Digital Image Fundamentals

Digital Image Processing (DIP) deals with manipulating digital images using computers to improve image quality or extract useful information.

Steps in Digital Image Processing

The digital image processing system follows a sequence of steps from image capture to decision-making.

Main Steps

Step	Description	Example
Image Acquisition	Capturing the image using a sensor	Camera captures a photo
Image Enhancement	Improving image quality	Increasing brightness
Image Restoration	Removing noise or blur	Noise removal
Color Image Processing	Processing color images	RGB image editing
Wavelets & Compression	Reducing image size	JPEG compression
Morphological Processing	Shape-based processing	Object boundary detection
Segmentation	Dividing image into regions	Face detection
Representation & Description	Feature extraction	Shape, texture
Recognition & Interpretation	Identifying objects	OCR recognition
Knowledge Base	Stores rules/data	AI model database

Exam Note: These steps are not always sequential; some may be skipped depending on the application.

Components of Digital Image Processing System

A digital image processing system consists of hardware and software elements.

System Components

Component	Function
Image Sensor	Converts light into electrical signals
Digitizer	Converts analog signal into digital form
Computer	Processes image data
Image Processing Software	Algorithms and tools
Mass Storage	Stores images
Display Devices	Monitor, printer
Networking	Image transmission

Block Diagram (Conceptual)

Image Sensor → Digitizer → Computer → Output Device

Elements of Visual Perception

Visual perception refers to how humans interpret visual information.

Human Eye Structure

Part	Function
Retina	Receives image
Rods	Low-light vision
Cones	Color vision
Optic Nerve	Sends signals to brain

Brightness Adaptation

The human eye can adjust to different light levels.

Example:

Coming from sunlight into a dark room
Eyes take time to adjust

Optical Illusions

Our brain may misinterpret images.

Example: Same color looks different on dark and light backgrounds

Importance in DIP

Helps in contrast enhancement
Used in medical image display
Improves image visualization

Image Sensing and Acquisition

This is the first step in digital image processing.

Image acquisition is the process of capturing an image and converting it into digital form.

Image Sensing

Uses sensors to capture images.

Sensor Type	Application
CCD (Charge Coupled Device)	Digital cameras
CMOS Sensor	Mobile phones
Infrared Sensors	Night vision
X-ray Sensors	Medical imaging

Image Acquisition Process

Light reflected from object
Sensor converts light into electrical signal
Digitizer converts signal to digital image

Real-Life Example

Mobile camera capturing a photo
MRI scan capturing brain image

Image Sampling and Quantization

These processes convert an analog image into a digital image.

Image Sampling

Sampling converts a continuous image into discrete pixels.

Explanation

Image is divided into a grid
Each grid point = pixel

Sampling Rate Effect

Sampling Rate	Image Quality
High	Clear image
Low	Blurred image

Example

High-resolution image = more pixels
Low-resolution image = fewer pixels

Image Quantization

Quantization assigns intensity values to each pixel.

Explanation

Converts continuous intensity into discrete levels

Quantization Levels

Levels	Quality
256 levels (8-bit)	High quality
16 levels	Poor quality

Sampling vs Quantization

Feature	Sampling	Quantization
Converts	Space	Intensity
Result	Pixels	Gray levels
Affects	Resolution	Contrast

Relationship Between Sampling & Quantization

Digital Image = Sampling (Space) + Quantization (Intensity)

Mathematically: Digital Image → f(x, y)

Applications of Digital Image Processing

Field	Application
Medical	MRI, CT Scan
Security	Face recognition
Satellite	Weather forecasting
Industry	Quality inspection
AI & ML	Object detection

Relationships Between Pixels

Pixel relationships define how a pixel interacts with its neighboring pixels and are essential for image analysis, segmentation, and enhancement.

Types of Pixel Neighbors

For a pixel p(x, y):

4-Neighborhood (N₄)

Pixels sharing a common edge.

N_{4} (p) = {(x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1)}

Diagonal Neighborhood (Nᴅ)

Pixels sharing a common corner.

