Image Processing 5-SpatialFiltering1.ppt

8/9/2019 Image Processing 5-SpatialFiltering1.ppt

1/33

1

of

19

Interesting article in

the March, 2006

issue of Wired

magazine

Read it here

http://www.wired.com/wired/archive/14.03/lapd.htmlhttp://www.wired.com/wired/archive/14.03/lapd.html


2/33

Course Website: htt:!!"""#com#dit#ie!bmacnamee

$igital Image %rocessing

Image &nhancement'(atial )iltering 1*

http://www.comp.dit.ie/bmacnameehttp://www.comp.dit.ie/bmacnamee


3/33

+

of

19Contents

In this lecture "e "ill loo at satial filteringtechni-ues:

. /eighbourhood oerations

. What is satial filtering . (moothing oerations

. What haens at the edges

. Correlation and conolution


4/33

of

19/eighbourhood 3erations

/eighbourhood oerations siml4 oerateon a larger neighbourhood of i5els than

oint oerations

/eighbourhoods aremostl4 a rectangle

around a central i5el

n4 size rectangleand an4 shae filter

are ossible

Origin x

y Image f (x, y)

(x, y)

Neighbourhood


5/33

7

of

19(imle /eighbourhood 3erations

(ome simle neighbourhood oerationsinclude:

. Min: (et the i5el alue to the minimum in

the neighbourhood . Max: (et the i5el alue to the ma5imum in

the neighbourhood

. Median: 8he median alue of a set of

numbers is the midoint alue in that set 'e#g#

from the set 1, , 17, 1;, 2< 17 is the

median*# (ometimes the median "ors better

than the aerage


6/33

6

of

19

(imle /eighbourhood 3erations

&5amle

12+ 12 12; 119 117 1+0

10 17 1; 17+ 16 12

1++ 17 1;+ 192 19 191

19 199 20 210 19; 197

16 10 17 162 1+ 171

Original Image x

y

Enhanced Image x

y


7/33

of

198he (atial )iltering %rocess

r s t

u v w

x y z

Origin x

y Image f (x, y)

e processed = v*e +

r *a + s*b + t *c +

u*d + w*f + x*g + y*h + z *i

Filter Simple 3*3

Neighbourhood e 3*3 Filter

a b c

d e f

g h i

Original ImagePixels

*

8he aboe is reeated for eer4 i5el in the

original image to generate the filtered image


8/33

;

of

19(atial )iltering: &-uation )orm

∑∑−= −=

++=

a

a s

b

bt

t y s x f t sw y x g ),(),(),(

)iltering can be gienin e-uation form as

sho"n aboe

/otations are basedon the image sho"n

to the left

I m a g e s t a e n f r o m = o n z a l e z > W o o d s ,

$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


9/33

9

of

19(moothing (atial )ilters

3ne of the simlest satial filteringoerations "e can erform is a smoothing

oeration

. (iml4 aerage all of the i5els in aneighbourhood around a central alue

. &seciall4 useful

in remoing noise

from images

. lso useful for

highlighting gross

detail

1!91!9

1!9

1!91!9

1!9

1!91!9

1!9

(imleaeraging

filter


10/33

10

of

19(moothing (atial )iltering

1!9 1!9 1!91!9

1!91!9

1!91!9

1!9

Origin x

y Image f (x, y)

e = 1/9*106 +1/9*104 +

1/9*100 +1/9*108 +

1/9*99 + 1/9*98 +1/9*95 +

1/9*90 +1/9*85

= 98.3333

Filter Simple 3*3

Neighbourhood 1!

10

99

97

100 10;

9;

90 ;7

1!91!9

1!9

1!91!9

1!9

1!91!9

1!9

3*3 Smoothing

Filter

1" 1 1#

$$ 1! $#

$% $ #%

Original ImagePixels

*

8he aboe is reeated for eer4 i5el in the

original image to generate the smoothed image


11/33


12/33

12

of

19Image (moothing &5amle


$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


13/33

1+

of



$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


14/33

1

of



$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


15/33

17

of



$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


16/33

16

of



$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


17/33

1

of



$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


18/33

1;

of

19Weighted (moothing )ilters

More effectie smoothing filters can begenerated b4 allo"ing different i5els in the

neighbourhood different "eights in the

aeraging function . %i5els closer to the

central i5el are more

imortant

. 3ften referred to as a

weighted averaging

1!162!16

1!16

2!16!16

2!16

1!162!16

1!16

Weighted

aeraging filter


19/33

19

of

19 nother (moothing &5amle

@4 smoothing the original image "e get ridof lots of the finer detail "hich leaes onl4

the gross features for thresholding


$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *

Original Image Smoothed Image Thresholded Image


20/33

20

of

19

eraging )ilter As# Median )ilter

&5amle

)iltering is often used to remoe noise fromimages

(ometimes a median filter "ors better than

an aeraging filter

Original Image

With Noise

Image After

Averaging Filter

Image After

Median Filter


$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


21/33

21

of

19


&5amle


$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


22/33

22

of

19


&5amle


$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


23/33

2+

of

19


&5amle


$ i g i t a l I m a

g e % r o c e s s i n g ' 2 0 0 2 *


24/33

2

of

19


&5amle

12+ 12 12; 119 117 1+0

10 17 1; 17+ 16 12

1++ 17 1;+ 192 19 191

19 199 20 210 19; 197

16 10 17 162 1+ 171

x

y


25/33

27

of

19(trange 8hings Baen t 8he &dges

Origin x

y Image f (x, y)

e

e

e

e

t the edges of an image "e are missingi5els to form a neighbourhood

e e

e

( 8hi B 8h &d


26/33

26

of

19

(trange 8hings Baen t 8he &dges

'contD*

8here are a fe" aroaches to dealing "ithmissing edge i5els:

. 3mit missing i5els

E 3nl4 "ors "ith some filtersE Can add e5tra code and slo" do"n rocessing

. %ad the image

E 84icall4 "ith either all "hite or all blac i5els

. Relicate border i5els

. 8runcate the image

. llo" i5els wrap around the image

E Can cause some strange image artefacts

(i l / i hb h d 3 ti


27/33

2

of

19


&5amle

12+ 12 12; 119 117 1+0

10 17 1; 17+ 16 12

1++ 17 1;+ 192 19 191

19 199 20 210 19; 197

16 10 17 162 1+ 171

x

y

(t 8hi B t 8h &d


28/33

2;

of

19


'contD*

3riginal

Image

)iltered Image:

Fero %adding

)iltered Image:

Relicate &dge %i5els

)iltered Image:

Wra round &dge %i5els

I m

a g e s t a e n f r o m = o n z a l e z > W o o d s ,

$ i g i t a l I m a g e % r o c e s s i n g ' 2 0 0 2 *

(t 8hi B t 8h &d


29/33

29

of

19


'contD*

I m



(t 8hi B t 8h &d


30/33

+0

of

19


'contD*

I m




31/33


32/33


33/33

++

of

19(ummar4

In this lecture "e hae looed at the idea ofsatial filtering and in articular:

. /eighbourhood oerations

. 8he filtering rocess

. (moothing filters

. $ealing "ith roblems at image edges "henusing filtering

. Correlation and conolution/e5t time "e "ill looing at shareningfilters and more on filtering and image

enhancement

Image Processing 5-SpatialFiltering1.ppt

Documents

Transcript of Image Processing 5-SpatialFiltering1.ppt