This Algorithm is better than canny by 0.7% but lacks the speed and optimization capability which can be changed by including Neural Network and PSO searching to the same. This used dual FIS Optimization technique to find the high frequency or the edges in the images and neglect the lower frequencies.

1. Digital Image Processing
Edge Detection using
Dual FIS Optimization
Ishaan Gupta
03914802810
7E123 – E2
Electronics and Communications
MAIT
Mentored By:
Prof. Nitin Sharma
Assistant Professor
Electronics and Communications Dept
MAIT

2. What is D.I.P. ?
• Processing of digital images by means of a digital computer.
• Output can be image and/or values.
• Deals with spatial coordinates, amplitude of ‘f’ at any pair coordinates
(x,y) called gray levels or intensity values which are finite and discrete.

3. Steps in
DIP
Image acquisition
Image filtering and
enhancement
Image restoration
Color Image
Processing.
Wavelets and
multi-resolution
Processing.
Compression
Morphological
Processing.
Segmentation
Representation &
Description.
Object Recognition

4. Image acquisition
• Done via:
• Camera – Visible spectrum
• Image matrix (Draw Functions / Convert intensity values -> Image)
• Techniques :
• Xray
• Gamma
• Ultrasound
• IR
• Satellite (Multi-resolution)

5. Image filters & enhancement
• Filters – LPF, HPF, BPF, Gaussian Filters, etc.
• Depth – Field view, panorama, IR based, Laser Based
• Enhancement – Brightness, Contrast, Smoothening, Equalization,
Saturation [RGB Master, R master, G Master, B Master] , etc.

6. Detection
• Edge
• Color
• Intensity / gray level - Binary and grayscale Images
• Objects and Object description.

7. Edge detection algos
• Gaussian - Canny’s Algo, Shen-Castan, etc
• LoG (Laplacian of Gaussian) – Marr-Hildreth – Second Derivative
• Zero Crossing – LoG based
• Classical - Prewitt
• Classical - Sobel

8. Comparisons
Operator Advantages Disadvantages
Classical (Sobel,
prewitt, Kirsch,…)
Simplicity,
Detection of edges and their
orientations
Sensitivity to
noise, Inaccurate
Zero
Crossing(Laplacian, Second
directional derivative)
Detection of
edges and their orientations. Having
fixed characteristics in all directions
Responding to
some of the existing edges,
Sensitivity to noise
Laplacian of
Gaussian(LoG) (Marr-Hildreth)
Finding the
correct places of edges, Testing wider
area around the pixel
Malfunctioning
at the corners, curves and where the
gray level intensity function varies.
Not finding the orientation of edge
because of using the Laplacian filter
Gaussian(Canny,
Shen-Castan)
Using
probability for finding error rate,
Localization and response. Improving
signal to noise ratio, Better detection
specially in noise conditions
Complex
Computations, False zero crossing,
Time consuming

9. Edge Detection
9

10. • Convert a 2D image into a set of curves
• Extracts salient features of the scene
• More compact than pixels
10

11. Origin of Edges
• Edges are caused by a variety of factors
depth discontinuity
surface color discontinuity
illumination discontinuity
surface normal discontinuity
11

12. Profiles of image intensity edges
12

13. Edge detection
1. Detection of short linear edge segments (edgels)
2. Aggregation of edgels into extended edges
• (maybe parametric description)
13

14. Edgel detection
•Difference operators
•Parametric-model matchers
14

15. Edge is Where Change Occurs
• Change is measured by derivative in 1D
• Biggest change, derivative has maximum magnitude
• Or 2nd derivative is zero.
15

16. Image gradient
• 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?
The edge strength is given by the gradient magnitude
16

17. 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)
17

18. The Sobel operator
• Better approximations of the derivatives exist
• The Sobel operators below are very commonly used
-1 0 1
-2 0 2
-1 0 1
1 2 1
0 0 0
-1 -2 -1
• The standard defn. of the Sobel operator omits the 1/8 term
– doesn’t make a difference for edge detection
– the 1/8 term is needed to get the right gradient value, however
18

19. Gradient operators
(a): Roberts’ cross operator (b): 3x3 Prewitt operator
(c): Sobel operator (d) 4x4 Prewitt operator
19

20. Effects of noise
• Consider a single row or column of the image
• Plotting intensity as a function of position gives a signal
20

