Digital Image Processing

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1 5 Imag Rsoraion and Rconsrcion Digial Imag Procssing Jn-i Chang Dparmn o Compr cinc Naional Chiao ng Unirsi 5. A Modl o h Imag Dgradaion/Rsoraion Procss 5. Nois Modls 5.3 Rsoraion in h Prsnc o Nois Onl - paial ilring 5.4 Priodic Nois Rdcion b rqnc Domain ilring 5.5 Linar Posiion-Inarian Dgradaions 5.6 Esimaing h Dgradaion ncion 5.7 Inrs ilring 5.8 Minimm Man qar Error Winr ilring 5.9 Consraind Las qars ilring 5. omric Man ilr 5. Imag Rconsrcion rom Procions 5. A Modl o h Imag Dgradaion/Rsoraion Procss 5. Nois Modls 5.. paial and rqnc Propris o Nois 5.. om Imporan Nois Probabili Dnsi ncions = + N sal & pppr Nois Modls 5.. paial and rqnc Propris o Nois 5.. om Imporan Nois Probabili Dnsi ncions E. 5. Nois imags and hir hisograms 5. Nois Modls 5.. paial and rqnc Propris o Nois 5.. om Imporan Nois Probabili Dnsi ncions E. 5. Nois imags and hir hisograms 5 6

2 5. Nois Modls 5..3 Priodic Nois 5. Nois Modls 5..4 Esimaion o Nois Paramrs Man & Varianc {a b} Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Man ilrs Arihmic Man ilr ˆ g s Q = mn s 5.3 Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Man ilrs E. 5. omric Man ilr ˆ s g s mn N 4 armonic Man ilr ˆ mn s g s Q = Conraharmonic Man ilr ˆ s s g s g s Q Q AM M Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Man ilrs E Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Man ilrs E. 5. pppr: % sal: % pppr: % sal: % ˆ s s g s Q g s Q ˆ s s g s Q g s Q CM: Q =.5 Q = CM: Q =.5 Q =.5

3 5.3 Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Ordr-aisic ilrs Mdian ilr ˆ mdian{ g s } s bipolar and nipolar impls nois Ma ilrs ˆ ma { g s } s pppr nois. Min ilrs ˆ min { g s } s sal nois. Midpoin ilr ˆ ma { g s } min { g s } s s assian nois and niorm nois. Alpha-rimmd Man ilr ˆ g r s mn d s mlipl ps o nois.g. a combinaion o sal-andpppr and assian nois Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Ordr-aisic ilrs E. 5.3 P a = P b = % Mdian- Mdian- Mdian Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Ordr-aisic ilrs E Rsoraion in h Prsnc o Nois Onl paial ilring 5.3. Ordr-aisic ilrs M A-Man d = 5 E. 5.3 pppr: % sal: % niorm + P & : % Ma Min 5 niorm: /8 AM Mdian Rsoraion in h Prsnc o Nois Onl paial ilring Adapi ilrs E Rsoraion in h Prsnc o Nois Onl paial ilring Adapi ilrs E. 5.5 Adapi mdian ilr N AM P a = P b = 5% Mdian Adapi mdian M ˆ g g m L L local nois rdcion A. I z min < z md < z ma go o sag B Els incras h window siz I window siz ma rpa sag A Els op z md B. I z min < z < z ma op z Els op z md. 7 8

4 5.4 Priodic Nois Rdcion b rqnc Domain ilring 5.4. Bandrc ilrs 5.4 Priodic Nois Rdcion b rqnc Domain ilring 5.4. Bandrc ilrs E. 5.6 Bandrc ilring or priodic nois rmoal abl Priodic Nois Rdcion b rqnc Domain ilring 5.4. Bandpass ilrs 5.4 Priodic Nois Rdcion b rqnc Domain ilring Noch ilrs E. 5.7 Bandpass ilring or racing nois parns 5.4 Priodic Nois Rdcion b rqnc Domain ilring Noch ilrs E. 5.8 Rmoal o priodic nois b noch ilring? 5.4 Priodic Nois Rdcion b rqnc Domain ilring Noch ilrs E. 5.8 Rmoal o priodic nois b noch ilring 3 4

