Video Data Analysis. Video Data Analysis, B-IT. Lecture plan:

Transcription

1 Vdeo Data Analss Image eatures Spatal lterng Lecture plan:. Medan lterng. Derental lters 3. Image eatures -> > mage edges 4. Edge detectors usng rst-order dervatve 5. Edge detectors usng second-order order dervatve 6. Buldng the LoG operator Marna Kolesnk

2 Medan lterng Readng: :4.3 For a values u u..u a the medan s the value stuated n the mddle poston o the sorted sequence o these a values. Medan lter replaces each pel value wth the medan o the values ound n the local neghborhood. Algorthm: Medan lter - Compute the medan med o the values n a n n neghborhood o : { : [ a a]; a n / } - Assgn g med Marna Kolesnk

3 Eample o medan lterng Image corrupted wth mpulse nose Marna Kolesnk

4 Nose reducton b spatal lterng Readng: :5.3 Algorthm: Adaptve Medan Flterng Three-purpose algorthm: - remove salt-andpepper nose; -smooth other nose; - reduce mage dstorton; Marna Kolesnk

5 Nose reducton b spatal lterng Readng: :5.3 Level A checks whether the medan value tsel s an mpulsve nose. Level B checks whether the center gra-value s an mpulsve nose. The medan lter perorms well the mpulse nose s not large P a P b <.. Adaptve medan lter can handle probabltes larger than these. Marna Kolesnk

6 Nose reducton n color mages Modcaton o the adaptve lterng or color mages. R Flter R G G Flter B B Flter Poor dea! The orderng o n vectors based on the cumulatve dstance uncton: R n j The ncreasng orderng o generates the ordered set o j scalar quanttes vectors { R R... R } {... } n n Gven a set o n vectors the vector medan s dened as satsng: j j j j Marna Kolesnk

7 Nose removal n colour mages K The Vector Medan Flterng where VMF: K K K K s the Kernel Functon whch s the uncton o the dstance between the central pel and the vector medan. Marna Kolesnk

8 Nose removal n colour mages Impulsve nose removal based on the Vector Medan and the Peer Group. The Peer Group P s the set o m neghbors o the central pel whose dstance to the central pel s not eceedng d: The peer d W j group j P m d : j Algorthm: Impulsve nose removal - I there est a Peer Group o at least m pels than the central pel s not corrupted b nose - otherwse appl the VMF or an other nose reducton algorthm; Marna Kolesnk

9 Sharpenng b spatal derentaton Readng: :3.7 Averagng leads to mage blurrng and s analogous to ntegraton. Logcall sharpenng could be accomplshed b spatal derentaton.. Frst dervatve s non-ero along the entre ramp thck-lne response the second one s at the onset and the end.. Second dervatve responses stronger to solated varatons. 3. Second dervatve generates double response to an solated pont. Concluson: Second dervatve produces stronger response to ne detals ncludng nose! than the rst one. Marna Kolesnk

10 Lecture 4 Marna Kolesnk Sharpenng usng rst and second dervatves Laplacan s an sotropc or rotaton nvarant operator. Second dervatves produce shaper response to dscontnutes and better emphase ne detals. Second dervatves are mplemented usng a Laplacan: 4 Readng: :3.7 Sharpenng b spatal Sharpenng b spatal derentaton derentaton

11 Lecture 4 Marna Kolesnk Laplacan Laplacan masks masks Readng: :3.7 Flter masks mplementng the dgtal Laplacan and ther etenson that ncludes the dagonal members: The lter masks are sotropc or rotatons n ncrements o 9. Laplacan s not separable the lter matr has rank rank necessar and sucent condton or the separaton. Image o the North Pole o the moon let ltered wth Laplacan mask center and scaled or dspla purposes rght.

