Image Filtering: Noise Removal, Sharpening, Deblurring. Yao Wang Polytechnic University, Brooklyn, NY11201
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1 Imag Filtring: Nois Rmoval, Sharpning, Dblurring Yao Wang Polytchnic Univrsity, Brooklyn, NY
2 Outlin Nois rmoval by avraging iltr Nois rmoval by mdian iltr Sharpning Edg nhancmnt Dblurring Yao Wang, 6 EE344: Imag Filtring
3 Nois Rmoval Imag Smoothing An imag may b dirty with dots, spckls,stains Nois rmoval: To rmov spckls/dots on an imag Dots can b modld as impulss salt-and-pppr or spckl or continuously varying Gaussian nois Can b rmovd by taking man or mdian valus o nighboring pixls.g. 3x3 window Equivalnt to low-pass iltring Problm with low-pass iltring May blur dgs Mor advancd tchniqus: adaptiv, dg prsrving Yao Wang, 6 EE344: Imag Filtring 3
4 Exampl Yao Wang, 6 EE344: Imag Filtring 4
5 Avraging Filtr Rplac ach pixl by th avrag o pixls in a squar window surrounding this pixl Trad-o btwn nois rmoval and dtail prsrving: Largr window -> can rmov nois mor ctivly, but also blur th dtails/dgs Yao Wang, 6 EE344: Imag Filtring 5
6 Exampl: 3x3 avrag Yao Wang, 6 EE344: Imag Filtring 6
7 Exampl Yao Wang, 6 EE344: Imag Filtring 7
8 Wightd Avraging Filtr Instad o avraging all th pixl valus in th window, giv th closr-by pixls highr wighting, and ar-away pixls lowr wighting. L ll L g m, n h k, l s m k, n l k L This typ o opration or arbitrary wighting matrics is gnrally calld -D convolution or iltring. Whn all th wights ar positiv, it corrsponds to wightd avrag. Wightd avrag iltr rtains low rquncy and supprsss high rquncy low-pass iltr Yao Wang, 6 EE344: Imag Filtring 8
9 Graphical Illustration Yao Wang, 6 EE344: Imag Filtring 9
10 Exampl Wighting Mask All wights must sum to on Yao Wang, 6 EE344: Imag Filtring
11 Yao Wang, 6 EE344: Imag Filtring Exampl: Wightd Avrag
12 Yao Wang, 6 EE344: Imag Filtring Filtring in -D: a Rviw Continuous-Tim Signal Extnsion to discrt tim D signals dt t h H H S G d t s h t h t s t g t τ τ τ Filtr rquncy rspons : Frquncy Domain : Tim Domain : / to / corrsponds to look at th rang only nds priodic, is Filtr rquncy rspons DTFT : Frquncy Domain : Tim Domain linar convolution : s n n m /, / - H n h H H S G m n s m h n h n s n s
13 Yao Wang, 6 EE344: Imag Filtring 3 Filtring in D.,/ /,,/ / to look at th squar rgion only nds priodic, is,,, th D Filtr Frquncy rspons o,,, In D rquncy domain,,, D Linar Convolution Wightd avraging H n m h H H S G l n k m s l k h n m g k k n n m l l m k k k l l l
14 Yao Wang, 6 EE344: Imag Filtring 4 Frquncy Rspons o Avraging Filtrs Avraging ovr a 3x3 window 9, n m h cos cos , H
15 H H, 3 H H cos, H cos 3 Sktch H Yao Wang, 6 EE344: Imag Filtring 5
16 Frquncy Rspons o Wightd Avraging Filtrs H b H u, v b b b b b b [ b ] b cosu b cosv / b b ; Yao Wang, 6 EE344: Imag Filtring 6
17 Avraging vs. Wightd Avraging H 9 H u, v [ ]; H b b b b [ b ] cos u cosv / 9 b H u, v b b b b cosu b cosv / b ; b Yao Wang, 6 EE344: Imag Filtring 7
18 Intrprtation in Frq Domain Filtr rspons Low-passd imag spctrum Original imag spctrum Nois spctrum Nois typically spans ntir rquncy rang, whr as natural imags hav prdominantly lowr rquncy componnts Yao Wang, 6 EE344: Imag Filtring 8
19 Mdian Filtr Problm with Avraging Filtr Blur dgs and dtails in an imag Not ctiv or impuls nois Salt-and-pppr Mdian iltr: Taking th mdian valu instad o th avrag or wightd avrag o pixls in th window Mdian: sort all th pixls in an incrasing ordr, tak th middl on Th window shap dos not nd to b a squar Spcial shaps can prsrv lin structurs Ordr-statistics iltr Instad o taking th man, rank all pixl valus in th window, tak th n-th ordr valu. E.g. max or min Yao Wang, 6 EE344: Imag Filtring 9
20 Exampl: 3x3 Mdian Matlab command: mdilta,[3 3] Yao Wang, 6 EE344: Imag Filtring
