Tran_EdgeDetection.ppt

Edge Detection
Hao Huy Tran
Computer Graphics and Image Processing
CIS 581 – Fall 2002
Professor: Dr. Longin Jan Latecki

Edge Detection
• What are edges in an image?
• Edge Detection
• Edge Detection Methods
• Edge Operators
• Matlab Program
• Performance

What are edges in an image?
 Edges are those places
in an image that
correspond to object
boundaries.
 Edges are pixels where
image brightness
changes abruptly.
Brightness vs. Spatial Coordinates

More About Edges
 An edge is a property attached to an
individual pixel and is calculated from the
image function behavior in a neighborhood
of the pixel.
 It is a vector variable (magnitude of the
gradient, direction of an edge) .
 More information about edges can be found
in Dr. Latecki’s Lecture on Filter.

Edge Detection
 Edge information in an image is found by looking
at the relationship a pixel has with its
neighborhoods.
 If a pixel’s gray-level value is similar to those
around it, there is probably not an edge at that
point.
 If a pixel’s has neighbors with widely varying gray
levels, it may present an edge point.

Edge Detection Methods
 Many are implemented with convolution
mask and based on discrete approximations
to differential operators.
 Differential operations measure the rate of
change in the image brightness function.
 Some operators return orientation
information. Other only return information
about the existence of an edge at each point.

Roberts Operator
 Mark edge point only
 No information about edge orientation
 Work best with binary images
 Primary disadvantage:
 High sensitivity to noise
 Few pixels are used to approximate the gradient

Roberts Operator (Cont.)
 First form of Roberts Operator
 Second form of Roberts Operator
   2
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Sobel Operator
 Looks for edges in both horizontal and vertical
directions, then combine the information into a
single metric.
 The masks are as follows:
Edge Magnitude = Edge Direction =
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Prewitt Operator
 Similar to the Sobel, with different mask
coefficients:
Edge Magnitude = Edge Direction =

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tan

Kirsch Compass Masks
 Taking a single mask and rotating it to 8
major compass orientations: N, NW, W, SW,
S, SE, E, and NE.
 The edge magnitude = The maximum value
found by the convolution of each mask with
the image.
 The edge direction is defined by the mask
that produces the maximum magnitude.

Kirsch Compass Masks (Cont.)
 The Kirsch masks are defined as follows:
 EX: If NE produces the maximum value, then the
edge direction is Northeast


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W
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S
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E

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





3
3
5
3
0
5
3
3
5
NW
















3
5
5
3
0
5
3
3
3
SW
















5
5
5
3
0
3
3
3
3
SE















5
5
3
5
0
3
5
3
3
NE

Robinson Compass Masks
 Similar to the Kirsch masks, with mask
coefficients of 0, 1, and 2:














1
0
1
2
0
2
1
0
1
N














0
1
2
1
0
1
2
1
0
W














1
2
1
0
0
0
1
2
1
S














2
1
0
1
0
1
0
1
2
E














1
0
1
2
0
2
1
0
1
NW








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


0
1
2
1
0
1
2
1
0
SW









 



1
2
1
0
0
0
1
2
1
SE














2
1
0
1
0
1
0
1
2
NE

Laplacian Operators
 Edge magnitude is approximated in digital
images by a convolution sum.
 The sign of the result (+ or -) from two
adjacent pixels provide edge orientation and
tells us which side of edge brighter

Laplacian Operators (Cont.)
 Masks for 4 and 8 neighborhoods
 Mask with stressed significance of the
central pixel or its neighborhood














0
1
0
1
4
1
0
1
0


















1
1
1
1
8
1
1
1
1














1
2
1
2
4
2
1
2
1














2
1
2
1
4
1
2
1
2

Edge Map In Matlab Program
 Implement all methods in this presentation
 Set up edge detection mask(s)
 Use convolution method (filter2 function)
 Calculate edge magnitude
 Show the result of edge map
 No calculation of edge direction

Performance
 Sobel and Prewitt methods are very
effectively providing good edge maps.
 Kirsch and Robinson methods require more
time for calculation and their results are not
better than the ones produced by Sobel and
Prewitt methods.
 Roberts and Laplacian methods are not very
good as expected.

A Quick Note
 Matlab’s image processing toolbox provides
edge function to find edges in an image.
 Edge function supports six different edge-
finding methods: Sobel, Prewitt, Roberts,
Laplacian of Gaussian, Zero-cross, and
Canny.
 Edge is a powerful edge-detection method

Tran_EdgeDetection.ppt

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