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Computer Vision

by: Roel Green

Computer Vision ECE 516

Roel Green
GPA 3.99


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Class Notes
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This 45 page Class Notes was uploaded by Roel Green on Wednesday September 23, 2015. The Class Notes belongs to ECE 516 at University of New Mexico taught by Staff in Fall. Since its upload, it has received 4 views. For similar materials see /class/212167/ece-516-university-of-new-mexico in Engineering Electrical & Compu at University of New Mexico.

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Date Created: 09/23/15
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X39z X2 XXz AX NJ CWYS 1139quot 2 Cross Xu Ylegi X43 9 MW M M M wk 1 m x er n Aw 3 3 Kg L X nvs 95 th big dif 4 Q2 m 9 si a L f 2 i KWH n 04 H L A Z gt I 311 gt m D lt 04 o4 H 049 VH 391 A 4 L I O FI D gtlt HQ 93 R gtltuxm ltUgt m n gtk o o o ltwxgt w 0 Q 1MgtAw beahro r1k8 Mo 98 L Fir LIx Qxfm 3J2 7 nwxdkuxQAjx cc 0 3V2 7 fo 92f sTMCFLL 7 gqub ski 35 pffhl 5 E 453 F r w 301 F r P w gg x Q Q I T O F a dbhw bN Q w p l Q NKGSXN 47 Arwv AKP HRM f A 3 111 97 HF 38 7f micahv ru P 015 AN OOWp Diem 91721 Woo m b n CTd 261 577ka 7 on as i Plea Fwtr QSm x r n m r mm m A sz QM Jy ma 2 9 W n A 2 if TVA NTV EFF v v b 6 n 371 5 5 9190 TIwa Cuba A xvka U3 5 r M2 gr y z a a a 270 VsLI 32 Announcements ECE 515 cs 532 HW2 will be posted today Computer Vision Femuca yifimm mamasquot Advanced Graphics Lab stairum mnuwm mp9quot cmrrmam mx Last time Today Linear lters and Fouriertransforms Edge detection A mwb mm eww ataxia9 Wm cmrrmam mx Edge detection Noise Noise can affect edge detection algorithms because they look for sharp changes in the image and noise creates these sharp changes were none exist One common model for noise is additive v stationary Gaussian noise mrsmmnervw 7 mp9quot f mr mmnuwm cuxsrrehuiwzm z 7 mp9quot cmrrmam mx which Is zero A 7525 WW Additive stationary Gaussian noise Each pier has a value chosen from a Gaussian probability distribution added to it The probability distribution of all pixels are The Gaussian distribution has a given standard deviation 5 and a mean u typically meme m Example o mag stairum mnuwm quotmpgquot my sz mx Problems with noise model Finite difference filters on noisy images Allows for negative pixel values 5 7 515 WW Every pixel is independent does not allow for noise correlation across pixels meme m By applying a nite difference derivative lterto itself we can generate a w ole family of derivative lters However these lters increase the standard deviation of the Gaussian noise AL 532 Wm cmrrmam mx Increasing standard deviation Smooth to reduce noise 3m mm H Menmve w 4m meme m So we must smooth the signal to reduce the noise problems We typically use a Gaussian to do this 555225 Wm cmrrmam mx Why a Gaussian Summary Ifyou convolve a Gaussian with a gaussian 39 5 you get a Gaussian mooth before you do any edge detection to get rid of noise artifacts This means you can repeatedly convolve the Do this by convolving with a Gaussia image with a Gaussian to get the effect of For edge detection you will want to convolve with convolving with a Gaussian with Iarg r a some kind of differentiation lter Gaussians are separable Since differentiation is linear and shift invariant wme a 2D Gaussian kernel as me this Is equivalent of convolving the Image directly multiplication oftwo 1D kernels 55393quot What kind of derivative lter do we want to use Aggmsmww Let Af zsmwm an Example Laplacian operator mm mm 5mme svnal A mwsmmmww mp9quot l39 mm 2 mm yamWWW mp9quot cmrrmam mx Laplacian of a Gaussian kernel Using the Laplacian to detect edges Convolve the image with the Laplacian of the Gaussian at some 5 Mark the pixels with zero values whe magnitude ofthe gradient rst derivative is greater than some thresho These are the edge pixelsquot mismmnervw 7 mp9quot mp9quot cmrrmam mx Example V mrsmmnervw 7 quotmpgquot cuxsrhhuawzm Bad behavior stairum mnuwm mm cmrrmam mx Gradientbased edge detectors Compute the image gradient From this calculate the magnitude of the gradient at every pier Identify points where the magnitude is maximal in the direction perpendicularto the edge in direction of gradient Label these as edge pixelsquot mrsmmnervw A We m Gradient magnitude w Gaussianwm a l stairum mnuwm mm E Wm Gradient mavnmde mmm Gradient mm m menu w Gaussianwnha 2 cmrrmam mx Nonmaximum suppression J mrsmmnervw mp9quot cuxsrrenuiwz m Edge following determ checking that it is m x m edge maximum along gradient stairum mnuwm mp9quot During nonmaximum suppression we ine Is a given point an edge point We do this by comparing it to its neighbors and 39 al If so where is the next edge point to check Follow the direction perpendic gradient to nd the possible continuation of ular to the Check these points to see ifthey are the local cmrrmam mx Hysteresis Implementauon e use We mneremnresnums ms1amne an edgE wmcn s amev 2 Fuvcummumg an edgE ann s smaHev 1 We nuw uuk aune detaHs u mp ememng a gramenenaseu Edge uetemun a gu mm Perhaps the best muwn 5 me detect Canny Edge en mtmduced m was LT M canny Edge Detecmr cannw A umpmatmna appruacm Edge neteeuuns EEE Trans Panern u a q 7141986 canny39s goals Guud detectmn ime a gu mm snumu mark as many rea Edges mme nnage as pussmxe snumu be msemtnetme en mnnnax respunseime Edges snuum umy be marked unee and nnage nmse snumu be suppressed is stem Nolse reduction Cumu ve WIN a Gausswantu reduce nmse Example Appmng a 5x5 Gaussan mrnex m an nnage g mm Example Applylng a 5x5 Gausslan xemellu an lmage l step 2 compmmg gradlem Calculateme magnltude andme angle at me gradlerlt 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