12 Lecture 4 Marna Kolesnk Sharpenng masks Sharpenng masks Sharpenng b subtracton addton o the Laplacan: coecent or the postve central coecent or the negatve central g 9 5 Readng: :3.7 Sharpenng lter masks :

13 Edges as mage eatures Readng: 5:4. What are mage eatures? The term mage eature reers to two possble enttes: - a global propert o an mage global eature. - a part o the mage wth some specal propertes local eature. Denton: Image eatures are local meanngul detectable parts o the mage. Meanngul means that the eatures are assocated to nterestng scene elements c.. sharp ntenst varatons or edges created b object contours; regons wth unorm ntenst etc. Detectable means that there est locaton algorthms detectng them. Output o these algorthms s a collecton o eature descrptors. The latter are used b hgher-level programs or mage analss c.. segmentaton matchng trackng etc. Usuall eature etracton s an ntermedate step not the goal o the vson sstem. Marna Kolesnk

14 Image Edges Readng: 5:4. Denton: Edge ponts or edges are pels at whch mage ntenst undergoes a sharp varaton. Edge s a propert attrbuted to an ndvdual pel and computed n ts neghborhood. The problem o Edge Detecton: Gven an mage o acquston nose locate the edges most lkel to be generated b scene elements not b nose. Edge detecton s tpcall a three steps procedure:. Nose smoothng.. Edge enhancement. 3. Edge localaton. Marna Kolesnk

15 Image Edges Readng: 5:4. Marna Kolesnk

16 Edge detectors Readng: :. Marna Kolesnk

17 Lecture 4 Marna Kolesnk Edge detectors: Edge detectors: gradent operator gradent operator G G mag G G tan φ Frst dervatves n mage processng are mplemented usng the gradent. Image edges can be descrbed n terms o the gradent s magntude and drecton: Edge magntude s the magntude o the gradent. Edge drecton s perpendcular to the drecton o the gradent. Readng: :3.7;. : 4.3 G G Q: s the appromate magntude an sotropc operator? The magntude o the gradent s an sotropc operator.

18 Lecture 4 Marna Kolesnk Gradent operators Gradent operators 3: G G mask a For Sobel operator: Readng: :. Prewtt operator: Denotng mage regon as: Robert s crossderence operator:

19 Sobel operators Sobel masks Readng: :3.7. Marna Kolesnk

20 Lecture 4 Marna Kolesnk Dagonal operators Dagonal operators Readng: :3.7. Prewtt operator: Sobel operator: Dagonal Sobel masks:

21 Edge detectors usng second-order order dervatve Zero-crossngs are easer to detect Readng: :3.7.; :4.3.3 Marna Kolesnk

22 Readng: :3.7. Edge detectors usng second-order order dervatve Laplacan: Marna Kolesnk

23 Zero-crossngs Step : Gaussan smoothng nose reducton: Readng: :3.7. :4.3.3 G r r e σ r Step : Computaton o the second dervatve the Laplacan o Gaussanwth respect to r: G r σ r σ c e σ 4 σ Step 3: Edge localaton - LoG lter; - Marr-Hldreth lter; - Mecan-hat operator Marna Kolesnk

24 Zero-crossngs The LoG operator: The LoG convoluton: G c σ σ 4 σ [ G σ ] e σ Readng: :3.7. :4.3.3 C s a scalng constant normalng the sum o LoG coecents to ero. Convoluton masks become larger or larger σ. 77 LoG lter mask Marna Kolesnk

25 Zero-crossngs Readng: :3.7. :4.3.3 NB: -Se o lter masks s crucal or the LoG-lterng. - Zero-crossngs are thnner than Sobel edges Marna Kolesnk

26 Zero-crossngs Zero-levels n the convolved mage dene the poston o edges thereore the nal step o edge detecton s: Step 3: Identcaton o eros n the LoG mage. Algorthm: Zero-crossng detector Readng: :3.7. : For each possble pel check the sgn and ts three neghbors n a wndow. - I the change o polartes occur n the wndow assgn an edge label ero-crossng to. To avod the detectng o non-sgncant egdes n regons wth almost unorm ntenst an addtonal condton s recommended: - assgn edge labels onl to those ero-crossngs wth sucentl strong value o the rst dervatve. Marna Kolesnk

