2 Contnts Digital Imag Procssing Imag Enhancmnt (Spatial Filtring ) In this lctur w will look at spatial filtring tchniqus: Nighbourhood oprations What is spatial filtring? Smoothing oprations What happns at th dgs? Corrlation and convolution Cours Wbsit: http://www.comp.dit.i/bmacnam 3 Nighbourhood Oprations Nighbourhood oprations simpl oprat on a largr nighbourhood pils than point oprations Nighbourhoods ar mostl a rctangl around a cntral pil An siz rctangl and an shap filtr ar possibl Nighbourhood Imag f (, ) (, ) 4 Simpl Nighbourhood Oprations Som simpl nighbourhood oprations includ: Min: St th pil valu to th minimum in th nighbourhood Ma: St th pil valu to th maimum in th nighbourhood Mdian: Th mdian valu a st numbrs is th midpoint valu in that st (.g. from th st [, 7, 5, 8, 24] 5 is th mdian). Somtims th mdian works bttr than th avrag IF-UTAMA
5 al Imag Simpl Nighbourhood Oprations Eampl 23 27 28 5 30 40 45 48 53 67 72 33 54 83 2 4 4 9 207 20 8 5 64 70 75 62 73 5 Enhancd Imag 6 Th Spatial Filtring Procss Simpl 33 Nighbourhood Imag f (, ) 33 Filtr a b c d f g h i al Imag Pils r s t u v w z Filtr procssd = v + ra + sb + tc + ud + wf + g + h + zi Th abov is rpatd for vr pil in th original imag to gnrat th filtrd imag 7 Spatial Filtring: Equation Form 8 Smoothing Spatial Filtrs Imags takn from Gonzalz & Woods, Digital Imag Procssing (2002) a b g (, ) = w( s, t) f ( + s, + t) s= at= b Filtring can b givn in quation form as shown abov Notations ar basd on th imag shown to th lft On th simplst spatial filtring oprations w can prform is a smoothing opration Simpl avrag all th pils in a nighbourhood around a cntral valu Espciall usful in rmoving nois from imags Also usful for highlighting gross dtail Simpl avraging filtr IF-UTAMA 2
9 Smoothing Spatial Filtring 0 Imag Smoothing Eampl Simpl 33 Nighbourhood 04 / 00 9 08 Imag f (, ) 95 99 / 06 9 / 33 Smoothing 9 98 / 9 / Filtr 9 90 85 04 00 08 99 06 98 95 90 85 al Imag Pils Filtr = 06 + 04 + 00 + 08 + 99 + 98 + 95 + 90 + 85 = 98.3333 Th abov is rpatd for vr pil in th original imag to gnrat th smoothd imag Imags takn from Gonzalz & Woods, Digital Imag Procssing (2002) Th imag at th top lft is an original imag siz 500500 pils Th subsqunt imags show th imag aftr filtring with an avraging filtr incrasing sizs 3, 5, 9, 5 and 35 Notic how dtail bgins to disappar Wightd Smoothing Filtrs 2 Anothr Smoothing Eampl Mor ffctiv smoothing filtrs can b gnratd b allowing diffrnt pils in th nighbourhood diffrnt wights in th avraging function Pils closr to th cntral pil ar mor important Oftn rfrrd to as a wightd avraging / 6 2 / 6 / 6 2 / 6 4 / 6 2 / 6 / 6 2 / 6 / 6 Wightd avraging filtr Imags takn from Gonzalz & Woods, Digital Imag Procssing (2002) B smoothing th original imag w gt rid lots th finr dtail which lavs onl th gross faturs for thrsholding al Imag Smoothd Imag Thrsholdd Imag IF-UTAMA 3
3 Avraging Filtr Vs. Mdian Filtr Eampl 4 Simpl Nighbourhood Oprations Eampl Imags takn from Gonzalz & Woods, Digital Imag Procssing (2002) al Imag With Nois Imag Aftr Avraging Filtr Imag Aftr Mdian Filtr Filtring is tn usd to rmov nois from imags Somtims a mdian filtr works bttr than an avraging filtr 23 27 28 5 30 40 45 48 53 67 72 33 54 83 2 4 4 9 207 20 8 5 64 70 75 62 73 5 5 Strang Things Happn At Th Edgs! At th dgs an imag w ar missing pils to form a nighbourhood Imag f (, ) 6 Strang Things Happn At Th Edgs! (cont ) Thr ar a fw approachs to daling with missing dg pils: Omit missing pils Onl works with som filtrs Can add tra cod and slow down procssing Pad th imag Tpicall with ithr all whit or all black pils Rplicat bordr pils Truncat th imag Allow pils wrap around th imag Can caus som strang imag artfacts IF-UTAMA 4
7 Simpl Nighbourhood Oprations Eampl 8 Strang Things Happn At Th Edgs! (cont ) 23 27 28 5 30 40 45 48 53 67 72 33 54 83 2 4 4 9 207 20 8 5 64 70 75 62 73 5 Imags takn from Gonzalz & Woods, Digital Imag Procssing (2002) al Imag Filtrd Imag: Zro Padding Filtrd Imag: Rplicat Edg Pils Filtrd Imag: Wrap Around Edg Pils Corrlation & Convolution Th filtring w hav bn talking about so far is rfrrd to as corrlation with th filtr itslf rfrrd to as th corrlation krnl Convolution is a similar opration, with just on subtl diffrnc a b c d f g h al Imag Pils r s t u v w z Filtr procssd = v + za + b + c + wd + u + tf + sg + rh For smmtric filtrs it maks no diffrnc 20 Summar In this lctur w hav lookd at th ida spatial filtring and in particular: Nighbourhood oprations Th filtring procss Smoothing filtrs Daling with problms at imag dgs whn using filtring Corrlation and convolution Nt tim w will looking at sharpning filtrs and mor on filtring and imag nhancmnt IF-UTAMA 5