I took an image from a computer by referring to a video of a mathematician on YouTube and found the outer edge based on the original image below.

img = Import[...]

img = Binarize[img~ColorConvert~"Grayscale"~ImageResize~500~Blur~3];


pts = DeleteDuplicates@
   Cases[Normal@
      ListContourPlot[Reverse@ImageData[img], 
       Contours -> {0.5}], _Line, -1][[1, 1]];

center = Mean@MinMax[pts] & /@ Transpose@pts;

pts = # - center & /@ pts[[;; ;; 20]];

potholePlot = ListPlot[pts, AspectRatio -> Automatic]


SetAttributes[toPt, Listable]
toPt[z_] := ComplexExpand[{Re@z, Im@z}] // Chop;

cf = Compile[{{z, _Complex, 1}}, 
   Module[{n = Length@z}, 
    1/n*Table[Sum[z[[k]]*Exp[-I*i*k*2 Pi/n], {k, 1, n}], {i, -m, m}]]];

z = pts[[All, 1]] + I*pts[[All, 2]];

m = 50;

cn = cf[z];

{f[t_], g[t_]} = 
  Sum[cn[[j]]*Exp[I*(j - m - 1)*t], {j, 1, 2 m + 1}] // toPt;


ParametricPlot[{f[t], g[t]}, {t, 0, 2 Pi}, AspectRatio -> Automatic]

The picture is the original image of the pothole.

I'm curious how to find the error between the exterior of the original pothole image and the exterior of the image obtained by Fourier technician, how can I get it? Even if I look for reference materials, I don't have the data I want.

I wonder if there's a way to find an error by overlapping the edges.

Please. Thank you.