5 5.4 Priodic Nois Rdcion b rqnc Domain ilring Opimm Noch ilring E Priodic Nois Rdcion b rqnc Domain ilring Opimm Noch ilring E. 5.9 con. g N = NP Priodic Nois Rdcion b rqnc Domain ilring Opimm Noch ilring 5.5 Linar Posiion-Inarian Dgradaion E. 5.9 con. ˆ g w Minimizaion o local arianc g g w Man ps o dgradaion can b approimad b linar posiioninarian conolion ingral rdholm ingral o h irs ind: g h dd poin sprad ncion = + N Esimaing h Dgradaion ncion 5.6. Esimaion b Imag Obsraion srong signals s s ˆ 5.6. Esimaion b Eprimnaion s 5.6 Esimaing h Dgradaion ncion Esimaion b Modling original 5 / =.5 6 h =. =.5 9 3

6 3 5.6 Esimaing h Dgradaion ncion Esimaion b Modling d g dd d dd g d dd d d d E. Imag blrring d o niorm linar moion 3 ppos = a/ and = b/ a a a a d d sin / sin b a b a b a 5.6 Esimaing h Dgradaion ncion Esimaion b Modling ppos h imag ndrgos niorm linar moion in h -dircion onl. E. con Esimaing h Dgradaion ncion Esimaion b Modling E. 5. = = / = g Inrs ilring ˆ ˆ N Ma cas problm or small canno b clos o zro or all Comp / onl a low rqncis 35 E. 5. D = 7 D = 85 D = 4 D = N 6 5 / 5.7 Inrs ilring Minimm Man qar Error Winr ilring } ˆ { E / / * * ˆ ˆ K Minimiz:

7 5.8 Minimm Man qar Error Winr ilring E Minimm Man qar Error Winr ilring E. 5.3 N 65 IV Winr N 65 IV D = N IV D = 7 Winr K=? N Consraind Las qars Rsoraion Vcor-mari orm o g = h+: g 5.9 Consraind Las qars Rsoraion E. 5.4 A comparison Winr Minimiz: C bc o: M N g - ˆ smoohnss ˆ * P Consraind Las qars p Consraind Las qars Rsoraion E omric Man ilr ˆ * * inrs ilr paramric Winr ilr corrc nois paramrs wrong nois paramrs = inrs ilr = paramric Winr ilr = = sandard Winr ilr = / = spcrm qalizaion ilr 4 4

8 5. Imag Rconsrcion rom Procions 5.. Inrodcion E. Rconsrcing an imag rom a sris o procions 5. Imag Rconsrcion rom Procions 5.. Inrodcion E. Rconsrcing an imag rom a sris o procions Imag Rconsrcion rom Procions 5.. Inrodcion E. Bacprocion o a simpl planar rgion conaining wo obcs 5. Imag Rconsrcion rom Procions 5.. Principls o Compd omograph C or gnraions o C scannrs Imag Rconsrcion rom Procions 5..3 Procions and h Radon ransorm 5. Imag Rconsrcion rom Procions 5..3 Procions and h Radon ransorm inograms Radon ransorm cos sin g dd g M N cos sin 47 48

9 5. Imag Rconsrcion rom Procions 5..3 Procions and h Radon ransorm Bac-procion or a id orinaion g g cos sin 5. Imag Rconsrcion rom Procions 5..3 Procions and h Radon ransorm E 5.8 Bacprocions o h sinograms Bac-procd Imag Laminogram: g cos sin d g cos sin Imag Rconsrcion rom Procions 5..4 h orir-lic horm 5. Imag Rconsrcion rom Procions 5..5 Rconsrcion Using Paralll-Bam ilrd Bacprocions g d cos sin cos sin cos ; sin cos sin cos sin dd dd cos ; sin ddd d dd dd cos sin cos sin cos sin cos sin dd dd d cos sin d c. g cos sin d dd Imag Rconsrcion rom Procions 5..5 Rconsrcion Using Paralll-Bam ilrd Bacprocions 5. Imag Rconsrcion rom Procions 5..5 Rconsrcion Using Paralll-Bam ilrd Bacprocions Bo ilr E 5.9 Bo amming c c cos h M M ohrwis c =.54 amming window c =.5 anning window 53 54

10 5. Imag Rconsrcion rom Procions 5..5 Rconsrcion Using Paralll-Bam ilrd Bacprocions E Imag Rconsrcion rom Procions 5..5 Rconsrcion Using Paralll-Bam ilrd Bacprocions paial-domain Implmnaion L s dno h inrs orir ransorm o. s g d cos sin cos sin d d g s cos sin d d Bo amming 55 56