ECSE4540: Homework#5 solution

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1. (10points.) Considertheimagegiveninthefile market.png. (a) Determine the gradient, its magnitude, and its angle at the point (205,696), using the estimate df dx = f (x+1,y)− f (x,y)(andsimilarlyfor df dy ). Throughoutthisproblem,interpretthexdirectionaspointingdowntherowsandthey directionaspointingacrossthecolumns(i.e.,Matlab/imagecoordinates). (b) Determine the gradient, its magnitude, and its angle at the point (205,696), using the Sobel operators divided by 8 to estimatethederivatives.
2. (15 points.) Use the Sobel operators divided by 8 to estimate the magnitude and angle of the gradient over the entire marketimage;thatis,createtwonewimagesmagandangcontainingtheestimatedgradientmagnitudeandangleateach pixel.
(a) Displayandinterprettheresultsofthebinaryimagecreatedbyfindingthepixelswhosemagnitudeisabove50. (b) Displayandinterprettheresultsofthebinaryimagecreatedbyfindingthepixelswhoseangleiswithin20◦ of45◦ (on eitherside). (c) DisplayandinterprettheresultsofthelogicalANDoftheprevioustwoimages.
3. (30points.) Here,we’lltrytofindthelonglinesinthe deck.png image.
(a) (5points.) First,extracttheCannyedges(usingthedefaultMatlabthresholds). Whatdoestheedgemaplooklike? (b) (10points.) Usetheseedgesastheinputtothe hough functiontoreturntheHougharrayandcorresponding ρ and θ vectors. Then use the houghpeaks function to find at most 50 highest peaks. Determine how to superimpose these linesontotheoriginalimageandreturntheresult. (c) (5points.) Dotheselinesmakesense? Whyorwhynot? Whyaretheremanylinesdetectedat±45◦? (d) (5points.) Now,extractedgesusingtheSobeloptiontotheedgecommand,insteadofCanny,andrepeattheprocess inpart(b)(again,usingallofMatlab’sdefaultthresholds). Explainwhatyousee. Isthisbetterthanpart(c)andwhy? (e) (5points.) Tunethethresholdoptiontohoughpeaksuntilyou’reabletoextractallthemajorlines(withoutdetecting anyspuriouslines). Howlowdidyouneedtosetthethresholdtogettothispoint?
4. (15 points.) The command imfindcirlces uses a Hough-transform-like method to find circles in an image. Load up the image curling.jpg and tweak the parameters to find as many circles as you can (without generating any spurious circles). You can try changing the objectpolarity and edgethreshold inputs, as well as trying different color channels oftheinputimage(e.g.,theredringwillstandoutbetterinthebluechannel). Describethesettingsyoueventuallyarrived at to get the best result. Note that you will need several calls to imfindcirlces with different radii since the function will complainifyouusetoowidearange.
5. (15points.) Thresholdthe important.png imagetofindpixelsaboveagrayscalelevelof180. Displaytheresultingimage. Use bwlabel and regionprops to automatically isolate the white region with the largest area, and display this as a new image.
6. (15points.) Considertheimagein page.png. Use graythresh tofindOtsu’sthresholdandapplyittotheimage(i.e.,turn everythingdarkerthanthethresholdtowhite). Howdoesitlook? Whyisaglobalthresholdsuboptimalforthistask? Now, use the blockproc command to process each 60×60 block of the image separately, returning white pixels where the pixelintensity p<µ−2σ,where µ isthemeanintensityoftheblockand σ isthestandarddeviationoftheblock. Interpret theresults. Whydoesthelocalthresholdworkbetter?