{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":42616,"title":"Detect circles in images","description":"Given an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\r\n\r\nYour detector will be judged on its \u003chttps://en.wikipedia.org/wiki/Precision_and_recall precision and recall\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass. \r\n\r\nFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\r\n\r\n*Additional notes:*\r\n\r\n* Circles can be brighter or darker than the background.\r\n* A detection is considered a match if its position and radius is within 5 pixels of a true circle.\r\n* To make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.","description_html":"\u003cp\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\u003c/p\u003e\u003cp\u003eYour detector will be judged on its \u003ca href = \"https://en.wikipedia.org/wiki/Precision_and_recall\"\u003eprecision and recall\u003c/a\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/p\u003e\u003cp\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAdditional notes:\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eCircles can be brighter or darker than the background.\u003c/li\u003e\u003cli\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/li\u003e\u003cli\u003eTo make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.\u003c/li\u003e\u003c/ul\u003e","function_template":"function [centers,radii] = detectcircles(I,R,N)\r\n  centers = [];\r\n  radii = [];\r\nend","test_suite":"%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circles.png'));\r\n[centers,radii] = detectcircles(I,[18 20],13);\r\nc = [119 222; 185 218; 124 116; 37 37; 178 184; 93 167; 37 72; 71 38; 93 132; 122 186; 97 96; 71 74; 151 204];\r\nr = 19*ones(13,1);\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circlesBrightDark.png'));\r\n[centers,radii] = detectcircles(I,[32 64],6);\r\nc = [75 250; 100 100; 250 400; 300 120; 450 240; 330 370];\r\nr = [35; 50; 60; 40; 50; 55];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coins.png'));\r\n[centers,radii] = detectcircles(I,[24 30],10);\r\nc = [236 174; 149 35; 56 50; 266 103; 217 71; 120 209; 110 85; 175 120; 96 146; 37 107];\r\nr = [25; 29; 25; 24; 29; 29; 24; 29; 29; 29];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coloredChips.png'));\r\n[centers,radii] = detectcircles(I,[20 28],26);\r\nc = [83 177; 304 336; 420 88; 434 165; 244 166; 327 297; 273 53; 130 44; 271 281; 408 265; 312 192; 420 346; 146 199; 228 232; 329 135; 175 297; 366 224; 150 258; 217 107; 345 119; 445 68; 372 293; 150 342; 251 8; 259 217; 198 107];\r\nr = [23; 24; 23; 23; 23; 23; 23; 23; 23; 23; 23; 24; 23; 23; 23; 24; 23; 24; 23; 23; 23; 24; 25; 23; 23; 25];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','eight.tif'));\r\n[centers,radii] = detectcircles(I,[35 40],4);\r\nc = [198 189; 247 72; 62 141; 124 58];\r\nr = [37; 37; 38; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','moon.tif'));\r\n[centers,radii] = detectcircles(I,[200 210],1);\r\nc = [253 287];\r\nr = [205];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','pillsetc.png'));\r\n[centers,radii] = detectcircles(I,[15 55],4);\r\nc = [103 240; 252 326; 119 130; 319 84];\r\nr = [17; 17; 50; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','tape.png'));\r\n[centers,radii] = detectcircles(I,[75 85],1);\r\nc = [236 172];\r\nr = [80];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','testpat1.png'));\r\n[centers,radii] = detectcircles(I,[110 120],1);\r\nc = [128 128];\r\nr = [116];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','toysnoflash.png'));\r\n[centers,radii] = detectcircles(I,[90 100],1);\r\nc = [267 506];\r\nr = [94];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2015-09-18T20:16:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-09-17T22:38:48.000Z","updated_at":"2026-04-02T22:38:30.000Z","published_at":"2015-09-17T23:22:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour detector will be judged on its\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Precision_and_recall\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eprecision and recall\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAdditional notes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCircles can be brighter or darker than the background.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":42616,"title":"Detect circles in images","description":"Given an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\r\n\r\nYour detector will be judged on its \u003chttps://en.wikipedia.org/wiki/Precision_and_recall precision and recall\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass. \r\n\r\nFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\r\n\r\n*Additional notes:*\r\n\r\n* Circles can be brighter or darker than the background.\r\n* A detection is considered a match if its position and radius is within 5 pixels of a true circle.