1. What Makes an Edge?
An edge is a location where there is a sudden change (discontinuity) in image intensity.
Most shape and object information in an image is contained within its edges.
🧠 Memory Trick:
Edge = Rapid Intensity Change
2. Goal of Edge Detection
Convert an image from a 2D pixel array into a collection of meaningful curves, contours, or line segments.
Main Idea: Detect strong gradients and post-process them into edges.
Exam Keyword:
Intensity Discontinuity
3. Derivatives and Edges
Edges occur where image intensity changes rapidly. Derivatives measure the rate of change.
Large derivative values indicate possible edge locations.
🧠 Remember:
High Derivative = Strong Edge
4. Partial Derivatives
Images have derivatives in both horizontal (x) and vertical (y) directions.
Finite differences are used to approximate derivatives in digital images.
Important:
Derivatives can be implemented using convolution filters.
5. Image Gradient
The gradient combines horizontal and vertical derivatives.
- Gradient Magnitude → Edge Strength
- Gradient Direction → Direction of maximum intensity increase
Strong edges produce large gradient magnitudes.
6. Effects of Noise
Noise creates false intensity changes that can be mistaken for edges.
Gradient operators respond strongly to noise.
Solution:
Smooth the image before detecting edges.
7. Derivative of Gaussian
Combine smoothing and differentiation into a single operation.
Because convolution is associative, smoothing and derivative operations can be merged.
🧠 Benefit:
Less computation, less noise sensitivity.
8. First-Order Gradient Filters
First derivatives produce large responses along edge regions.
Edge responses often appear as thick ridges rather than thin lines.
9. Laplacian of Gaussian (LoG)
Uses the second derivative of the Gaussian function.
Edges are detected at zero-crossings of the filter response.
Also Known As:
Marr-Hildreth Edge Detector
🧠 Remember:
LoG → Zero Crossing Detection
10. Difference of Gaussians (DoG)
Approximation of LoG using two Gaussian blurred images.
DoG = Gaussian(σ₁) − Gaussian(σ₂)
Faster than computing the full LoG filter.
11. Effect of Sigma (σ)
| σ Value |
Result |
| Small σ |
Detects fine details and noise |
| Large σ |
Detects only major edges |
🧠 Sigma Rule:
Larger σ → More smoothing → Fewer edges
12. Finite Difference Filters
Approximate image gradients using small convolution masks.
Common edge operators are based on finite differences.
13. Mask Properties
| Smoothing Masks |
Derivative Masks |
| Positive values |
Positive and negative values |
| Weights sum to 1 |
Weights sum to 0 |
| Preserve constant regions |
No response in constant regions |
Exam Answer:
Derivative Mask Sum = 0
14. Designing an Edge Detector
An optimal edge detector should:
- Good Detection
- Good Localization
- Single Response per Edge
🧠 Remember:
Detect, Locate, Respond Once
15. Thresholding
Separate edge pixels from non-edge pixels using a threshold value.
Pixel ≥ t → 1
Pixel < t → 0
Threshold selection strongly affects edge quality.
16. Choosing a Threshold
Different threshold values produce different edge maps.
| Threshold |
Effect |
| Low |
More edges, more noise |
| High |
Less noise, possible missing edges |
Exam Answer:
High threshold may miss real edges.
17. Canny Edge Detector
The most widely used edge detector because it is stable and consistent.
Three Main Steps:
- Gaussian Smoothing + Gradient Computation
- Non-Maximum Suppression
- Hysteresis Thresholding & Edge Linking
18. Step 1: Gaussian Filtering
Smooth image and compute gradient magnitude and orientation.
Derivative of Gaussian filters can perform both operations together.
19. Step 2: Non-Maximum Suppression
Removes thick edge responses by keeping only local maxima.
Produces thin, one-pixel-wide edges.
🧠 Goal:
Thick Ridge → Thin Edge
20. Step 3: Hysteresis Thresholding
Uses two thresholds instead of one.
| Threshold |
Meaning |
| High Threshold |
Strong edges |
| Low Threshold |
Weak edges |
Weak edges connected to strong edges are preserved.
21. Edge Linking
Connect weak edges to strong edges using 8-neighbourhood searching.
Noise responses are usually isolated and therefore removed.
🧠 Remember:
Strong Edges Guide Weak Edges
22. Effect of Sigma in Canny
| σ |
Result |
| Small |
Many fine edges |
| Large |
Only major edges |
23. Knowing True Edges
Not all detected edges correspond to meaningful object boundaries.
Human perception is often used as ground truth for evaluating edge detectors.
24. Human Segmentation vs Edge Detection
Human-labelled boundaries are compared against detector outputs.
Evaluation Metrics:
Precision = Correct detected edges / Total detected edges
Recall = Correct detected edges / Total true edges
25. Modern Edge Detection
Machine learning and deep learning can learn edge patterns directly from data.
- Structured Forest Edge Detection
- Holistically-Nested Edge Detection (HED)
- DeepContour
Modern methods outperform traditional hand-crafted edge filters.
26. Final Exam Summary
Most Important Points
- Edge: Sudden intensity change.
- Gradient: Measures intensity change.
- Gradient Magnitude: Edge strength.
- Noise: Causes false edge responses.
- Derivative of Gaussian: Smooth + Differentiate.
- LoG: Detect edges using zero crossings.
- DoG: Fast approximation of LoG.
- Sigma: Controls smoothing scale.
- Thresholding: Separate edges from background.
- Canny: Gaussian → Non-Max Suppression → Hysteresis.
- Non-Maximum Suppression: Produces thin edges.
- Hysteresis: Uses low and high thresholds.
- Edge Linking: Strong edges guide weak edges.
- Precision & Recall: Evaluate edge quality.