Colour Image
Question
1. (a) Define the terms: radiance, luminance, and gray level. How many different
shades of gray are there in a color RGB system in which each RGB image is an 8-
bit image? (4.75)
(b) Explain the concept of color gamut and its significance in color models. (4)
2. (a) Why do we use color in image processing? Categorize color image processing
with a suitable example. (2.75)
(b) Describe the HSI color model. (3)
(c) Convert RGB (29, 104, 215) values to HSI values. (3)
3. (a) What are the purposes of a color model? What are the types of color model? 3
(b) Describe about RGB color model. 3.75
(c) What are hue and saturation? 2
4. (a) Define radiance, luminance, and brightness. (3)
(b) Explain briefly about HSV color model. (2.75)
(c) Discuss briefly about chromaticity diagram. (3)
5. (a) What are the purposes of a color model? What are the types of color models?
(2)
(b) Describe the RGB color model. (3)
(c) Briefly explain the chromaticity diagram. (3)
(d) What do you mean by safe web color? (0.75)
6. a) Define radiance, luminance, and brightness. (3)
b) What are hue and saturation? (2)
c) Explain how the HSI model can be formed from the RGB model. (3.75)
a) Definitions:
Radiance: The total electromagnetic energy emitted from a surface per unit area
per unit solid angle. It is a physical quantity measured in W/(sr·m²).
Luminance: The perceived brightness of an image, derived from radiance but
adjusted according to human visual sensitivity to different wavelengths (mostly
green). It influences how bright a pixel appears.
Gray level: A single intensity value assigned to a pixel, indicating brightness. In
digital images, it ranges from 0 (black) to 255 (white) in an 8-bit system.
Shades of Gray in 8-bit RGB:
Each color channel (R, G, B) has 256 levels.
A gray pixel requires R = G = B (e.g., (0,0,0), (1,1,1), ..., (255,255,255)).
⇒ Total gray shades = 256.
(b) Color Gamut and Its Significance (4 marks)
Color Gamut:
The range of colors a device or model can represent.
Subset of the visible spectrum, visualized in color spaces like CIE 1931.
Varies by device, color model, and application.
Significance:
1. Model-Based Variation:
RGB: Additive; large gamut; used in displays.
CMYK: Subtractive; smaller gamut; used in printing.
HSV/HSL: Human-friendly; editing-focused.
CIELAB: Device-independent; perceptually uniform.
2. Device Limitations:
Each device has a device-dependent gamut.
Color clipping occurs when out-of-gamut colors are forced into displayable
range.
Gamut mapping ensures smoother transitions across devices.
3. Color Consistency:
Gamut mismatch causes distorted color appearance.
ICC profiles manage consistent rendering across screens and printers.
4. Applications:
Essential in image processing, digital photography, printing, medical imaging,
and cinema.
Accurate gamut handling avoids banding, posterization, and loss of detail.
Examples of Gamuts:
sRGB: Standard for displays/web (~35% of visible colors).
Adobe RGB: Wider than sRGB; for pro editing (~50%).
DCI-P3: Cinema, HDR content.
CMYK: Print-oriented; limited saturation range.
(a) Use of Color in Image Processing & Its Categorization (2.75
marks)
Why color is used:
Enhances visual perception by utilizing human sensitivity to chromatic
information.
Helps in object recognition, segmentation, and feature extraction due to richer
data.
Improves accuracy in tasks like face detection, medical imaging, and content-
based retrieval.
Color Image Processing Categories:
1. Pseudo-color processing:
Applies artificial color to grayscale images based on intensity values.
Example: Assigning blue to low intensities and red to high in thermal images.
2. Full-color processing:
Operates on true-color images captured using color sensors.
Each pixel has three components (R, G, B or other models).
Example: Enhancing a digital photograph using histogram equalization in RGB
or HSV space.
(b) HSI Color Model (3 marks)
HSI stands for Hue, Saturation, and Intensity — designed to represent color in a way
that aligns with human perception.
Hue (H):
Represents the color type (e.g., red, green, blue).
Measured in degrees (0°–360°) on the color wheel.