21. Solution: Smooth first
21

22. Derivative theorem of convolution
• This saves us one operation:
22

23. Laplacian of Gaussian
• Consider
Laplacian of Gaussian
operator
23

24. 2D edge detection filters
• is the Laplacian operator:
Laplacian of Gaussian
Gaussian derivative of Gaussian
24

25. Optimal Edge Detection: Canny
• Assume:
• Linear filtering
• Additive iid 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.
25

26. Optimal Edge Detection: Canny (continued)
• Optimal Detector is approximately Derivative of Gaussian.
• Detection/Localization trade-off
• More smoothing improves detection
• And hurts localization.
26

27. The Canny edge detector
• original image (Lena)
27

28. The Canny edge detector
norm of the gradient
28

29. The Canny edge detector
thresholding
29

30. The Canny edge detector
thinning
(non-maximum suppression) 30

31. Non-maximum suppression
• Check if pixel is local maximum along gradient
direction
• requires checking interpolated pixels p and r
31

32. 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) 32

33. 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.
33

34. Effect of (Gaussian kernel size)
Canny with Canny withoriginal
The choice of depends on desired behavior
• large detects large scale edges
• small detects fine features
34

35. Scale
• Smoothing
• Eliminates noise edges.
• Makes edges smoother.
• Removes fine detail.
35

36. 36

37. fine scale
high
threshold
37

38. coarse
scale,
high
threshold
38

39. coarse
scale
low
threshold
39

40. Scale space
• Properties of scale space (w/ 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
larger
Gaussian filtered signal
first derivative peaks
40

41. Edge detection by subtraction
original
41

42. Edge detection by subtraction
smoothed (5x5 Gaussian)
42

43. Edge detection by subtraction
smoothed – original
(scaled by 4, offset +128)
Why does
this work?
filter demo 43

44. Gaussian - image filter
Laplacian of Gaussian
Gaussian delta function
44

45. An edge is not a line...
45

46. Finding lines in an image
• Option 1:
• Search for the line at every possible position/orientation
• What is the cost of this operation?
• Option 2:
• Use a voting scheme: Hough transform
46

47. Finding lines in an image
• Connection between image (x,y) and Hough (m,b)
spaces
• A line in the image corresponds to a point in Hough space
• To go from image space to Hough space:
• given a set of points (x,y), find all (m,b) such that y = mx + b
x
y
m
b
m0
b0
image space Hough space
47

48. Finding lines in an image
• Connection between image (x,y) and Hough (m,b) spaces
• A line in the image corresponds to a point in Hough space
• To go from image space to Hough space:
• given a set of points (x,y), find all (m,b) such that y = mx + b
• What does a point (x0, y0) in the image space map to?
x
y
m
b
image space Hough space
– A: the solutions of b = -x0m + y0
– this is a line in Hough space
x0
y0
48

49. Corners contain more edges than
lines.
• A point on a line is hard to match.
Corner detection
49

50. Corners contain more edges than lines.
• A corner is easier
50

51. Edge Detectors Tend to Fail at Corners
51

52. Finding Corners
Intuition:
• Right at corner, gradient is ill defined.
• Near corner, gradient has two different
values.
52

53. Fuzzy Logic
&
Fuzzy Inference System (FIS)

54. Introduction to Fuzzy Sets
• Introduced by A. L. Zadeh (1965)
• Fuzzy sets provide the mechanism for dealing with imprecise
information
• Based and related closely to usage of probability in crisp information.
• Provides margin for error and its correction possibilities in both input
and output values.
• Takes into account full or partial membership and relationship
between one value to another.

55. Fuzzy
Inference
System
(FIS)
FIS
Types
Mamdani
Sugeno
Components
Membership
Functions
IF-THEN
Rules
Logical
Operations
Applications
DIP
Localizations
Network
Analysis

56. Steps in FIS

57. FIS Toolbox in MATLAB

58. Conventional FIS usage in DIP
FIS(4Input) Image processor Edge

59. My usage
Image
Restoration
Image
Enhancement
Noise
Removal using
LoG
FIS OutDIP2
Edge
Detection2
DIP 1
Edge
detection1
Mat2Gray
out1
FIS
Image
processor
FIS
Image
Processor
Edge Out
Mat2Gray
out
Filtration
Noise
Removal
Image
enhancement
Image
restoration

60. FIS 1

61. Membership Function of Input

62. Membership of Output

63. IF-THEN Rule set = 16

64. FIS2

65. Membership Function of Input

66. Membership of Output

67. IF-THEN Ruleset = 28 +10

68. Final
Outputs
Compare
d

69. Thank You