1. Image Formation
A digital camera captures light using a sensor array.
Each sensor cell converts incoming photons into electrical signals.
๐ง Remember:
Camera Sensor = Modern replacement for photographic film.
2. Digital Images
Computers store images as discrete numerical values.
Continuous real-world images must be digitized before processing.
Digitization consists of:
3. Sampling and Quantization
| Process |
Description |
| Sampling |
Select points on a regular grid |
| Quantization |
Convert values into discrete integers |
Exam Keyword:
Continuous Image โ Sampling โ Quantization โ Digital Image
4. Pixel Values
A pixel is the smallest unit of a digital image.
| Image Type |
Representation |
| Grayscale |
0 โ 255 |
| RGB |
[R,G,B] |
| HSV |
[H,S,V] |
| Lab |
[L,a,b] |
5. Images as Functions
An image can be represented as a mathematical function:
f(x,y)
f(x,y) returns the pixel intensity at position (x,y).
๐ง Think:
Coordinates โ Pixel Value
6. Image Representation in Memory
Colour images are stored as 3D arrays (matrices).
im[0,0,0] โ Red value of top-left pixel
im[0,0] โ Complete RGB value of top-left pixel
7. Image Bits and Storage
Number of gray levels:
L = 2แต
Storage requirement:
B = M ร N ร k
Frequently tested calculation.
8. Image Resolution
Resolution determines the amount of visual detail.
- Higher resolution โ More detail
- Higher resolution โ Larger file size
- Lower resolution โ Information loss
9. Subsampling Problems
- Blurred images
- Pixelation
- Distortion
- Loss of details
Checkerboard Effect:
Occurs when resolution becomes too low.
False Contouring:
Occurs when gray levels are insufficient.
10. Image Size Calculation
Example:
1024 ร 768 RGB image
8 bits per channel
๐ง Formula:
Total Bits =
Width ร Height ร Channels ร Bits per Channel
Common exam calculation question.
11. Pixel (Point)-Based Processing
Every pixel is transformed independently using a transformation function T.
Input Pixel โ T(r) โ Output Pixel
12. Arithmetic Operations
| Operation |
Purpose |
| Addition |
Combine images |
| Weighted Blend |
Create smooth mixtures |
| Subtraction |
Detect changes |
| Absolute Difference |
Highlight changes clearly |
13. Linear Contrast Stretching
Expands a narrow intensity range into a wider range.
Original:
[100,150]
Target:
[0,255]
Improves image contrast automatically.
14. Piecewise Linear Stretching
Multiple linear segments can be used to emphasize specific intensity ranges.
Thresholding:
Produces a binary image using only two output values.
15. Histograms
A histogram shows the distribution of pixel intensities.
๐ง Histogram tells us:
How pixel values are distributed.
16. Normalized Histogram
Each histogram bin is divided by the total number of pixels.
Sum of all normalized histogram values = 1
Represents probability distribution of pixel intensities.
17. Histogram Interpretation
| Histogram Pattern |
Meaning |
| Left Concentrated |
Dark Image |
| Right Concentrated |
Bright Image |
| Narrow |
Low Contrast |
| Wide |
High Contrast |
๐ง Histogram shows intensity distribution,
NOT spatial arrangement.
18. Histogram Equalization
Histogram Equalization automatically redistributes intensity values to improve contrast.
Goal:
Make the histogram more uniform.
Uses the cumulative distribution function (CDF)
to remap pixel values.
19. Histogram Equalization Example (Exam Favorite)
Histogram Equalization transforms pixel values using the
Cumulative Distribution Function (CDF).
๐ง Exam Workflow:
Step 1 โ Calculate Histogram h(fโ)
Step 2 โ Calculate Probability pF(l)
Step 3 โ Calculate CDF
Step 4 โ Compute New Gray Level gโ
Step 5 โ Build New Distribution pG(l)
| Column |
Meaning |
| fโ |
Original gray level |
| h(fโ) |
Number of pixels |
| pF(l) |
Probability = h(fโ)/Total Pixels |
| CDF (ฤโ) |
Cumulative probability |
| gโ |
Equalized gray level |
| pG(l) |
New probability distribution |
Example:
Total Pixels = 400
Gray Levels = 8
Therefore:
L = 8
L โ 1 = 7
Probability Formula:
pF(l) = h(fโ) / Total Pixels
CDF Formula:
CDF(k) = Sum of all probabilities from level 0 to k
Equalization Formula:
gโ = floor(CDF ร (L โ 1))
| Original Level |
CDF |
gโ |
| 0 | 0.19 | 1 |
| 1 | 0.44 | 3 |
| 2 | 0.65 | 4 |
| 3 | 0.81 | 5 |
| 4 | 0.89 | 6 |
| 5 | 0.95 | 6 |
| 6 | 0.98 | 6 |
| 7 | 1.00 | 7 |
Final Mapping:
0 โ 1
1 โ 3
2 โ 4
3 โ 5
4 โ 6
5 โ 6
6 โ 6
7 โ 7
Exam Shortcut:
After finding CDF,
multiply by (L โ 1),
then take FLOOR value.
๐ง Common Mistake:
Histogram Equalization does NOT guarantee a perfectly
uniform histogram.
It only attempts to spread intensities more evenly.
20. Neighbourhood Processing
Pixel values can be modified using information from neighbouring pixels.
๐ง Instead of:
Pixel โ Pixel
Use:
Neighbourhood โ Pixel
21. Image Filtering
A filter (mask) slides across the image and performs computations using nearby pixels.
3ร3 Averaging Filter:
Replaces each pixel with the average of itself and its neighbours.
Used for noise reduction and image smoothing.
22. Final Exam Summary
Most Important Points
- Digitization: Sampling + Quantization
- Pixel: Smallest image element
- Image Function: f(x,y)
- Storage: B = M ร N ร k
- Subsampling: Can cause pixelation and checkerboard effects
- Point Processing: Transform each pixel independently
- Histogram: Distribution of pixel intensities
- Histogram Equalization: Automatic contrast enhancement
- Neighbourhood Processing: Uses surrounding pixels
- Filtering: Foundation of image processing techniques