Pure red = 0°, green = 120°, blue = 240°.
Saturation (S):
Indicates the purity or vividness of a color.
Ranges from 0 (gray) to 1 (pure color).
Lower S = more washed out; higher S = more intense.
Intensity (I):
Refers to the brightness or grayscale equivalent.
Calculated as the average of RGB components:
R + G + B
I =
3
Advantages of HSI:
Separates chromatic content (H, S) from brightness (I).
Ideal for color enhancement, segmentation, and illumination-invariant
processing.
Closer to how humans interpret color than RGB.
Application Example:
In image editing, changing I brightens the image without altering H or S — useful in
face detection, remote sensing, etc.
RGB to HSI Conversion (3 Marks)
Given:
RGB = (29, 104, 215)
Step 1: Normalize RGB to [0,1]
′
29 ′
104 ′
215
R = = 0.1137, G = = 0.4078, B = = 0.8431
255 255 255
Step 2: Compute Intensity (I)
′ ′ ′
R + G + B 0.1137 + 0.4078 + 0.8431
I = = = 0.4549
3 3
Step 3: Compute Saturation (S)
′ ′ ′
min(R , G , B ) 0.1137
S = 1 − = 1 − = 0.7500 (75%)
I 0.4549
1
[(r − g) + (r − b)]
−1 2
θ = cos ( )
√ (r − g)2 + (r − b)(g − b)
1 1
Numerator = [(0.114 − 0.408) + (0.114 − 0.843)] = [−0.294 − 0.729] = −0.5115
2 2
2
Denominator = √ (−0.294) + (−0.729)(0.408 − 0.843)
= √ 0.086 + (−0.729)(−0.435)
= √ 0.086 + 0.317
= √ 0.403 ≈ 0.6348
−1
−0.5115 −1 ∘
θ = cos ( ) ≈ cos (−0.8055) ≈ 143.6
0.6348
d) Adjust for Correct Hue Quadrant:
Since B > G :
′ ′
H = 360° − θ = 360° − 143.6° = 216.4°
Final HSI Values:
H = 216.4°, S = 0.7500, I = 0.4549
3. (a) Purposes and Types of Color Models (3 marks)
Purposes of a color model:
Provides a mathematical framework to represent colors for digital processing
Enables accurate color reproduction across different devices (displays,
printers)
Supports efficient color manipulation like filtering, segmentation,
enhancement
Facilitates conversion between devices with differing color capabilities
Helps in human interpretation of colors via models aligned with perception
(e.g., HSI)
Types of color models:
RGB (Red, Green, Blue): Additive model; combines light; used in monitors and
cameras
CMYK (Cyan, Magenta, Yellow, Key/Black): Subtractive model; used in printing
processes
HSI/HSV (Hue, Saturation, Intensity/Value): Separates color components for
easier editing and analysis
CIELAB: Device-independent, designed to be perceptually uniform; used in
color correction and quality control
YUV/YIQ: Used in video compression and broadcasting for separating
luminance and chrominance
(b) Describe about RGB color model (3.75 marks)
RGB stands for Red, Green, Blue — a fundamental additive color model used in
digital image processing.
Principle:
Based on combining light of the three primary colors: Red, Green, and Blue.
Varying each component's intensity from 0 to 255 (8-bit) produces a wide
range of colors.
White = (255, 255, 255), Black = (0, 0, 0), Pure red = (255, 0, 0), etc.
Color Space:
All colors lie within a cube where each axis represents a primary color.
Total colors possible = 256 3
= 16, 777, 216 (24-bit color).
Application Areas:
Monitors, TVs, Cameras, Scanners: All use RGB for display and capture.
Computer Graphics, Game Design, Web Development: Common in rendering
pipelines.
Basis for color models like HSV, HSL, and YUV through transformations.
Advantages:
Directly matches hardware light emission.
Efficient for image storage and rendering.
Limitations:
Device-dependent: Appearance may vary across screens.
Not perceptually uniform — hard to process by human-intuitive parameters
(e.g., hue).