27 Zero-crossngs Readng: :4.3.3 Marna Kolesnk

28 Lecture 4 Marna Kolesnk Implementaton o the Implementaton o the LoG LoG operator operator Readng: 3:6..4 Q: Is the LoG operator separable? σ σ σ σ σ t t j k k j k k e C t c e t C t c where j c c j c c j c e j K j c j j c p h [ ] [ ] [ ] [ ] g g g u c u c u c u c The mplementaton o the LoG operator takes place n two runs each one contanng two parallel processes:

29 - The wdth o the postve part o the LoG: w σ - Optmal samplng nterval: τ. 74σ - Number o dscreet samples or the postve part: W 3.8 W 4 - The wdth o the LoG kernel: n 3W 3 Buldng the nteger LoG kernel Readng: 3:6..4 From the samplng theorem o the sgnal theor the ampltude spectrum o the LoG-lter s ero or the spatal requenc ω and has ts mamum at: ω ω / σ m The ampltude decreases practcall to ero at cuto requenc: ωg 3ω m Samplng nterval whch satses the samplng theorem s gven b: π πσ τ. 74σ ω g 3 The number o dscreet samples whch alls nsde the postve part o the LoG-lter s then: W w σ 3.8 τ.74σ The LoG-kernel should have at least 3 pels to avod alasng: n 3W 3 pels Marna Kolesnk

30 Buldng the nteger LoG kernel Readng: 3:6..4 The coecents o the two dscreet -D convoluton kernels are determned b samplng the contnuous varable t or nteger values k n the range between [-.5W.5W] : k σ t k τ wth W n / 3 Substtutng nto the kernel unctons: n W s the kernel se n pels t h t C ep[ t σ h t C ep[ t σ ] σ ] We obtan: 8 k 4 k c k C ep[ ] C 8 3k n ep[ 4 3k W W 4 k 6 c k ep[ ] ep[ 4 3k n ] πw W n π or k [ n / ; n / ] n ] Marna Kolesnk

31 Buldng the nteger LoG kernel Readng: 3:6..4 The coecents have to sats: : C c k : C c k Interpretaton: or a constant gra value the result must be ero Interpretaton: the result o smoothng a constant gra value must gve the orgnal value. To sats these two condtons the computed coecents are corrected b the value C /n or the uncton c t and b the value -C /n or the unctons c t. Marna Kolesnk

32 Buldng the nteger LoG kernel Readng: 3:6..4 Algorthm: Computaton o the LoG-lter coecents Input nteger value n the wdth o the samplng wndow Marna Kolesnk

33 Zero-Crossngs: Summar Readng: :4.3 Advantages:. Zero-crossng edges are thnner than the gradent edges.. Fndng o ero-crossngs s ver robust. 3. Large local area are taken nto account. 4. Due to Gaussan smoothng erocrossngs are robust to nose. 5. Produce sngle-pck response per edge. 6. Scale-space propert. 7. Is supported b neurophsologcal evdence Dsadvantages:. Zero-edges orm closed loops.. Due to smoothng sharp corners are lost. 3. The orentaton o edges s lost. 4. Computatonall etensve. Marna Kolesnk

34 Buldng the nteger LoG kernel Readng: 3:6..4 The LoG-lter can be appromated b the derence o two Gaussans called the DoG-lter also separable!: σ G σ c σ σ 4 σ For a gven LoG the best appromaton s obtaned when: e σ σ σ γ ; σ γσ or.6 There est neurophslogcal evdence that retnal ganglon cells perorm ver smlar to LoG DoG operatons: each ganglon cell responds to lght stmul n a local neghborhood called the receptve eld whch has a center-surround organaton o two complementar tpes o-center and on-center. Marna Kolesnk