21 Exampl Yao Wang, 6 EE344: Imag Filtring
22 Matlab Dmo: nriltdmo Original Imag Corruptd Imag Filtrd Imag Can choos btwn man, mdian and adaptiv Winr iltr with dirnt window siz Yao Wang, 6 EE344: Imag Filtring
23 Nois Rmoval by Avraging Multipl Imags Yao Wang, 6 EE344: Imag Filtring 3
24 Imag Sharpning Sharpning : to nhanc lin structurs or othr dtails in an imag Enhancd imag original imag scald vrsion o th lin structurs and dgs in th imag Lin structurs and dgs can b obtaind by applying a dirnc oprator high pass iltr on th imag Combind opration is still a wightd avraging opration, but som wights can b ngativ, and th sum. In rquncy domain, th iltr has th highmphasis charactr Yao Wang, 6 EE344: Imag Filtring 4
25 Frquncy Domain Intrprtation Filtr rspons high mphasis sharpnd imag spctrum Original imag spctrum Yao Wang, 6 EE344: Imag Filtring 5
26 Yao Wang, 6 EE344: Imag Filtring 6 Highpass Filtrs Spatial opration: taking dirnc btwn currnt and avraging wightd avraging o narby pixls Can b intrprtd as wightd avraging linar convolution Can b usd or dg dtction Exampl iltrs All coicints sum to! ; 8 ; 8 ; 4 ; 4
27 Yao Wang, 6 EE344: Imag Filtring 7 Exampl Highpass Filtrs
28 Exampl o Highpass Filtring Original imag Isotropic dg dtction Binary imag Yao Wang, 6 EE344: Imag Filtring 8
29 Dsigning Sharpning Filtr Using High Pass Filtrs Th dsird imag is th original plus an appropriatly scald high-passd imag Sharpning iltr λ s h h s m, n δ m, n λh m, n h x gxx*h h x s xxagx x x x Yao Wang, 6 EE344: Imag Filtring 9
30 Yao Wang, 6 EE344: Imag Filtring 3 Exampl Sharpning Filtrs x x x s xxagx x gxx*h h x λ with H H s h λ with H H s h
31 Yao Wang, 6 EE344: Imag Filtring 3 Exampl o Sharpning 6 8 H s 8 4 H h
32 Exampl o Sharpning λ 4 λ 8 Yao Wang, 6 EE344: Imag Filtring 3
33 Challngs o Nois Rmoval and Imag Sharpning How to smooth th nois without blurring th dtails too much? How to nhanc dgs without ampliying nois? Still a activ rsarch ara Yao Wang, 6 EE344: Imag Filtring 33
34 Wavlt-Domain Filtring Courtsy o Ivan Slsnick Yao Wang, 6 EE344: Imag Filtring 34
35 Fatur Enhancmnt by Subtraction Taking an imag without incting a contrast agnt irst. Thn tak th imag again atr th organ is inctd som spcial contrast agnt which go into th bloodstrams only. Thn subtract th two imags --- A popular tchniqu in mdical imaging Yao Wang, 6 EE344: Imag Filtring 35
36 Imag Dblurring Nois rmoval considrd thus ar assums th imag is corruptd by additiv nois Each pixl is corruptd by a nois valu, indpndnt o nighboring pixls Imag blurring Whn th camra movs whil taking a pictur Or whn th obct movs Each pixl valu is th sum o surrounding pixls Th blurrd imag is a iltrd vrsion o th original Dblurring mthods: Invrs iltr: can advrsly ampliy nois Winr iltr gnralizd invrs iltr Many advancd adaptiv tchniqus Yao Wang, 6 EE344: Imag Filtring 36
37 Exampl o Motion Blur Yao Wang, 6 EE344: Imag Filtring 37
38 Invrs Filtring vs. Winr Filtring Yao Wang, 6 EE344: Imag Filtring 38
39 Constraind Last Squars Filtring Yao Wang, 6 EE344: Imag Filtring 39
40 What Should You Know How dos avraging and wightd avraging iltr works? How dos mdian iltr works? What mthod is bttr or additiv Gaussian nois? What mthod is bttr or salt-and-pppr nois? How dos high-pass iltring and sharpning work? For smoothing and sharpning: Can prorm spatial iltring using givn iltrs Driving rquncy rspons is not rquird, but should know th dsird shap or th rquncy rsponss in dirnt applications What is th challng in nois rmoval and sharpning? What causs blurring? Principl o dblurring: tchnical dtails not rquird Yao Wang, 6 EE344: Imag Filtring 4
41 Rrncs Gonzalz and Woods, Digital imag procssing, nd dition, Prntic Hall,. Chap 4 Sc 4.3, 4.4; Chap 5 Sc pags and -43 Yao Wang, 6 EE344: Imag Filtring 4
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