240-373: Chapter 8: Edge Detection 1 Montri Karnjanadecha [email protected] . ac.th/~montri 240-373 Image Processing

240-373: Chapter 8: Edge Detection

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Montri [email protected]://fivedots.coe.psu.ac.th/~montri

240-373 Image Processing


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Chapter 8

Edge Detection


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Basic Edge Detection

• Edge detection, ideally, identifies all the lines that outline the objects in an image.

• Template for edge detection:

- 1Y_difference(x,y) = value(x,y) value(x,y+ )

ii iiiiiiiiii ii iiiiiiiiii iiii iiiii iiii i i2 1x template

1

-1


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X_difference(x,y) = value(x,y) - value(x-1,y)

use the template-1 1

– Once X_difference and Y_difference are computed to create the single measurement of “gradient magnitude” (strength of the edge)


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– It is also useful to divide Y_difference by X_difference and identify a gradient direction (the angle of the edge between the regions)

ceX_differen

ceY_differentan),(irectiongradient_d 1yx


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Example

Image X_difference Y_difference Gradient Direction

1 1 1 1 1 0 0 0 0 * 0 0 0 0 0

* * * * *

1 1 1 1 1 0 0 0 0 * 0 0 0 1 1

* * *

- 1 1 1 0 0 0 0 1 0 * 0 0 1 0 0

* * * *

- 1 1 0 0 0 0 1 0 0 * 0 0 0 0 0

* * * *

- 1 1 0 0 0 0 1 0 0 * * * * * *

* * * *


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Example

4Technique : Sobel edge detection 3 3The Sobel x templates are normally given

ii

i-iiiiiiiii i-iiiiiiiii- 1 0 1 1 2 1

- 202 0 0 0

- 1 0 1 - - -1 2 1


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Example

Image abs A + abs B Threshold at 12

3444332100

2342334010

3333433100

3233420200

2420001000

3302000000

8642212122

42421014104

061216201086

414121410464

00000110

00000100

00111000

01110000


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10


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Second-order edge detection

• An image such as

• The basic Sobel vertical edge operator yields

987654321

987654321

987654321

987654321

987654321

101

202

101

8888888

8888888

8888888


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• Applying the edge operator again yields

• This is similar to the differentiation opera tor applied to a straight line, e.g.

if y 3= x - 2 , then

00000

0 and 32

2

dx

yd

dx

dy


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Laplacian template

– can reduce gradient of lighting– iiiiiiii iiiii

111

181

111

or

010

141

010


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Pyramid Edge Detection

5:Technique Pyramid edge detection USE: To enhance substantial (strong and l

ong) edges but to ignore the weak or sho rt edges

THEORY:– iii ii iii ii iii iii i ii iiiiiii– iiii iiiii ii iii iiiiiii-iiii iiiii ii i

i iiiiiii ii iii iiii iiiiiiiiiiiii iiii - l s i n t he f ul l si ze i mage


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THEORY: (cont’d)– This repeats until unwanted edges are invisi

iii– ii iiii iiiiiiii ii iiiiiii ii iii iiiiiiii

image and where edge pixels have been fou nd, an edge detector is applied to the corres

ponding four pixels in the next largest image


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OPERATION:– iiiiii i iiiiii iiiii ii iiii 2m/ i 2n/

by eval uat i ng f or each i i0 < < and 0< j < n

– This is repeated and each generated image is kept

– With the smallest image, perform some edge detection--such as Sobel

)1,1()1,(),1(),(4

1

2,

2

jiIjiIjiIjiI

jiI


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OPERATION: (cont’d)

– In pixels where edges are discovered, perform as edge detection operation on the group of four corresponding pixels in the next largest image

– Continue to find the best edges down through the pyramid of images until the main edges in the original image have been discovered


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Edge Following

7Technique : Simple edge following USE: Knowing that a pixel is on an edge, the

edge will be followed so that an objected i s outlined

OPERATION:– Suppose that a position on the edge has been

identified, call it (x,y) and flag this position asused

– Evaluate all the 3x3 Sobel gradient values cen tered on each of the eight pixels surrounding (

x,y)


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Edge Following


– Choose the three pixels with the greatest abs olute gradient magnitude

– - Put these three pixel in a three column array– Order them in row according to the gradient

magnitude– Choose the one with greatest gradient magni

tude


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Edge Following


– - 07Now this pixel will be one of the direction wiii iiiiiii ii iii iiiii (x,y) iiiii ii iii iiiiii

ing map, where * is the position of pixel (x,y) 012

7*3

6 5 4

– iiii iii iiiiiiiii ii iiiiii d– iiiiii iii iiiiiiiii iii iiii ii iiii iiiiii ii

d , (d i+ 1 ) 8 , and (d- 1 8) mod iiiiiiiiii


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Edge Following


– If no suitable high value of gradient magnitu de is found, remove the pixel from the list an

d choose the next one of the three stored. M ove up one row if all three are removed

– Stop when the original pixel is reached, or ex ecution has gone too long, or the number of r

ii i ii iii iiii ii iiii iiiii

Documents

240-373: Chapter 8: Edge Detection 1 Montri Karnjanadecha [email protected] . ac.th/~montri 240-373 Image Processing