param[x_, m_, t_] :=
Module[{f, n = Length[x], nf},
f = Chop[Fourier[x]][[;; Ceiling[Length[x]/2]]];
nf = Length[f];
Total[Rationalize[
 2 Abs[f]/Sqrt[n] Sin[
   Pi/2 - Arg[f] + 2. Pi Range[0, nf - 1] t], .01][[;;
 Min[m, nf]]]]]

tocurve[Line[data_], m_, t_] := param[#, m, t] & /@ Transpose[data]
SetDirectory["/home/jacobh/WORKING/Pictures"]
img=Import["Coronal Holes.jpg"]
img = Binarize[img~ColorConvert~"Grayscale"];
lines = Cases[
Normal@ListContourPlot[Reverse@ImageData[img],
 Contours -> {0.5}], _Line, -1];

ParametricPlot[
Evaluate[tocurve[#, 100000000, t] & /@ lines], {t, 0, 1},
Frame -> True, Axes -> False, ImageSize -> Large]
ParametricEquations = Evaluate[tocurve[#, 100000000, t] & /@ lines]
n = Length[ParametricEquations]
img2 = Binarize[img~ColorConvert~"Grayscale"];

bsFs = Cases[
Normal@ListContourPlot[Reverse@ImageData[img2], Contours -> {0.5}],
Line[x_] :> BSplineFunction[x], All];

ParametricPlot[Evaluate[Through@bsFs@t], {t, 0, 1}, Frame -> True,
 Axes -> False, ImageSize -> Large, Axes -> false, Frame -> True]
stepsize = 0.0001
list = Table[
N[Evaluate[Through@bsFs@t] /. t -> i], {t, 0, 1, stepsize}]
xmatrix =
Table[Table[list[[i, j, 1]], {i, 1, (1/stepsize) + 1}], {j, 1, n}]
ymatrix =
Table[Table[list[[i, j, 2]], {i, 1, (1/stepsize) + 1}], {j, 1, n}]
Minx = Table[xmatrix[[i, Ordering[xmatrix[[i]], 1]]], {i, 1, n}]
Miny = Table[ymatrix[[i, Ordering[ymatrix[[i]], 1]]], {i, 1, n}]
x = Table[ParametricEquations[[i, 1]], {i, 1, n}]
y = Table[ParametricEquations[[i, 2]], {i, 1, n}]
Mx = Table[NMinValue[{x[[i]], 0 <= t <= 1}, t], {i, 1, n}]
My = Table[NMinValue[{y[[i]], 0 <= t <= 1}, t], {i, 1, n}]
NewParametricEquations =
Table[{x[[i]] - (Mx[[i]] - Minx[[i]]),
y[[i]] - (My[[i]] - Miny[[i]])}, {i, 1, n}]
ParametricPlot[NewParametricEquations, {t, 0, 1}, ImageSize -> Large,
Axes -> False, Frame -> True]
xCentroids =
Table[NIntegrate[
NewParametricEquations[[i, 1]]^2*
 D[NewParametricEquations[[i, 2]], t], {t, 0, 1}]/
NIntegrate[
2*NewParametricEquations[[i, 1]]*
 D[NewParametricEquations[[i, 2]], t], {t, 0, 1}], {i, 1, n}]
yCentroids =
Table[NIntegrate[-NewParametricEquations[[i, 2]]^2*
 D[NewParametricEquations[[i, 1]], t], {t, 0, 1}]/
NIntegrate[-2*NewParametricEquations[[i, 2]]*
 D[NewParametricEquations[[i, 1]], t], {t, 0, 1}], {i, 1, n}]
Centroids = Table[{xCentroids[[i]], yCentroids[[i]]}, {i, 1, n}]