Banane = Import[
  "https://images-na.ssl-images-amazon.com/images/I/31%2BF3QfjUrL._\
US500_.jpg"]
Banane = ImageResize[Binarize[Banane], 200]
points = ListContourPlot[Reverse[ImageData[Banane]], Contours -> 1];
pointsC = Cases[Normal[points], _Line, -1][[1, 1]];
elephantPlot = ListPlot[pointsC, AspectRatio -> Automatic]
center = Mean[MinMax[pointsC]];
pts = pointsC[[;; ;; 1]] - 0.5*center;
elephantPlot = ListPlot[pts, AspectRatio -> Automatic]
(*pts*)
ptsX = First /@ pts;
ListPlot[ptsX]
ptsY = Last /@ pts;
ListPlot[ptsY]

M = Length[pts];
Nombre = 10;
xa0 = 1/M*Sum[Part[ptsX, i], {i, 1, M}];
ya0 = 1/M*Sum[Part[ptsY, i], {i, 1, M}];
xak = {};
For[k = 1, k <= Nombre, k++,
 xak = Append[xak,
   2/M*Sum[Part[ptsX, j]*Cos[(2*k*Pi*j)/M], {j, 1, M}]]]
(*xak*)

xbk = {};

For[k = 1, k <= Nombre, k++,
 xbk = Append[xbk, 2/M*Sum[Part[ptsX, j]*Sin[k*2*Pi*j/M], {j, 1, M}]]]
(*xbk*)

X[t_] := xa0 +
   Sum[Part[xak, l]*Cos[l*t] + Part[xbk, l]*Sin[l*t], {l, 1, Nombre}];
yak = {};
For[k = 1, k <= Nombre, k++,
 yak = Append[yak, 2/M*Sum[Part[ptsY, j]*Cos[k*2*Pi*j/M], {j, 1, M}]]]
(*yak*)
ybk = {};

For[k = 1, k <= Nombre, k++,
 ybk = Append[ybk, 2/M*Sum[Part[ptsY, j]*Sin[k*2*Pi*j/M], {j, 1, M}]]]
(*ybk*)
Y[t_] := ya0 +
  Sum[Part[yak, l]*Cos[l*t] + Part[ybk, l]*Sin[l*t], {l, 1, Nombre}]
(*X[t]
Y[t]*)

Plot[X[t], {t, 0, 140}]
Plot[Y[t], {t, 0, 140}]
ParametricPlot[{X[t], Y[t]}, {t, 0, 2*Pi},
 PlotRange -> {{Min[ptsX] - 10, Max[ptsX] + 10}, {Min[ptsY] - 10,
    Max[ptsY] + 10}}]
Manipulate[
 ParametricPlot[{X[t], Y[t]}, {t, 0, a},
  PlotRange -> {{Min[ptsX] - 10, Max[ptsX] + 10}, {Min[ptsY] - 10,
     Max[ptsY] + 10}}], {a, 0.001, 6.28}]
Animate[ParametricPlot[{X[t], Y[t]}, {t, 0, a},
  PlotRange -> {{Min[ptsX] - 10, Max[ptsX] + 10}, {Min[ptsY] - 10,
     Max[ptsY] + 10}}], {a, 0.001, 2*Pi}]