Topic 3 - Image Enhancement. (Part 2) Spatial Filtering

Transcription

1 Topic 3 - Image Enhancement Part Spatial Filtering Spatial iltering - iltering operations that are perormed directl on the piels o an image Use o spatial mask Spatial iltering Operation moing the mask rom point to point in an image

2 Initial mask position Operation irection o moement o the mask is top let to bottom right o the image Image Final mask position R w w w 3 Inpt Otpt w 4 w 5 w 6 w 7 w 8 w 9 A 33 mask with arbitrar coeicients Reslt or Response o Linear Filtering R R w w w33... w9 w mask coeicients 9 9 i w i i ales o the image gra leels corresponding to the those coeicients

3 Problem when implementing neighborhood operations when the center o the ilter approaches the border o image Mask Soltion: Inpt Image. To limit the mask to operate at a distance n / piels awa rom the border o the image; n sie o n n mask Otpt image sie smaller than Inpt image sie. To pad the image b adding rows and colmns o 0 s or other gra ales or replicate rows and colmns Otpt image sie Inpt image sie Use o Forier transorm Freqenc iltering Lowpass ilter Highpass ilter Bandpass ilter Low-pass Filter LPF Retains onl gross image eatres Smoothens an image High-pass Filter HPF Retains onl the detailed eatres Sharpens edges and other details in an image Band-pass Filter BPF Retains intermediate leel eatres 3

4 Freqenc omain Time omain Smoothing Filters Applications o Smoothing Filters:. For Blrring Blrring: sed in preprocessing to remoe small details rom an image and or bridging small gaps in lines/cres. For Noise Redction The concept behind smoothing ilters: Vale o eer piel in an image is replaced with the gra leels in the neighborhood deined b the ilter mask This cases the otpt image to hae redced sharp transitions in gra leels 4

5 Lowpass spatial iltering Shape indicates all positie coeicients Gassian nction I all ale are iide b 9 AVERAGE Filter Need to remoe details simple aeraging Use eqal mask weights Bigger the mask greater the smoothing /9 /9 /9 Eample /9 /9 /9 /9 /9 /9 33 LPF mask Smoothing sing aeraging original Ater repeated aeraging 5

6 Smoothing- Median iltering Nonlinear masking/iltering operation Otpt piel median ale among all the neighborhood piels Eects: Ecellent in remoing salt and pepper tpe o noise oes not shit bondaries oes not aect brightness change across steps Median iltering -eample Piels within a 33 window Ranked list: otpt piel ale Median 7 6

7 Smoothing a nois image Nois original Ater aeraging Ater median iltering Appl Median ilter

8 High pass spatial ilter HPF is complement o low pass iltering Remoe gross inormation rom the image Retain ine details HPF image Original image LPF image High pass ilter mask Wt. at centre wt. at centre or lowpass Other wts 0 corresponding wt. or lowpass 33 LPF mask /9 /9 /9 /9 /9 /9 /9 /9 /9 33 HPF mask -/9 -/9 -/9 -/9 8/9 -/9 -/9 -/9 -/9 8

9 Sm o all coeicient is ero Area o low ariation O/p 0 I high ariation - O/p high Eliminates ero reqenc term Redces aerage gra leel Otpt will be enhanced edges with black backgrond Better reslt b high-boost ilter High boost ilter Highpass Original Lowpass High boost A Original Lowpass A- Original Original -Lowpass A- Original Highpass I A Yields Highpass ilter I A> - restores partiall the low reqenc components lost de to highpass iltering 9

10 Smoothing: Smmar Prpose Smoothing: blrring & noise redction eriatie Filter Integration Aeraging smoothing ierentiation Sharpening Prpose o Sharpening: highlight ine detail or enhance detail that has been blrred b error or natral eect o the the image acqisition method ierentiation/eriatie to detect change Strength o the response o deriatie ilter/operator degree o discontinit So image dierentiation enhances edges/other discontinities eg. noise and does not emphasie on areas with slowl changing gra-leel ales 0

11 eriatie Filter Properties o the deriaties in a digital contet: Otpt o First-order eriatie Zero in lat Segments area o constant gra-leel ales Nonero at the beginning o a gra-leel ramp/step Nonero along ramps Otpt o Second-order eriatie Zero in lat areas Nonero at the beginning and end o a gra-leel ramp/step Zero along ramps o constant slope eriatie Filter Sharpening ilters based on irst and secondorder deriaties A Partial First-order deriatie: B Partial Second-order deriatie:

12 SUMMARY:. First-order deriaties prodce thicker edges in an image oble Line. Second-order deriaties hae stronger response to ine details like thin lines and points and prodce a doble response at step changes in gra leel nd -order deriatie: sited or enhancement becase it can enhance ine detail Second-Order eriatie Filter: The Laplacian Laplacian [ ] 4 a b - ; - ; b: Laplacian inclding diagonal neighbors c is a ariation to a and d is a ariation to b c d

13 Second-Order eriatie Filter: The Laplacian Laplacian highlights gra-leel discontinities edges and not emphasiing on slowl aring gra leels Otpt o Laplacian edges and no eatre backgrond To get a sharpened image with backgrond eatre the otpt rom Laplacian can be added to or sbtracted rom the original image g I the center coeicient o the Laplacian Mask -e I the center coeicient o the Laplacian Mask e Original Image Otpt Image ater Laplacian ilter Scaled Otpt Image ater Laplacian ilter Enhanced Otpt Image 3

14 4 Combine the mask o Laplacian with that o the image according to: g ] [ 5 4 ] [ g iagonal Piels o the Neighborhood also considered Original Image Sharpened sing Mask b Sharpened sing Mask a a b

15 5 First-Order eriatie Filter: Gradient First-order deriatie: implemented sing the magnitde o the gradient magnitde o gradient is reerred to as Gradient mag ] [ ] [ Roberts Cross-Gradient Operator: 3 3 region o an image; gra-leel ales Gradient in the and -direction Approimated as:

16 Roberts Filters 3 3 ilter Σ All Coeicients in the Mask 0 Response o Area o Constant Gra Leel 0 Sobel Operators ierence between the 3 rd ROW and st ROW approimates the deriatie in -direction ierence between the 3 rd COLUMN and st COLUMN approimates the deriatie in -direction 6

17 Enhancement in Freqenc omain Otpt image IFTFTimage * Filter I - [G] I - [FH] Applied in Image restoration 7

18 Lowpass Filter Highpass Filter Gassian Freqenc omain Lowpass Filter Highpass Filter Spatial omain Propert o Freqencies in the Forier Transorm: Low Freqencies in the Forier Transorm responsible or the general gra-leel appearance o an image oer smooth areas High Freqencies in the Forier Transorm responsible or detail eg. edges and noise Propert o Filters: Lowpass ilter pass low reqencies and rejects high reqencies Highpass ilter pass high reqencies and rejects low reqencies Propert o Filtered Images: Lowpass-iltered Image has less sharp detail than the original Highpass-iltered Image less gra leel ariations in smooth areas and emphasied detail eg. image looks sharper 8

19 9 Forier Spectrm or the aboe Image Lowpass Filter Less Sharp etail Highpass Filter Less Gra-leel ariations in smooth areas where distance rom point to the center o the reqenc rectangle Lowpass Filters: Tpes i i H F H G > A Ideal ilter o constant ct-o reqenc

20 B Btterworth ilter Lowpass Filters: Tpes H H [ / ] [ 0.44 [ / 0 ] 0 n n ][ / 0 ] n C Gassian ilter Lowpass Filters: Tpes H / o e 0

21 A Ideal ilter B Btterworth ilter C Gassian ilter Applications o Lowpass Filtering Using Gassian Lowpass Filter GLPF

22 Highpass Filter: Tpes > i i H A Ideal ilter n n n H H ] / 0.44[ ] / ][ [ ] / [ B Btterworth ilter / o e H C Gassian ilter Ideal Highpass Filter Btterworth Filter Gassian Filter Highpass Filter: Tpes

23 Highpass Filtered-Image: Eamples Ideal Highpass Filter Btterworth Filter Gassian Filter Homomorphic Filtering Homomorphic Filtering: based on Illmination and Relectance Model Image i r; i illmination & r relectance component In spatial domain: i Illmination component o an image changes slowl ii Relectance component changes abrptl sddenl In reqenc domain: i Low reqencies o the Forier Transorm related to Illmination component ii High reqencies o the Forier Transorm related to Relectance component 3

24 Homomorphic Filtering Homomorphic Filter H acts dierentl on illmination component and relectance component I γ L < γ H > the aboe ilter decreases the contribtion o low reqencies components illmination and ampli the contribtion o high reqencies components relectance Otpt Image Reslt: Brightness compression and Contrast Enhancement Modiied Form o the Gassian Highpass Filter: H c / o γ H γ L[ e ] γ L Homomorphic Filtering 4