Compare the Shape of Different Countries

Use CanonicalWarpingDistance to find similarity between shapes of different countries.

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names = {"USA", "Poland", "Portugal", "Vietnam", "Brazil", "Finland"}; borders = <|# -> ArrayResample[CountryData[#, "Polygon"][[1, 1, 1]], 200] & /@ names|>;

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shapes = Graphics[CountryData[#, "Shape"][[1]], ImageSize -> {50, 50}] & /@ Keys[borders]

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Calculate shape distances using canonical time warping.

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dm = DistanceMatrix[Values[borders], DistanceFunction -> (Chop[ CanonicalWarpingDistance[##, MaxIterations -> 6]] &)];

Show the distance matrix.

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In[4]:=

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MatrixPlot[dm, FrameTicks -> {{MapIndexed[{#2[[1]], #1} &, shapes], None}, {MapIndexed[{#2[[1]], Rotate[#1, \[Pi]/4]} &, names], None}}, Mesh -> True, ColorFunction -> "BlueGreenYellow", PlotLegends -> Automatic, PlotLabel -> "Distance based on country shape", ImageSize -> Medium]

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