue is unreliable at low saturation or low value.
5. Fix white balance and exposure, calibrate thresholds on your own images, check the channel order, and combine colour with other cues.

References and further reading

The table was computed with the formulas on this page.

• Smith, A. R. (1978). Color gamut transform pairs. SIGGRAPH ’78: the original definition of the HSV colour model.
• ITU-R Recommendation BT.601: the luminance coefficients 0.299, 0.587 and 0.114.
• Szeliski, R. (2022). Computer Vision: Algorithms and Applications, 2nd ed. Springer: colour spaces and white balance.
• OpenCV documentation, Changing colorspaces: BGR channel order and the 0 to 179 hue range for 8-bit images.

Knowledge check

Three conceptual questions. Write an answer, then reveal the explanation. Your answers stay in your browser.

What’s next

Next: filtering. How to reduce noise in an image, what each filter keeps, and what it destroys.

Related content

Nothing below is required to finish this lesson.

• Before
  P2-T1: Pixels, Image Dimensions and Color Representations

  Describe an image as a grid of numbers with dimensions, channels and bit depth.

• Lab
  P2-L1: Detect Colored Objects in an Image

  Find coloured objects in an image with a colour-space threshold and locate their centres.