ASSIGNMENT 5

GRADIENT AND EDGE DETECTION I. CalculateGradientinXandinYdirection:

Thisisrathersimple,Ijustiteratethrougheverypixel,andsetittothedifferenceofthepixelinthenextcolumn/nextrow.Belowisthecode.AlsoImadesuretoassigntheboundaryvaluestozeros.

defimageGradientX(image):ret=np.copy(image)

foriinrange(0,ret.shape[0]): forjinrange(0,ret.shape[1]1): ret[i][j]=abs(int(ret[i][j+1])int(ret[i][j])) ret[i][ret.shape[1]1]=0

returnretdefimageGradientY(image):

ret=np.copy(image)foriinrange(0,image.shape[0]1):

forjinrange(0,image.shape[1]): ret[i][j]=abs(int(ret[i+1][j])int(ret[i][j]))

forjinrange(0,image.shape[1]): ret[image.shape[0]1][j]=0

returnretII. CalculateCorrelationbyapplyingakerneltothepicture:

Thisisalsostraightforward.Ijustiteratethrougheverypixel,andforeachpixel,applytheformulafromthelecture.BelowisthecodedefcomputeGradient(image,kernel):

ret=np.copy(image)forjinrange(0,image.shape[1]):

ret[0][j]=0 ret[image.shape[0]1][j]=0

foriinrange(0,image.shape[0]): ret[i][0]=0 ret[i][image.shape[1]1]=0

foriinrange(1,image.shape[0]1): forjinrange(1,image.shape[1]1): val=0 foruinrange(0,3): forvinrange(0,3): val=val+kernel[u][v]*image[i+u1][j+v1] ret[i][j]=int(val)

returnretIII. EdgeDetection:

1. OriginalPicture:

2.Methods:

ItriedseveralmethodsotherthanCannysEdgeDetector,andhavefoundtwowaystodeliverdecentresults.

A. Method1:a. CalculateGradientinXandinYdirectionb. Foreachpixel,getthemaxofthevalues.Theresultisshownbelow

c. Now,toshowtheedgesinthepicture,Iusethekernelofsize3x3tosmoothoutthenoisefirst,thenchoosethethresholdtobetheaverageofallthepixel.I

d. Iteratethroughallpixel,assignitto255ifitsvalueisgreaterthan3timestheaverage,and0otherwise.Belowisthepicture

B.Method2:

a. CalculateGradientinXandinYdirection(Similartomethod1)b. Foreachpixel,getthemaxofthevalues.(Similartomethod1)c. Now,toshowtheedgesinthepicture,Iusethekernelofsize3x3tosmoothoutthe

noisefirst,thenchoosethethresholdtobetheaverageofallthepixel.Id. Now,treattheproblemofedgedetectorasanomalydetection.Wewillusearolling

windows(Ipickedthesize30x30)tomoveacrossthepicture.e. Calculatemeanandstandarddeviationofallvaluesfromthatwindows.Anypixelwith

valuegreaterthanmean+stdisconsideredasanomaly,andhencechangethevalueto255.Otherwise,weassign0toothers.Belowistheresult

3.CannyEdgeDetectionForcomparisonpurposes,IhaveattachedtheresultofCannysEdgeDetectionbelowtoshowthedifferences.

4.FurtherDevelopment:Asonecansee,mymethodsdonthavetheresultasgoodasCannysEdgeDetectionyet.Howevertheyhavealotofpotentialandcanbeimprove.Wecanchangethesizeofthekerneltoimprovesmoothing,wecanalsofinetunethethresholdtogetbetterresults.ThebestimprovementIbelieveistocombinemultiplemethodtogether,andhavesomevotingmechanismtotellwhetherapixelshouldbelongtoanedgeornot.