\r\n* To make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.","description_html":"\u003cp\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\u003c/p\u003e\u003cp\u003eYour detector will be judged on its \u003ca href = \"https://en.wikipedia.org/wiki/Precision_and_recall\"\u003eprecision and recall\u003c/a\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/p\u003e\u003cp\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAdditional notes:\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eCircles can be brighter or darker than the background.\u003c/li\u003e\u003cli\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/li\u003e\u003cli\u003eTo make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.\u003c/li\u003e\u003c/ul\u003e","function_template":"function [centers,radii] = detectcircles(I,R,N)\r\n  centers = [];\r\n  radii = [];\r\nend","test_suite":"%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circles.png'));\r\n[centers,radii] = detectcircles(I,[18 20],13);\r\nc = [119 222; 185 218; 124 116; 37 37; 178 184; 93 167; 37 72; 71 38; 93 132; 122 186; 97 96; 71 74; 151 204];\r\nr = 19*ones(13,1);\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','circlesBrightDark.png'));\r\n[centers,radii] = detectcircles(I,[32 64],6);\r\nc = [75 250; 100 100; 250 400; 300 120; 450 240; 330 370];\r\nr = [35; 50; 60; 40; 50; 55];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coins.png'));\r\n[centers,radii] = detectcircles(I,[24 30],10);\r\nc = [236 174; 149 35; 56 50; 266 103; 217 71; 120 209; 110 85; 175 120; 96 146; 37 107];\r\nr = [25; 29; 25; 24; 29; 29; 24; 29; 29; 29];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','coloredChips.png'));\r\n[centers,radii] = detectcircles(I,[20 28],26);\r\nc = [83 177; 304 336; 420 88; 434 165; 244 166; 327 297; 273 53; 130 44; 271 281; 408 265; 312 192; 420 346; 146 199; 228 232; 329 135; 175 297; 366 224; 150 258; 217 107; 345 119; 445 68; 372 293; 150 342; 251 8; 259 217; 198 107];\r\nr = [23; 24; 23; 23; 23; 23; 23; 23; 23; 23; 23; 24; 23; 23; 23; 24; 23; 24; 23; 23; 23; 24; 25; 23; 23; 25];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','eight.tif'));\r\n[centers,radii] = detectcircles(I,[35 40],4);\r\nc = [198 189; 247 72; 62 141; 124 58];\r\nr = [37; 37; 38; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','moon.tif'));\r\n[centers,radii] = detectcircles(I,[200 210],1);\r\nc = [253 287];\r\nr = [205];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','pillsetc.png'));\r\n[centers,radii] = detectcircles(I,[15 55],4);\r\nc = [103 240; 252 326; 119 130; 319 84];\r\nr = [17; 17; 50; 37];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','tape.png'));\r\n[centers,radii] = detectcircles(I,[75 85],1);\r\nc = [236 172];\r\nr = [80];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','testpat1.png'));\r\n[centers,radii] = detectcircles(I,[110 120],1);\r\nc = [128 128];\r\nr = [116];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)\r\n\r\n%%\r\nI = imread(fullfile(matlabroot,'toolbox','images','imdata','toysnoflash.png'));\r\n[centers,radii] = detectcircles(I,[90 100],1);\r\nc = [267 506];\r\nr = [94];\r\nd1 = squeeze(sqrt(sum(bsxfun(@minus,centers,permute(c,str2num('3 2 1'))).^2,2)));\r\nd2 = squeeze(sqrt(sum(bsxfun(@minus,radii,permute(r,str2num('3 2 1'))).^2,2)));\r\nmask = d1\u003c5 \u0026 d2\u003c5;\r\nRe = mean(any(mask));\r\nPr = sum(any(mask))/size(mask,1);\r\nassert(Pr\u003e=0.5)\r\nassert(Re\u003e=0.75)","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2015-09-18T20:16:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-09-17T22:38:48.000Z","updated_at":"2026-04-02T22:38:30.000Z","published_at":"2015-09-17T23:22:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-by-2 array of circle centers (x,y positions in the image) and an m-by-1 vector of radii corresponding to m circles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour detector will be judged on its\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Precision_and_recall\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eprecision and recall\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The recall must be 0.75 or higher and the precision must be 0.5 or higher to pass.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if an image has 4 true circles, you can miss at most 1 of the circles and have at most 4 false detections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAdditional notes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCircles can be brighter or darker than the background.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA detection is considered a match if its position and radius is within 5 pixels of a true circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo make things easier, the target number of circles (N) is provided as an input. Pat yourself on the back if you do not need it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"term":"tag:\"circle 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