1. IT472 Digital Image Processing
Asim Banerjee
Faculty Block #1, Room No. 1109
Extn. # 554

2. IT472 - Digital Image Processing
Edge - Types
IT472 - Digital Image Processing

3. Edge – Derivatives of Intensity Profiles
IT472 - Digital Image Processing

4. IT472 - Digital Image Processing
Gradient Operators
IT472 - Digital Image Processing

5. IT472 - Digital Image Processing
Gradient Operators
IT472 - Digital Image Processing

6. IT472 - Digital Image Processing
Gradient Operators
IT472 - Digital Image Processing

7. Gradient Operators - Application
IT472 - Digital Image Processing

8. Gradient Operators - Applicationb c d e f g
Original image
Sobel gradient
Spatial Gaussian smoothing function
Laplacian mask
LoG
Thresholded LoG
Zero crossings.
IT472 - Digital Image Processing

9. IT472 - Digital Image Processing
Edge Detection Steps
There are two basic steps of edge detection
Detection of short linear edge segments (edgels)
Aggregation of edgels into extended edges (maybe parametric description)
IT472 - Digital Image Processing

10. IT472 - Digital Image Processing
Any Questions?
IT472 - Digital Image Processing

11. Edgel Detection Methods
Difference operators
Parametric-model matchers
IT472 - Digital Image Processing

12. Edge is Where Change Occurs
Change is measured by derivative in 1D
Biggest change, derivative has maximum magnitude
Or 2nd derivative is zero.
IT472 - Digital Image Processing

13. IT472 - Digital Image Processing
Image Gradient (1/2)
The gradient of an image:
The gradient points in the direction of most rapid change in intensity
The gradient direction is given by:
how does this relate to the direction of the edge?
IT472 - Digital Image Processing

14. IT472 - Digital Image Processing
Image Gradient (2/2)
The edge strength is given by the gradient magnitude
IT472 - Digital Image Processing

15. IT472 - Digital Image Processing
The Discrete Gradient
How can we differentiate a digital image f[x,y]?
Option 1: reconstruct a continuous image, then take gradient
Option 2: take discrete derivative (finite difference)
How would you implement this as a cross-correlation?
IT472 - Digital Image Processing

16. IT472 - Digital Image Processing
The Sobel Operator (1/2)
Better approximations of the derivatives exist
The Sobel operators below are very commonly used -1 1 -2 2 1 2 -1 -2
IT472 - Digital Image Processing

17. IT472 - Digital Image Processing
The Sobel Operator (2/2)
The standard definition of the Sobel operator omits the 1/8 term
Doesn’t make a difference for edge detection
However, the 1/8 term is needed to get the right gradient value,
IT472 - Digital Image Processing

18. IT472 - Digital Image Processing
Gradient Operators
(a) Roberts’ cross operator (b) 3x3 Prewitt operator
(c) Sobel operator (d) 4x4 Prewitt operator
IT472 - Digital Image Processing

19. IT472 - Digital Image Processing
Any Questions?
IT472 - Digital Image Processing

20. IT472 - Digital Image Processing
Effects Of Noise (1/2)
Consider a single row or column of the image
Plotting intensity as a function of position gives a signal
Where is the edge?
IT472 - Digital Image Processing

21. IT472 - Digital Image Processing
Effects Of Noise (2/2)
(a)
(b)
(c)
Original image and its edge output
Noise added (zero mean and σ = 0.03) and edge output
Noise added (zero mean and σ = 0.09) and edge output
IT472 - Digital Image Processing

22. Solution: Smooth First
Where is the edge?
Look for peaks in
IT472 - Digital Image Processing

23. Derivative Theorem Of Convolution
This saves us one operation:
IT472 - Digital Image Processing

24. Laplacian of Gaussian (LoG)
Consider
Laplacian of Gaussian
operator
Where is the edge?
Zero-crossings of bottom graph
IT472 - Digital Image Processing

25. 2D edge detection filters
Laplacian of Gaussian
Gaussian
derivative of Gaussian
is the Laplacian operator:
IT472 - Digital Image Processing

26. Optimal Edge Detection: Canny (1/2)
Assume:
Linear filtering
Additive Gaussian noise
Edge detector should have:
Good Detection. Filter responds to edge, not noise.
Good Localization: detected edge near true edge.
Single Response: one per edge.
IT472 - Digital Image Processing

27. Optimal Edge Detection: Canny (2/2)
Optimal Detector is approximately Derivative of Gaussian.
Detection/Localization trade-off
More smoothing improves detection
And hurts localization.
This is what you might guess from above
(detect change) + (remove noise)
IT472 - Digital Image Processing

28. Edge Detection Tutorials
An interesting tutorial on edge detection is available at
An interesting tutorial on Canny edge detector is available at
IT472 - Digital Image Processing

29. The Canny Edge Detector (1/4)
original image (Lena)
IT472 - Digital Image Processing

30. The Canny Edge Detector (2/4)
norm of the gradient
IT472 - Digital Image Processing

31. The Canny Edge Detector (3/4)
thresholding
IT472 - Digital Image Processing

32. The Canny Edge Detector (4/4)
thinning
(non-maximum suppression)
IT472 - Digital Image Processing

33. Non-maximum Suppression
Check if pixel is local maximum along gradient direction
requires checking interpolated pixels p and r
IT472 - Digital Image Processing

34. IT472 - Digital Image Processing
Predicting
the next
edge point
Assume the marked point is an edge point. Then we construct the tangent to the edge curve (which is normal to the gradient at that point) and use this to predict the next points (here either r or s).
(Forsyth & Ponce)
IT472 - Digital Image Processing

35. IT472 - Digital Image Processing
Hysteresis
Check that maximum value of gradient value is sufficiently large
drop-outs? use hysteresis
use a high threshold to start edge curves and a low threshold to continue them.
IT472 - Digital Image Processing

36. Effect of  (Gaussian kernel size)
Canny with
original
The choice of depends on desired behavior
large detects large scale edges
small detects fine features
IT472 - Digital Image Processing

37. Scale Smoothing Eliminates noise edges. Makes edges smoother.
Source (Forsyth & Ponce)
Smoothing
Eliminates noise edges.
Makes edges smoother.
Removes fine detail.
Figures show gradient magnitude of zebra at two different scales
IT472 - Digital Image Processing

38. IT472 - Digital Image Processing
Scale Space (1/5)
IT472 - Digital Image Processing

39. IT472 - Digital Image Processing
Scale Space (2/5)
fine scale
high
threshold
IT472 - Digital Image Processing

40. IT472 - Digital Image Processing
Scale Space (3/5)
coarse
scale,
high
threshold
IT472 - Digital Image Processing

41. IT472 - Digital Image Processing
Scale Space (4/5)
coarse
scale
low
threshold
IT472 - Digital Image Processing

42. IT472 - Digital Image Processing
Scale Space (5/5)
larger
Gaussian filtered signal
first derivative peaks
Properties of scale space (with Gaussian smoothing)
edge position may shift with increasing scale ()
two edges may merge with increasing scale
an edge may not split into two with increasing scale
IT472 - Digital Image Processing

43. Gaussian - Image filter
Laplacian of Gaussian
Gaussian
delta function
IT472 - Digital Image Processing

44. IT472 - Digital Image Processing
Any Questions?
IT472 - Digital Image Processing

45. That’s all for now. We shall continue in the next class.
IT472 - Digital Image Processing