1. Edge Detection Phil Mlsna, Ph.D. Dept. of Electrical Engineering
Northern Arizona University

2. Some Important Topics in Image Processing
Contrast enhancement
Filtering (both spatial and frequency domains)
Restoration
Segmentation
Image Compression
etc.
EE 460/560 course, Fall 2003
(formerly CSE 432/532)
Edge Detection uses spatial filtering to extract
important information from a scene.

3. Types of Edges Physical Edges Image Edges
Different objects in physical contact
Spatial change in material properties
Abrupt change in surface orientation
Image Edges
In general: Boundary between contrasting regions in image
Specifically: Abrupt local change in brightness
Image edges are important clues for identifying and interpreting physical edges in the scene.

4. Goal: Produce an Edge Map
Original Image
Edge Map

5. Edge Detection Concepts in 1-D
Edges can be characterized as either:
local extrema of
zero-crossings of

6. Continuous Gradient But is a vector.
We really need a scalar that gives a measure of edge
“strength.”
This is the gradient magnitude. It’s isotropic.

7. Classification of Points
Let points that satisfy be edge points.
PROBLEM: T
Non-zero edge width
Stronger gradient magnitudes produce thicker edges.
To precisely locate the edge, we need to thin. Ideally,
edges should be only one point thick.

8. Practical Gradient Algorithm
Compute for all points.
Threshold to produce candidate edge points.
Thin by testing whether each candidate edge point is a local maximum of along the direction of
. Local maxima are classified as edge points.

9. Cameraman
image
Thresholded
Gradient
Thresholded and
Thinned

10. Directional Edge Detection
Horizontal operator
(finds vertical edges)
Vertical operator (finds horizontal edges)
finds edges perpendicular to the direction

11. Horizontal Difference
Directional Examples
Horizontal Difference
Operator
Vertical Difference
Operator

12. Discrete Gradient Operators
Pixels are samples on a discrete grid.
Must estimate the gradient solely from these samples.
STRATEGY: Build gradient estimation filter kernels and convolve them with the image.
Two basic filter concepts
First difference:
Central difference:

13. Simple Filtering Example in 1-D
Convolving
with
[ ]
[ 0]

14. Simple Filtering Example in 1-D
Convolving
with
[ ]
[ 0 0]

15. Simple Filtering Example in 1-D
Convolving
with
[ ]
[ ]

16. Simple Filtering Example in 1-D
Convolving
with
[ ]
produces:
[ ]

17. Gradient Estimation 1. Create orthogonal pair of filters,
2. Convolve image with each filter:
3. Estimate the gradient magnitude:

18. Roberts Operator Small kernel, relatively little computation
First difference (diagonally)
Very sensitive to noise
Origin not at kernel center
Somewhat anisotropic

19. Noise Noise is always a factor in images.
Derivative operators are high-pass filters.
High-pass filters boost noise!
Effects of noise on edge detection:
False edges
Errors in edge position
Key concept:
Build filters to respond to edges and suppress noise.

20. Prewitt Operator Larger kernel, somewhat more computation
Central difference, origin at center
Smooths (averages) along edge, less sensitive to noise
Somewhat anisotropic

21. Sobel Operator 3 x 3 kernel, same computation as Prewitt
Central difference, origin at center
Better smoothing along edge, even less sensitive to noise
Still somewhat anisotropic

22. Discrete Operators Compared
Original
Roberts

23. Roberts
Prewitt

24. Prewitt
Sobel

25. T = 5
T = 10
Roberts
T = 40
T = 40
T = 20

26. Continuous Laplacian This is a scalar. It’s also isotropic.
Edge detection: Find all points for which
No thinning is necessary.
Tends to produce closed edge contours.

27. Discrete Laplacian Operators
Origin at center
Only one convolution needed, not two
Can build larger kernels by sampling Laplacian of Gaussian

28. Laplacian of Gaussian (Marr-Hildreth Operator)
Let:
Then:

29. LoG Filter Impulse Response

30. LoG Filter Frequency Response

31. Laplacian of Gaussian Examples

32. LoG Properties One filter, one convolution needed
Zero-crossings are very sensitive to noise (2nd deriv.)
Bandpass filtering reduces noise effects
Edge map can be produced for a given scale
Scale-space or pyramid decomposition possible
Found in biological vision!!
Practical LoG Filters:
Kernel at least 3 times width of main lobe, truncate
Larger kernel  more computation

33. Summary Edges can be detected from the derivative:
Extrema of gradient magnitude
Zero-crossings of Laplacian
Practical filter kernels; convolve with image
Noise effects
False edges
Imprecise edge locations
Correct filtering attempts to control noise
Edge map is the goal

34. Questions?