Grayscale, Color Images, and Color Models

CSS Optional — Paper-II, Section-B · P-II.V.VII · Syllabus: Gray-scale and Color Images; Color Models (RGB, CMYK and HSI) ("HIS" in the syllabus = HSI). Asked in 2019 (RGB vs HSI) and 2021 (need for multiple colour models; CMY vs CMYK) — second only to histograms in frequency.

1. Grayscale vs Colour Images

Colour → grayscale (luminance, weighted by eye sensitivity): Y = 0.299R + 0.587G + 0.114B. Green gets the highest weight because the eye is most sensitive to it; a plain average (R+G+B)/3 looks less natural.

Pseudo-colour (false colour): assigning colours to gray levels to make detail visible (thermal images, weather maps, X-ray baggage scanners) — different from true colour.

2. Colour Fundamentals

• The eye has three types of cones sensitive roughly to red, green and blue (≈ 65%, 33%, 2% of cones). All perceived colours are combinations of these responses — hence three primaries.
• Colour is described by brightness (intensity), hue (dominant wavelength — "which colour") and saturation (purity — how much white is mixed in). Hue + saturation together = chromaticity.
• Additive mixing (light): R + G + B = white; used by emitters (screens, projectors).
• Subtractive mixing (pigment): each ink absorbs its complement; C + M + Y ≈ black; used by printers.

3. RGB Model

• Additive, hardware-oriented; each colour is a point in a unit cube with black at (0,0,0), white at (1,1,1) and the grey scale along the main diagonal.
• Used by monitors, cameras, scanners, TVs.
• Limitations: not intuitive for humans ("how much blue makes this orange warmer?"); R, G and B are highly correlated, so brightness changes affect all three.

4. CMY and CMYK Models

• Subtractive, used for printing. Cyan absorbs red, magenta absorbs green, yellow absorbs blue.
• Conversion (normalized): C = 1 − R, M = 1 − G, Y = 1 − B.
• Why add K (black)? Equal C + M + Y inks give a muddy dark brown, not true black. Adding black ink gives: true, deep black; sharper black text; lower ink cost (one ink instead of three); faster drying and less paper soaking; fewer colour-registration problems.
• CMY → CMYK: K = min(C, M, Y); C' = (C − K)/(1 − K), M' = (M − K)/(1 − K), Y' = (Y − K)/(1 − K) (if K = 1, the colour is pure black: C' = M' = Y' = 0).

CMY vs CMYK (CSS 2021):

5. HSI Model

• Perception-oriented: separates intensity (I) from colour information (H and S), matching how humans describe colour.
• Geometry: a double cone / cylinder — H is an angle (0° red, 120° green, 240° blue), S is distance from the central axis (0 = grey, 1 = pure), I is height along the axis (black → white).
• RGB → HSI (normalized R, G, B):
  • I = (R + G + B) / 3
  • S = 1 − 3·min(R, G, B) / (R + G + B)
  • θ = cos⁻¹{ ½[(R − G) + (R − B)] / √[(R − G)² + (R − B)(G − B)] }; H = θ if B ≤ G, else H = 360° − θ
• Why it matters for DIP: you can process intensity alone — e.g. histogram-equalize I without shifting hues — and segment by hue independently of lighting.

RGB vs HSI (CSS 2019):

6. Why More Than One Colour Model? (CSS 2021)

No single model suits every task: devices, printers and people "think" about colour differently.

7. Colour Image Processing — Two Approaches

• Per-channel: process R, G and B separately (fine for linear filtering, e.g. smoothing).
• Vector-based / intensity-based: treat each pixel as a vector or convert to HSI and work on I — needed for histogram equalization and edge detection to avoid colour distortion.
• Colour segmentation: in HSI, threshold on hue (and saturation); in RGB, use distance from a reference colour vector.

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📐 Worked Numericals

N1 — RGB → CMY: orange RGB (255, 128, 0) → normalized (1, 0.502, 0) → CMY = (0, 0.498, 1).

N2 — RGB → CMYK: RGB (100, 50, 50).

1. Normalize: R = 0.392, G = B = 0.196
2. CMY: C = 0.608, M = Y = 0.804
3. K = min = 0.608; 1 − K = 0.392
4. C' = 0/0.392 = 0; M' = Y' = (0.804 − 0.608)/0.392 = 0.5
5. CMYK = (0, 0.5, 0.5, 0.608)

N3 — RGB → HSI: normalized (0.6, 0.4, 0.2).

1. I = 1.2/3 = 0.4
2. S = 1 − 3(0.2)/1.2 = 0.5
3. Numerator = ½[(0.2) + (0.4)] = 0.3; denominator = √[0.04 + (0.4)(0.2)] = √0.12 = 0.3464
4. θ = cos⁻¹(0.866) = 30°; B (0.2) ≤ G (0.4) → H = 30° (an orange hue)

N4 — Grayscale conversion: RGB (200, 100, 50) → Y = 59.8 + 58.7 + 5.7 = 124.2 ≈ 124 (a plain average would give 116.7).

N5 — Colour count: 24-bit → 2^24 = 16,777,216 colours; 16-bit "high colour" (5-6-5 bits) → 65,536.

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🎯 CSS Exam Angle

• RGB vs HSI: comparison table + one sentence on why HSI helps processing (intensity decoupled from colour) + the RGB → HSI formulas. A small cube and cone sketch earns quick marks.
• "Need for more than one model": the 5-row table in section 6 — the key idea is hardware-oriented vs perception-oriented vs transmission-oriented.
• CMY vs CMYK: table + the five reasons for adding K.

