Use Image Contours to Count Gear Teeth

Develop a convex hull–based algorithm to analyze the shape of gears

Use an image of a gear to count its teeth:

In[1]:=

gear=

;

Do a filling transform to create a mask:

In[2]:=

mask=FillingTransform[Binarize[gear,{0,.7}]]

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Find points on the image contour and highlight it:

In[3]:=

contours=ImageMeasurements[mask,"PerimeterPositions"];HighlightImage[gear,contours]

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Write a function to get the

ConvexHullMesh

of the contours and compute the defects. Using

PeakDetect

, you can also find the point of minimal indentation:

In[4]:=

convexityDefects[contour_List,args___]:=Map[convexityDefects[#,args]&,contour]convexityDefects[contour_List?MatrixQ,scale_:3,t_:2]:=Module[{convexHull,dist,defects,peaks,peakCount},convexHull=ConvexHullMesh[contour,ImageSizeTiny];dist=RegionDistance[RegionBoundary@convexHull][contour];defects=UnitStep[dist-t];peaks=PeakDetect[GaussianFilter[-dist,scale],0,Automatic,-t];peakCount=Count[Split[peaks],{1..}];If[First[peaks]Last[peaks]1,peakCount-=1];AssociationThread[{"Contour","ConvexHull","Distance","Defects","Peaks","Teeth"},{contour,convexHull,dist,defects,peaks,peakCount}]]

In[5]:=

First[convexityDefects[contours]]//Dataset

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Break the contour down into its shape and peaks:

In[6]:=

defectsGraphics[contour_Association,opts___]:=Graphics{Lighter[Blue,.8],MeshPrimitives[contour["ConvexHull"],2],Black,Line[contour["Contour"]],Red,AbsolutePointSize[3],Point[Pick[contour["Contour"],contour["Peaks"],1]]},



In[7]:=

defectsGraphics[convexityDefects[First[contours]]]

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Write a utility function to show the sequence of distances of pixels on the contour to its convex hull:

In[8]:=

distancePlot[contour_Association,opts___]:=ListLinePlotMeanFilter[contour["Distance"],3],



In[9]:=

distancePlot[convexityDefects[First[contours]],ImageSizeMedium]

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Combine all the previous visualizations together with the estimated number of teeth:

In[10]:=

summary[contour_,opts___]:=With[{c=convexityDefects[contour]},distancePlot[c,opts,FrameTicksFalse,Epilog{Text["Teeth: "<>ToString[c["Teeth"]],Scaled[{0.05,0.95}],Scaled[{0,1}]],Inset[defectsGraphics[c],Center,Center,Scaled[.6]]}]]

Show the summary for the test gear:

In[11]:=

summary[contours〚1〛]

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Now, repeat the process with a more complex image:

In[12]:=

mask=DeleteBorderComponents[FillingTransform[Binarize[image,.9]]];contourList=ComponentMeasurements[mask,"PerimeterPositions",#Count>1500&]〚All,2,1〛;HighlightImage[image,{AbsolutePointSize[1],contourList}]

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Compute the defects and group the gears by their approximate teeth count:

In[13]:=

defects=convexityDefects[contourList];GroupBy[defects,Round[#Teeth,10]&,Graphics[Polygon[Lookup[#,"Contour"]],ImageSizeTiny]&]//KeySort

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Inspect multiple gears:

In[14]:=

Table[summary[contourList〚i〛],{i,{3,5,10,15}}]

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

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Contributed by: Wolfram Staff

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Use Image Contours to Count Gear Teeth

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Use Image Contours to Count Gear Teeth

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