(c) What are hue and saturation? (2 marks)
Hue:
Refers to the dominant wavelength of color; represents the type of color
(e.g., red, green, blue).
Measured as an angle (0°–360°) on the color wheel:
0° = Red, 120° = Green, 240° = Blue
Independent of brightness and intensity.
Saturation:
Describes the purity or vividness of a color.
High saturation = pure, intense color;
Low saturation = dull, faded, or grayish appearance.
Affects how much white light is mixed with the hue.
4. (a) Define radiance, luminance, and brightness (3 marks)
Radiance:
Measures the total amount of energy emitted from a surface per unit area,
per unit solid angle in a given direction.
Unit: Watt/(steradian·m²)
Depends on angle, wavelength, and distance; fundamental quantity in image
formation.
Luminance:
Photometric equivalent of radiance; measures perceived brightness of light
emitted or reflected from a surface in a specific direction.
Unit: Candela/m² (cd/m²)
Accounts for human visual sensitivity to different wavelengths (peaks in
green).
Brightness:
Subjective perception of luminance by the human eye.
Not a physical quantity; depends on context, adaptation, and surroundings.
Two surfaces with the same luminance may appear to have different
brightness.
4. (b) HSV color model (2.75 marks)
HSV stands for Hue, Saturation, Value, a color model derived from RGB to match
human color perception.
Components:
Hue (H):
Represents the type of color (e.g., red, green, blue).
Measured in degrees (0°–360°) on the color wheel.
0° = Red, 120° = Green, 240° = Blue.
Saturation (S):
Indicates purity or intensity of the color.
Range: 0 to 1 (or 0% to 100%)
0 = Gray (no color), 1 = Fully saturated (pure color).
Value (V):
Defines brightness of the color.
Range: 0 to 1;
0 = Black, 1 = Brightest version of the color.
Advantages:
More intuitive than RGB for color selection and manipulation.
Useful in image segmentation, filtering, and object detection based on color.
4. (c) Chromaticity diagram (3 marks)
Chromaticity diagram is a 2D representation of color information excluding
brightness, based on the CIE 1931 color space.
Axes:
Plots x (red) and y (green) chromaticity coordinates;
z (blue) is omitted as x + y + z = 1.
Every visible color is represented by a point within the horseshoe-shaped
diagram.
Key Features:
Spectral locus: Curve representing pure spectral colors (wavelengths from
~400–700 nm).
Line of purples: Straight line connecting the extremes of the spectral locus
(non-spectral colors).
White point: Central region where R, G, B are balanced (e.g., D65 illuminant).
Uses:
Visualize color gamuts (e.g., sRGB, Adobe RGB) as enclosed triangles.
Useful for color matching, conversion, and analysis in imaging systems.
Helps in understanding color perception limits of devices and the human eye.
4. (d) What do you mean by safe web color? (0.75 mark)
Safe web colors are a set of 216 standardized colors that appear consistently
across all browsers and monitors, especially older 256-color displays.
Each RGB component takes one of 6 fixed values: 0, 51, 102, 153, 204, 255.
Ensures color stability and avoids dithering or distortion on limited-color systems.
4. (c) HSI from RGB model (3.75 marks)
HSI model separates color into Hue (H), Saturation (S), and Intensity (I) — more
aligned with human perception than RGB.
Step-by-step conversion:
Let R, G, B ∈ [0, 1]. Normalize if in [0,255] by dividing each by 255.
Intensity (I):
R + G + B
I =
3
Saturation (S):
3
S = 1 − ⋅ min(R, G, B)
R + G + B
If R + G + B = 0, then S = 0 .
Hue (H):
0.5[(R − G) + (R − B)]
−1
θ = cos ( )
√ (R − G)2 + (R − B)(G − B)
θ, if B ≤ G
H = { ∘
360 − θ, if B > G
Result:
Final HSI values:
H in degrees (0 ∘ ∘
− 360 )
S and I in range [0, 1]
Purpose:
Decouples color info (H, S) from brightness (I).
Useful in segmentation, enhancement, filtering, where brightness must be
treated separately from chromaticity.