📌 Past CSS Paper Frequency

⚠️ MCQ Traps

• RGB is additive; CMY(K) is subtractive.
• K in CMYK stands for Key (black), not "blacK" or "Kelvin".
• Hue is an angle; saturation is purity; intensity is brightness.
• Hue is undefined when S = 0 (greys); saturation is undefined when I = 0 (black).
• Luminance weights green highest (0.587), blue lowest (0.114).
• Pseudo-colour is not true colour — it's a display mapping of gray levels.
• JPEG converts RGB to YCbCr, not HSI, before compression.

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✅ Self-Check (with Answers)

Q1. Why is RGB called additive and CMY subtractive?

Ans: RGB adds emitted light — R + G + B = white (screens). CMY inks absorb (subtract) wavelengths from white light — cyan absorbs red, magenta absorbs green, yellow absorbs blue; C + M + Y ≈ black (printers).

Q2. Give three reasons for adding black (K) in CMYK.

Ans: Mixing C + M + Y gives a muddy brown, not true black; one black ink costs less than three coloured inks; black text is sharper (no colour-registration errors); less ink means faster drying and less paper soaking.

Q3. Convert normalized RGB (0.2, 0.4, 0.6) to CMY.

Ans: C = 1 − 0.2 = 0.8, M = 1 − 0.4 = 0.6, Y = 1 − 0.6 = 0.4.

Q4. Convert that CMY (0.8, 0.6, 0.4) to CMYK.

Ans: K = min = 0.4; 1 − K = 0.6. C' = 0.4/0.6 = 0.667, M' = 0.2/0.6 = 0.333, Y' = 0 → CMYK = (0.667, 0.333, 0, 0.4).

Q5. Why is HSI preferred for colour image processing?

Ans: It separates intensity from colour. Intensity can be enhanced alone without shifting colours, and objects can be segmented by hue regardless of shadows or lighting — which matches how humans describe colour.

Q6. Why does green get the largest weight (0.587) in grayscale conversion?

Ans: The eye is most sensitive to green wavelengths, so green contributes most to perceived brightness; blue contributes least (0.114).

Q7. Name a colour model used in JPEG compression and why.

Ans: YCbCr — it separates luminance (Y) from chrominance (Cb, Cr), so chroma can be subsampled heavily with little visible loss, since the eye is less sensitive to colour detail.

📜 Past-Paper Questions & MCQs (CSS 2016–2026)

2016 · Paper-II · Q7(b) and 2021 · Paper-II · Q7(c) · 6 marks each

Q. Differentiate between the CMY and CMYK colour models used in digital image processing. Explain the CMY colour model and its use.

Ans.

• CMY (cyan, magenta, yellow) is a subtractive model used for printing and plotting. Each ink absorbs (subtracts) part of the white light. The relation with RGB is C = 1 − R, M = 1 − G, Y = 1 − B. Mixing all three should give black.
• CMYK adds K (black, the "key") as a fourth ink.

2019 · Paper-II · Q6(b) · 6 marks

Q. Compare the RGB and HSI colour models in the context of digital image processing.

Ans.

2020 · Paper-II · Q7(b) · 8 marks and 2021 · Paper-II · Q7(b) · 6 marks

Q. Explain the types of colour models, and the most common hardware-oriented colour models in detail. Is there a need for more than one colour model?

Ans.

• A colour model is a coordinate system that represents each colour as a numeric tuple.
• Hardware-oriented models:
  • RGB: additive, for monitors, TVs, cameras and scanners. Colours are formed by adding light (a cube with black at the origin and white at the opposite corner).
  • CMY / CMYK: subtractive, for printers.
  • YIQ / YUV / YCbCr: luminance plus colour difference, for TV broadcasting and JPEG, which allows chroma subsampling.
• Perception-oriented models: HSI, HSV, HSL describe colour as hue, saturation and intensity or value.
• Need for more than one: different devices and tasks work in different spaces. Displays need RGB, printers need CMYK, compression and TV need luma/chroma, and segmentation or enhancement is easier in HSI. Conversions are used between them.

2022 · Paper-II · Q6(b) · 8 marks

Q. The R, G and B component images of an RGB image have the horizontal intensity profiles shown (red falls linearly from 1.0 to 0 across the width, green rises from 0 to 1.0 at the middle and falls back to 0, blue rises linearly from 0 to 1.0). Identify the colour a person would see in the middle column.

Ans.

• At the middle column (position N/2):
  • Red = 0.5 (halfway down its linear fall)
  • Green = 1.0 (the peak)
  • Blue = 0.5 (halfway up its linear rise)
• Colour = (R, G, B) = (0.5, 1.0, 0.5), which is a light (pale) green: green at full strength, with equal red and blue added, which lightens it towards white.

MCQs

2024 P-II · Q15. Which of the following is true?

• (A) Brightness gives a measure of the degree to which a pure colour is diluted by white light
• (B) Saturation gives a measure of the degree to which a pure colour is diluted by white light ✅
• (C) Hue gives a measure of the degree to which a pure colour is diluted by white light
• (D) None of these
• Answer: (B).
• Why: saturation is the purity of a colour (red is highly saturated, pink is red diluted with white). Hue is the colour type (red, green, blue), and brightness (intensity) is how light or dark it is.