N_{D} (p) = {(x + 1, y + 1), (x + 1, y - 1), (x - 1, y + 1), (x - 1, y - 1)}

8-Neighborhood (N₈)

Combination of 4-neighbors and diagonal neighbors.

N_{8} (p) = N_{4} (p) \cup N_{D} (p)

Comparison Table

Neighborhood	Connectivity	Application
4-neighbor	Edge	Simple segmentation
Diagonal	Corner	Pattern recognition
8-neighbor	Edge + Corner	Object detection

Adjacency of Pixels

Adjacency defines whether two pixels are connected.

Types of Adjacency

Type	Description
4-adjacency	Pixels share edge
8-adjacency	Pixels share edge or corner
m-adjacency	Modified adjacency to avoid ambiguity

Distance Between Pixels

Distance Measures

Distance Type	Formula
Euclidean	$\sqrt{(x₁-x₂)^2 + (y₁-y₂)^2}$
City Block (D₄)	(
Chessboard (D₈)	(\max(

Color Image Fundamentals

A color image is composed of multiple channels representing different color components.

Color Representation

Color perception depends on:

Brightness
Hue
Saturation

Color Models

A color model defines how colors are represented numerically.

RGB Color Model

RGB is an additive color model based on Red, Green, and Blue components.

Characteristics

Feature	Description
Type	Additive
Components	R, G, B
Value Range	0–255
Used In	Cameras, monitors

RGB Color Cube

Black → (0,0,0)
White → (255,255,255)
Red → (255,0,0)

Advantages & Limitations

Advantages	Limitations
Simple hardware	Not intuitive for humans
Direct display	Poor for color editing

HSI Color Model

HSI represents colors in terms of Hue, Saturation, and Intensity, matching human perception.

Components

Component	Meaning
Hue (H)	Color type (0°–360°)
Saturation (S)	Purity of color
Intensity (I)	Brightness

HSI Color Space Shape

Hue → Angle
Saturation → Radius
Intensity → Vertical axis

RGB vs HSI

Feature	RGB	HSI
User-friendly	No	Yes
Hardware oriented	Yes	No
Image enhancement	Difficult	Easy

Two-Dimensional Mathematical Preliminaries

These mathematical tools form the foundation of digital image processing.

Image as a Function

A digital image is represented as:

f (x, y)

Where:

x, y → spatial coordinates
f → intensity value

Common 2D Functions

Operation	Description
Addition	Image blending
Multiplication	Contrast control
Convolution	Filtering
Correlation	Pattern matching

Convolution in 2D

g (x, y) = f (x, y) * h (x, y)

Where:

f → input image
h → filter mask
g → output image

Two-Dimensional Transforms

Transforms convert images from spatial domain to frequency domain.

Discrete Fourier Transform (DFT)

DFT decomposes an image into its frequency components.

2D DFT Equation

F (u, v) = \sum_{x = 0}^{M - 1} \sum_{y = 0}^{N - 1} f (x, y) e^{- j 2 π (\frac{u x}{M} + \frac{v y}{N})}

Properties of DFT

Property	Description
Linearity	Output linear
Periodicity	Frequency repetition
Symmetry	Complex conjugate
Shift property	Spatial shift affects phase

Applications

Image filtering
Noise removal
Edge detection

Discrete Cosine Transform (DCT)

DCT converts image into cosine frequency components only.

2D DCT Equation

C (u, v) = α (u) α (v) \sum_{x = 0}^{M - 1} \sum_{y = 0}^{N - 1} f (x, y) \cos [\frac{(2 x + 1) u π}{2 M}] \cos [\frac{(2 y + 1) v π}{2 N}]

Advantages of DCT

Feature	Benefit
Energy compaction	Most energy in low frequency
Real values	Easy computation
Compression friendly	JPEG standard

DFT vs DCT

Feature	DFT	DCT
Output	Complex	Real
Used in	Filtering	Compression
Boundary effects	High	Low

Practical Applications

Technique	Application
Pixel adjacency	Segmentation
RGB/HSI	Color enhancement
DFT	Frequency filtering
DCT	Image compression

Digital Image Fundamentals